{"id":856,"date":"2025-08-06T11:55:15","date_gmt":"2025-08-06T06:25:15","guid":{"rendered":"https:\/\/codeanddebug.in\/blog\/?p=856"},"modified":"2025-08-06T11:55:17","modified_gmt":"2025-08-06T06:25:17","slug":"infix-postfix-prefix-conversions-explained-in-python","status":"publish","type":"post","link":"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/","title":{"rendered":"Infix, Postfix, Prefix Conversions explained in Python"},"content":{"rendered":"\n<p>Postfix, prefix, and infix are three common notations used to write arithmetic expressions. In\u00a0<strong>infix notation<\/strong>, the operator is placed between operands (e.g., A + B), and is the most familiar to humans.\u00a0<strong>Prefix notation<\/strong>\u00a0(Polish notation) places the operator before the operands (e.g., + A B), while\u00a0<strong>postfix notation<\/strong>\u00a0(Reverse Polish notation) places the operator after the operands (e.g., A B +). Prefix and postfix notations are widely used in computer science as they allow efficient expression evaluation without parentheses.<\/p>\n\n\n<div style=\"max-width: -moz-fit-content; \" class=\"wp-block-ub-table-of-contents-block ub_table-of-contents ub_table-of-contents-collapsed\" id=\"ub_table-of-contents-bdf5d26f-a261-414a-8328-56c5b1c38f2d\" data-linktodivider=\"false\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" data-enablesmoothscroll=\"true\" data-initiallyhideonmobile=\"true\" data-initiallyshow=\"false\"><div class=\"ub_table-of-contents-header-container\" style=\"\">\n\t\t\t<div class=\"ub_table-of-contents-header\" style=\"text-align: left; \">\n\t\t\t\t<div class=\"ub_table-of-contents-title\">Contents:<\/div>\n\t\t\t\t<div class=\"ub_table-of-contents-header-toggle\">\n\t\t\t<div class=\"ub_table-of-contents-toggle\" style=\"\">\n\t\t\t\u00a0[<a class=\"ub_table-of-contents-toggle-link\" href=\"#\" style=\"\">show<\/a>]\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div><div class=\"ub_table-of-contents-extra-container\" style=\"\">\n\t\t\t<div class=\"ub_table-of-contents-container ub_table-of-contents-1-column ub-hide\">\n\t\t\t\t<ul style=\"\"><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#0-infix-to-postfix-conversion-explanation-\" style=\"\">Infix to Postfix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#1-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#2-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#3-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#4-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#5-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#6-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#7-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#8-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#9-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#10-infix-to-prefix-conversion-explanation-\" style=\"\">Infix to Prefix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#11-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#12-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#13-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#14-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#15-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#16-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#17-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#18-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#19-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#20-postfix-to-infix-conversion-explanation-\" style=\"\">Postfix to Infix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#21-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#22-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#23-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#24-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#25-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#26-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#27-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#28-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#29-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#30-prefix-to-infix-conversion-explanation-\" style=\"\">Prefix to Infix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#31-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#32-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#33-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#34-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#35-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#36-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#37-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#38-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#39-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#40-postfix-to-prefix-conversion-explanation-\" style=\"\">Postfix to Prefix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#41-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#42-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#43-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#44-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#45-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#46-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#47-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#48-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#49-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#50-prefix-to-postfix-conversion-explanation-\" style=\"\">Prefix to Postfix Conversion Explanation<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#51-approachintuition-\" style=\"\">Approach\/Intuition<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#52-code-\" style=\"\">Code<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#53-code-explanation-\" style=\"\">Code Explanation<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#54-dry-run-example-\" style=\"\">Dry Run Example<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#55-edge-cases-to-consider-\" style=\"\">Edge Cases to Consider<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#56-time-and-space-complexity-\" style=\"\">Time and Space Complexity<\/a><ul><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#57-time-complexity-on-\" style=\"\">Time Complexity: O(n)<\/a><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#58-space-complexity-on-\" style=\"\">Space Complexity: O(n)<\/a><\/li><\/ul><\/li><li style=\"\"><a href=\"https:\/\/codeanddebug.in\/blog\/infix-postfix-prefix-conversions-explained-in-python\/#59-applications-\" style=\"\">Applications<\/a><\/li><\/ul><\/li><\/ul>\n\t\t\t<\/div>\n\t\t<\/div><\/div>\n\n\n<h1 class=\"wp-block-heading\" id=\"0-infix-to-postfix-conversion-explanation-\"><strong>Infix to Postfix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Infix, postfix, and prefix are different ways of writing mathematical expressions. Infix notation is what we commonly use in everyday mathematics (e.g., &#8220;3 + 4&#8221;), where operators are placed between operands. Postfix notation (also known as Reverse Polish Notation) places operators after their operands (e.g., &#8220;3 4 +&#8221;).<\/p>\n\n\n\n<p>The key advantage of postfix notation is that it eliminates the need for parentheses and operator precedence rules. This makes postfix expressions much easier for computers to evaluate using a simple stack-based algorithm.<\/p>\n\n\n\n<p>The conversion from infix to postfix relies on understanding operator precedence and using a stack to properly reorder the elements. The core intuition involves:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Operands (numbers, variables) go directly to the output.<\/li>\n\n\n\n<li>Opening parentheses go onto the stack.<\/li>\n\n\n\n<li>Closing parentheses trigger popping operators from the stack until the matching opening parenthesis.<\/li>\n\n\n\n<li>When encountering an operator, pop operators with higher or equal precedence from the stack to the output.<\/li>\n\n\n\n<li>Finally, pop any remaining operators from the stack to the output.<\/li>\n<\/ol>\n\n\n\n<p>This approach ensures that operators are sequenced in the correct order of evaluation in the postfix expression.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def precedence(self, ch):\n\u00a0 \u00a0 \u00a0 \u00a0 # Define operator precedence hierarchy\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;+&quot; or ch == &quot;-&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 1\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;*&quot; or ch == &quot;\/&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 2\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;^&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 3\n\u00a0 \u00a0 \u00a0 \u00a0 return 0\u00a0 # For non-operators like '(' and ')'\n\n\u00a0 \u00a0 def InfixtoPostfix(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\u00a0 \u00a0 # Stack to help with operator ordering\n\u00a0 \u00a0 \u00a0 \u00a0 result = [] \u00a0 # To store the postfix expression\n\n\u00a0 \u00a0 \u00a0 \u00a0 for char in s:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operand, add it directly to result\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if (&quot;a&quot; &lt;= char &lt;= &quot;z&quot;) or (&quot;A&quot; &lt;= char &lt;= &quot;Z&quot;) or (&quot;0&quot; &lt;= char &lt;= &quot;9&quot;):\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is '(', push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 elif char == &quot;(&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is ')', pop until '(' is encountered\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 elif char == &quot;)&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while stack and stack[-1] != &quot;(&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.pop()\u00a0 # Discard the '('\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operator\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Pop operators with higher or equal precedence\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while stack and self.precedence(stack[-1]) &gt;= self.precedence(char):\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\u00a0 # Push current operator\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Pop remaining operators from the stack\n\u00a0 \u00a0 \u00a0 \u00a0 while stack:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\n\u00a0 \u00a0 \u00a0 \u00a0 return &quot;&quot;.join(result)\u00a0 # Convert list to string\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">precedence<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">ch<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Define operator precedence hierarchy<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;+&quot;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;-&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;*&quot;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;\/&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;^&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">\u00a0 <\/span><span style=\"color: #6A9955\"># For non-operators like &#39;(&#39; and &#39;)&#39;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">InfixtoPostfix<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []\u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Stack to help with operator ordering<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 result = [] \u00a0 <\/span><span style=\"color: #6A9955\"># To store the postfix expression<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> char <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> s:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operand, add it directly to result<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;a&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;z&quot;<\/span><span style=\"color: #D4D4D4\">) <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;A&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;Z&quot;<\/span><span style=\"color: #D4D4D4\">) <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;0&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;9&quot;<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is &#39;(&#39;, push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">elif<\/span><span style=\"color: #D4D4D4\"> char == <\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is &#39;)&#39;, pop until &#39;(&#39; is encountered<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">elif<\/span><span style=\"color: #D4D4D4\"> char == <\/span><span style=\"color: #CE9178\">&quot;)&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack <\/span><span style=\"color: #569CD6\">and<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">] != <\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Discard the &#39;(&#39;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operator<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Pop operators with higher or equal precedence<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack <\/span><span style=\"color: #569CD6\">and<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.precedence(stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]) &gt;= <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.precedence(char):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\u00a0 <\/span><span style=\"color: #6A9955\"># Push current operator<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Pop remaining operators from the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #CE9178\">&quot;&quot;<\/span><span style=\"color: #D4D4D4\">.join(result)\u00a0 <\/span><span style=\"color: #6A9955\"># Convert list to string<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation consists of two main functions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>precedence(ch)<\/strong>: This helper function assigns a numeric value to each operator representing its precedence:\n<ul class=\"wp-block-list\">\n<li>Higher numbers indicate higher precedence<\/li>\n\n\n\n<li>Addition and subtraction have precedence 1<\/li>\n\n\n\n<li>Multiplication and division have precedence 2<\/li>\n\n\n\n<li>Exponentiation has precedence 3<\/li>\n\n\n\n<li>Other characters (including parentheses) have precedence 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>InfixtoPostfix(s)<\/strong>: This is the main conversion function:\n<ul class=\"wp-block-list\">\n<li>It uses a stack for temporary storage of operators and parentheses<\/li>\n\n\n\n<li>It processes each character in the input string one by one:\n<ul class=\"wp-block-list\">\n<li><strong>For operands<\/strong> (letters and digits): Directly append to the result list<\/li>\n\n\n\n<li><strong>For opening parenthesis &#8216;(&#8216;<\/strong>: Push onto the stack to mark its position<\/li>\n\n\n\n<li><strong>For closing parenthesis &#8216;)&#8217;<\/strong>: Pop operators from the stack and append to result until the matching opening parenthesis is found. Then discard the opening parenthesis without adding it to the result.<\/li>\n\n\n\n<li><strong>For operators<\/strong> (+, -, *, \/, ^):\n<ul class=\"wp-block-list\">\n<li>While there are operators on stack with higher or equal precedence, pop them and append to result<\/li>\n\n\n\n<li>Then push the current operator onto the stack<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>After processing all characters, any remaining operators on the stack are popped and appended to the result<\/li>\n\n\n\n<li>Finally, join the result list into a string and return it<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>The algorithm ensures that operators appear in the postfix expression in the correct order of evaluation, respecting operator precedence and parentheses.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the infix expression &#8220;a+b*(c^d-e)^(f+g*h)-i&#8221; to postfix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Initialize: stack = [], result = []<\/li>\n\n\n\n<li>Process &#8216;a&#8217;: Append to result \u2192 result = [&#8216;a&#8217;]<\/li>\n\n\n\n<li>Process &#8216;+&#8217;: Stack is empty, push to stack \u2192 stack = [&#8216;+&#8217;], result = [&#8216;a&#8217;]<\/li>\n\n\n\n<li>Process &#8216;b&#8217;: Append to result \u2192 result = [&#8216;a&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;*&#8217;: Has higher precedence than &#8216;+&#8217;, push to stack \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;], result = [&#8216;a&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;(&#8216;: Push to stack \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;, &#8216;(&#8216;], result = [&#8216;a&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;c&#8217;: Append to result \u2192 result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;^&#8217;: Push to stack \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;, &#8216;(&#8216;, &#8216;^&#8217;], result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;d&#8217;: Append to result \u2192 result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;]<\/li>\n\n\n\n<li>Process &#8216;-&#8216;: Lower precedence than &#8216;^&#8217;, pop &#8216;^&#8217; \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;, &#8216;(&#8216;, &#8216;-&#8216;], result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;, &#8216;^&#8217;]<\/li>\n\n\n\n<li>Process &#8216;e&#8217;: Append to result \u2192 result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;, &#8216;^&#8217;, &#8216;e&#8217;]<\/li>\n\n\n\n<li>Process &#8216;)&#8217;: Pop operators until &#8216;(&#8216; \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;], result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;, &#8216;^&#8217;, &#8216;e&#8217;, &#8216;-&#8216;]<\/li>\n\n\n\n<li>Process &#8216;^&#8217;: Higher precedence than &#8216;*&#8217;, push to stack \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;, &#8216;^&#8217;], result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;, &#8216;^&#8217;, &#8216;e&#8217;, &#8216;-&#8216;]<\/li>\n\n\n\n<li>Process &#8216;(&#8216;: Push to stack \u2192 stack = [&#8216;+&#8217;, &#8216;*&#8217;, &#8216;^&#8217;, &#8216;(&#8216;], result = [&#8216;a&#8217;, &#8216;b&#8217;, &#8216;c&#8217;, &#8216;d&#8217;, &#8216;^&#8217;, &#8216;e&#8217;, &#8216;-&#8216;]<\/li>\n\n\n\n<li>Continue with remaining characters&#8230;<\/li>\n<\/ol>\n\n\n\n<p>Final result after processing all characters: &#8220;abcd^e-fg<em>h+^<\/em>+i-&#8220;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would return an empty string, which is correct.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Only Operators<\/strong>: Not a valid infix expression, but the algorithm would attempt to process it.<\/li>\n\n\n\n<li><strong>Unbalanced Parentheses<\/strong>: If the input has unbalanced parentheses, the algorithm may give incorrect results or fail.<\/li>\n\n\n\n<li><strong>Invalid Characters<\/strong>: The algorithm assumes valid input with operands and supported operators.<\/li>\n\n\n\n<li><strong>Multiple Digit Numbers<\/strong>: The current implementation treats each digit as a separate operand. For multi-digit numbers, additional logic would be needed to group consecutive digits.<\/li>\n\n\n\n<li><strong>Negative Numbers<\/strong>: The algorithm doesn&#8217;t handle unary operators (like a negative sign at the beginning of a number). This would require additional logic.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"7-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We iterate through the input string once, and each character is processed in constant time.<\/li>\n\n\n\n<li>Each character is pushed onto the stack at most once and popped at most once.<\/li>\n\n\n\n<li>Therefore, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"8-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the worst case (e.g., an expression with many opening parentheses), the stack might need to store a significant portion of the input.<\/li>\n\n\n\n<li>The result list will eventually contain all operands and operators from the input.<\/li>\n\n\n\n<li>Therefore, the space complexity is also linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>Infix to postfix conversion has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compiler Design<\/strong>: Postfix notation is used in compilers for expression evaluation.<\/li>\n\n\n\n<li><strong>Calculator Implementation<\/strong>: Many calculators convert infix expressions to postfix for evaluation.<\/li>\n\n\n\n<li><strong>Expression Evaluation Engines<\/strong>: Databases and spreadsheet applications often use postfix for formula evaluation.<\/li>\n\n\n\n<li><strong>Programming Languages<\/strong>: Some languages like Forth and PostScript use postfix notation natively.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"10-infix-to-prefix-conversion-explanation-\"><strong>Infix to Prefix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Prefix notation (also known as Polish notation) is a way to write mathematical expressions where operators precede their operands. For example, the infix expression &#8220;a + b&#8221; becomes &#8220;+ a b&#8221; in prefix notation. This format, like postfix notation, eliminates the need for parentheses and simplifies expression evaluation for computers.<\/p>\n\n\n\n<p>The key insight for converting infix to prefix is that we can leverage our knowledge of infix to postfix conversion with some clever modifications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Reverse the infix expression<\/li>\n\n\n\n<li>Swap opening and closing parentheses (since we reversed the string)<\/li>\n\n\n\n<li>Apply a modified infix to postfix algorithm<\/li>\n\n\n\n<li>Reverse the result to get the prefix expression<\/li>\n<\/ol>\n\n\n\n<p>This approach works because reversing an infix expression and swapping parentheses essentially transforms the problem into a &#8220;right-to-left&#8221; version of the infix to postfix conversion. After we obtain the &#8220;reverse postfix&#8221; expression, reversing it again gives us the correct prefix notation.<\/p>\n\n\n\n<p>The clever part of this algorithm is recognizing that we don&#8217;t need to design a completely new conversion algorithm &#8211; we can adapt the infix to postfix algorithm with minimal changes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def precedence(self, ch):\n\u00a0 \u00a0 \u00a0 \u00a0 # Define operator precedence hierarchy\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;+&quot; or ch == &quot;-&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 1\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;*&quot; or ch == &quot;\/&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 2\n\u00a0 \u00a0 \u00a0 \u00a0 if ch == &quot;^&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 return 3\n\u00a0 \u00a0 \u00a0 \u00a0 return 0\u00a0 # For non-operators like '(' and ')'\n\n\u00a0 \u00a0 def infixToPrefix(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 # Step 1: Reverse the infix expression\n\u00a0 \u00a0 \u00a0 \u00a0 s = s[::-1]\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Step 2: Swap opening and closing parentheses\n\u00a0 \u00a0 \u00a0 \u00a0 s = s.replace(&quot;(&quot;, &quot;temp&quot;).replace(&quot;)&quot;, &quot;(&quot;).replace(&quot;temp&quot;, &quot;)&quot;)\n\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\n\u00a0 \u00a0 \u00a0 \u00a0 result = []\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Step 3: Modified infix to postfix algorithm\n\u00a0 \u00a0 \u00a0 \u00a0 for char in s:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operand, add it directly to result\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if (&quot;a&quot; &lt;= char &lt;= &quot;z&quot;) or (&quot;A&quot; &lt;= char &lt;= &quot;Z&quot;) or (&quot;0&quot; &lt;= char &lt;= &quot;9&quot;):\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is '(', push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 elif char == &quot;(&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is ')', pop until '(' is encountered\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 elif char == &quot;)&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while stack and stack[-1] != &quot;(&quot;:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.pop()\u00a0 # Discard the '('\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operator\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Note the change to '&gt;' from '&gt;=' in the infix to postfix algorithm\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # This handles right-associativity properly\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 while stack and self.precedence(stack[-1]) &gt; self.precedence(char):\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\u00a0 # Push current operator\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Pop remaining operators from the stack\n\u00a0 \u00a0 \u00a0 \u00a0 while stack:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Step 4: Reverse the result to get prefix expression\n\u00a0 \u00a0 \u00a0 \u00a0 return &quot;&quot;.join(result[::-1])\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">precedence<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">ch<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Define operator precedence hierarchy<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;+&quot;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;-&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;*&quot;<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;\/&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> ch == <\/span><span style=\"color: #CE9178\">&quot;^&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">\u00a0 <\/span><span style=\"color: #6A9955\"># For non-operators like &#39;(&#39; and &#39;)&#39;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">infixToPrefix<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Step 1: Reverse the infix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 s = s[::-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Step 2: Swap opening and closing parentheses<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 s = s.replace(<\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #CE9178\">&quot;temp&quot;<\/span><span style=\"color: #D4D4D4\">).replace(<\/span><span style=\"color: #CE9178\">&quot;)&quot;<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">).replace(<\/span><span style=\"color: #CE9178\">&quot;temp&quot;<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #CE9178\">&quot;)&quot;<\/span><span style=\"color: #D4D4D4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 result = []<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Step 3: Modified infix to postfix algorithm<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> char <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> s:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operand, add it directly to result<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;a&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;z&quot;<\/span><span style=\"color: #D4D4D4\">) <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;A&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;Z&quot;<\/span><span style=\"color: #D4D4D4\">) <\/span><span style=\"color: #569CD6\">or<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #CE9178\">&quot;0&quot;<\/span><span style=\"color: #D4D4D4\"> &lt;= char &lt;= <\/span><span style=\"color: #CE9178\">&quot;9&quot;<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is &#39;(&#39;, push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">elif<\/span><span style=\"color: #D4D4D4\"> char == <\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is &#39;)&#39;, pop until &#39;(&#39; is encountered<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">elif<\/span><span style=\"color: #D4D4D4\"> char == <\/span><span style=\"color: #CE9178\">&quot;)&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack <\/span><span style=\"color: #569CD6\">and<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">] != <\/span><span style=\"color: #CE9178\">&quot;(&quot;<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Discard the &#39;(&#39;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operator<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Note the change to &#39;&gt;&#39; from &#39;&gt;=&#39; in the infix to postfix algorithm<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># This handles right-associativity properly<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack <\/span><span style=\"color: #569CD6\">and<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.precedence(stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]) &gt; <\/span><span style=\"color: #569CD6\">self<\/span><span style=\"color: #D4D4D4\">.precedence(char):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\u00a0 <\/span><span style=\"color: #6A9955\"># Push current operator<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Pop remaining operators from the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> stack:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 result.append(stack.pop())<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Step 4: Reverse the result to get prefix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #CE9178\">&quot;&quot;<\/span><span style=\"color: #D4D4D4\">.join(result[::-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">])<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation consists of the same precedence function from the infix to postfix conversion, plus the main infixToPrefix function:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>precedence(ch)<\/strong>: This helper function assigns a numeric value to each operator representing its precedence:\n<ul class=\"wp-block-list\">\n<li>Addition and subtraction have precedence 1<\/li>\n\n\n\n<li>Multiplication and division have precedence 2<\/li>\n\n\n\n<li>Exponentiation has precedence 3<\/li>\n\n\n\n<li>Other characters have precedence 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>infixToPrefix(s)<\/strong>: The main conversion function with four key steps:\n<ul class=\"wp-block-list\">\n<li><strong>Step 1<\/strong>: Reverse the input string using slice notation s[::-1].<\/li>\n\n\n\n<li><strong>Step 2<\/strong>: Swap opening and closing parentheses, since they need to be flipped after reversal. This is done using sequential replacements with a temporary placeholder to avoid conflicts.<\/li>\n\n\n\n<li><strong>Step 3<\/strong>: Apply a modified infix to postfix algorithm:\n<ul class=\"wp-block-list\">\n<li>Process each character in the (reversed) input<\/li>\n\n\n\n<li>Operands go directly to the result list<\/li>\n\n\n\n<li>Opening parentheses go onto the stack<\/li>\n\n\n\n<li>Closing parentheses trigger popping operators until the matching opening parenthesis<\/li>\n\n\n\n<li>For operators, pop operators with <em>strictly higher<\/em> precedence (note the > instead of >= used in postfix conversion &#8211; this subtle change handles operator associativity correctly in the prefix notation)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Step 4<\/strong>: Reverse the result using result[::-1] to get the final prefix expression<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>The subtle but important difference in the operator precedence comparison (&gt; instead of &gt;=) ensures that the order of operations is preserved correctly for prefix notation, especially for operators with the same precedence level.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the infix expression &#8220;a+b*c&#8221; to prefix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reverse the infix<\/strong>: &#8220;c*b+a&#8221;<\/li>\n\n\n\n<li><strong>Swap parentheses<\/strong>: No parentheses in this example, so the string remains &#8220;c*b+a&#8221;<\/li>\n\n\n\n<li><strong>Apply modified infix to postfix<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Initialize: stack = [], result = []<\/li>\n\n\n\n<li>Process &#8216;c&#8217;: Append to result \u2192 result = [&#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;*&#8217;: Stack is empty, push to stack \u2192 stack = [&#8216;*&#8217;], result = [&#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;b&#8217;: Append to result \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;+&#8217;: Lower precedence than &#8216;<em>&#8216;, pop &#8216;<\/em>&#8216; \u2192 stack = [&#8216;+&#8217;], result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;]<\/li>\n\n\n\n<li>Process &#8216;a&#8217;: Append to result \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;, &#8216;a&#8217;]<\/li>\n\n\n\n<li>No more characters. Pop remaining operators: \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;, &#8216;a&#8217;, &#8216;+&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Reverse the result<\/strong>: &#8220;+&#8221; + &#8220;a&#8221; + &#8220;<em>&#8221; + &#8220;b&#8221; + &#8220;c&#8221; = &#8220;+a<\/em>bc&#8221;<\/li>\n<\/ol>\n\n\n\n<p>The final prefix expression is &#8220;+a<em>bc&#8221;, which correctly represents &#8220;a+b<\/em>c&#8221; in prefix notation.<\/p>\n\n\n\n<p>Let&#8217;s try a more complex example with parentheses: &#8220;a+(b*c)&#8221;<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Reverse the infix<\/strong>: &#8220;)c*b(+a&#8221;<\/li>\n\n\n\n<li><strong>Swap parentheses<\/strong>: &#8220;(c*b)+a&#8221;<\/li>\n\n\n\n<li><strong>Apply modified infix to postfix<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Initialize: stack = [], result = []<\/li>\n\n\n\n<li>Process &#8216;(&#8216;: Push to stack \u2192 stack = [&#8216;(&#8216;], result = []<\/li>\n\n\n\n<li>Process &#8216;c&#8217;: Append to result \u2192 result = [&#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;*&#8217;: Push to stack \u2192 stack = [&#8216;(&#8216;, &#8216;*&#8217;], result = [&#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;b&#8217;: Append to result \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;)&#8217;: Pop until &#8216;(&#8216; \u2192 stack = [], result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;]<\/li>\n\n\n\n<li>Process &#8216;+&#8217;: Push to stack \u2192 stack = [&#8216;+&#8217;], result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;]<\/li>\n\n\n\n<li>Process &#8216;a&#8217;: Append to result \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;, &#8216;a&#8217;]<\/li>\n\n\n\n<li>Pop remaining operators: \u2192 result = [&#8216;c&#8217;, &#8216;b&#8217;, &#8216;*&#8217;, &#8216;a&#8217;, &#8216;+&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Reverse the result<\/strong>: &#8220;+a*bc&#8221;, which is the correct prefix form.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"15-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would return an empty string, which is correct.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Only Operators<\/strong>: Not a valid infix expression, but the algorithm would attempt to process it.<\/li>\n\n\n\n<li><strong>Unbalanced Parentheses<\/strong>: If the input has unbalanced parentheses, the algorithm may give incorrect results or fail.<\/li>\n\n\n\n<li><strong>Right-Associative Operators<\/strong>: The algorithm handles right-associative operators like exponentiation (^) correctly due to the > comparison in the precedence check.<\/li>\n\n\n\n<li><strong>Multiple Digit Numbers<\/strong>: The current implementation treats each digit as a separate operand. For multi-digit numbers, additional logic would be needed.<\/li>\n\n\n\n<li><strong>Negative Numbers<\/strong>: The algorithm doesn&#8217;t handle unary operators (like a negative sign). This would require additional preprocessing.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"16-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"17-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We process each character in the input string once.<\/li>\n\n\n\n<li>String reversal takes O(n) time.<\/li>\n\n\n\n<li>Parenthesis swapping takes O(n) time.<\/li>\n\n\n\n<li>The infix to postfix conversion part takes O(n) time, with each character pushed and popped at most once.<\/li>\n\n\n\n<li>Final result reversal takes O(n) time.<\/li>\n\n\n\n<li>Overall, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"18-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The reversed input string requires O(n) space.<\/li>\n\n\n\n<li>The stack might store up to O(n) characters in the worst case.<\/li>\n\n\n\n<li>The result list will eventually store O(n) characters.<\/li>\n\n\n\n<li>Therefore, the space complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"19-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>Prefix notation has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compiler Design<\/strong>: Some programming language compilers use prefix notation as an intermediate representation.<\/li>\n\n\n\n<li><strong>Functional Programming<\/strong>: Languages like LISP use prefix notation for function calls and expressions.<\/li>\n\n\n\n<li><strong>Expression Evaluation<\/strong>: Prefix notation can be evaluated using a simple algorithm with a stack.<\/li>\n\n\n\n<li><strong>Logical Expressions<\/strong>: Prefix notation is sometimes used in logical expressions and Boolean algebra.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"20-postfix-to-infix-conversion-explanation-\"><strong>Postfix to Infix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"21-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Converting from postfix notation back to infix notation is an interesting problem that showcases the power of stack-based parsing. While infix notation is the standard mathematical notation we&#8217;re all familiar with (e.g., &#8220;a + b&#8221;), postfix notation (also known as Reverse Polish Notation) places operators after their operands (e.g., &#8220;ab+&#8221;).<\/p>\n\n\n\n<p>The key insight for this conversion is that postfix expressions are designed to be evaluated using a stack. When converting to infix, we can use a similar stack-based approach, but instead of computing values, we build infix expression strings.<\/p>\n\n\n\n<p>The algorithm works as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scan the postfix expression from left to right<\/li>\n\n\n\n<li>When an operand is encountered, push it onto the stack<\/li>\n\n\n\n<li>When an operator is encountered, pop the top two elements from the stack (these are the operands)<\/li>\n\n\n\n<li>Combine these operands with the operator, surrounded by parentheses, to form a partial infix expression<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n\n\n\n<li>After processing the entire postfix expression, the stack will contain a single element &#8211; the complete infix expression<\/li>\n<\/ol>\n\n\n\n<p>The parentheses around each operation ensure that the resulting infix expression preserves the correct order of operations that was encoded in the postfix expression.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"22-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def postToInfix(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 # Stack to store operands or partial infix expressions\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\n\n\u00a0 \u00a0 \u00a0 \u00a0 for char in s:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operand (letter or digit), push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if char.isalnum():\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operator, pop two operands\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 # Second operand (popped first)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 # First operand (popped second)\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Combine operands with the operator, surrounded by parentheses\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = f&quot;({operand1}{char}{operand2})&quot;\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Push the resulting expression back onto the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)\n\n\u00a0 \u00a0 \u00a0 \u00a0 # The final element in the stack is the complete infix expression\n\u00a0 \u00a0 \u00a0 \u00a0 return stack[-1]\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">postToInfix<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Stack to store operands or partial infix expressions<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> char <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> s:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operand (letter or digit), push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> char.isalnum():<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operator, pop two operands<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Second operand (popped first)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># First operand (popped second)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Combine operands with the operator, surrounded by parentheses<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = <\/span><span style=\"color: #569CD6\">f<\/span><span style=\"color: #CE9178\">&quot;(<\/span><span style=\"color: #569CD6\">{<\/span><span style=\"color: #D4D4D4\">operand1<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">char<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">operand2<\/span><span style=\"color: #569CD6\">}<\/span><span style=\"color: #CE9178\">)&quot;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Push the resulting expression back onto the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># The final element in the stack is the complete infix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"23-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation uses a single stack and processes each character in the postfix expression one at a time:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Stack Initialization<\/strong>: We create an empty list to serve as our stack for storing operands and intermediate expressions.<\/li>\n\n\n\n<li><strong>Character Processing<\/strong>:\n<ul class=\"wp-block-list\">\n<li>For each character in the postfix expression:\n<ul class=\"wp-block-list\">\n<li>If it&#8217;s an alphanumeric character (operand), we push it directly onto the stack<\/li>\n\n\n\n<li>If it&#8217;s an operator, we:\n<ul class=\"wp-block-list\">\n<li>Pop the top element from the stack (second operand in infix notation)<\/li>\n\n\n\n<li>Pop the next element from the stack (first operand in infix notation)<\/li>\n\n\n\n<li>Combine them with the operator in the form &#8220;(operand1 operator operand2)&#8221;<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Final Result<\/strong>: After processing all characters, the stack will contain exactly one element &#8211; the complete infix expression.<\/li>\n<\/ol>\n\n\n\n<p>The key aspects of this implementation are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Using isalnum() to identify operands (both letters and numbers)<\/li>\n\n\n\n<li>The order of popping operands matters: the second operand is popped first, and the first operand is popped second<\/li>\n\n\n\n<li>Adding parentheses around each operation to preserve precedence<\/li>\n\n\n\n<li>Using f-strings for clean string concatenation<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"24-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the postfix expression &#8220;ab+cd-*&#8221; to infix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Initialize: stack = []<\/li>\n\n\n\n<li>Process &#8216;a&#8217;: Push to stack \u2192 stack = [&#8216;a&#8217;]<\/li>\n\n\n\n<li>Process &#8216;b&#8217;: Push to stack \u2192 stack = [&#8216;a&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;+&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;b&#8217;, operand1 = &#8216;a&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;(a+b)&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;(a+b)&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Process &#8216;c&#8217;: Push to stack \u2192 stack = [&#8216;(a+b)&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;d&#8217;: Push to stack \u2192 stack = [&#8216;(a+b)&#8217;, &#8216;c&#8217;, &#8216;d&#8217;]<\/li>\n\n\n\n<li>Process &#8216;-&#8216;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;d&#8217;, operand1 = &#8216;c&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;(c-d)&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;(a+b)&#8217;, &#8216;(c-d)&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Process &#8216;*&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;(c-d)&#8217;, operand1 = &#8216;(a+b)&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;((a+b)*(c-d))&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;((a+b)*(c-d))&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Final result: &#8220;((a+b)*(c-d))&#8221;<\/li>\n<\/ol>\n\n\n\n<p>This infix expression correctly represents the computation encoded in the original postfix expression &#8220;ab+cd-<em>&#8220;, which means &#8220;(a+b)<\/em>(c-d)&#8221;.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"25-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would attempt to access an empty stack, causing an error. Input validation should be added.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Invalid Postfix Expression<\/strong>: If the input isn&#8217;t a valid postfix expression (e.g., not enough operands for operators), the algorithm will fail when attempting to pop from the stack.<\/li>\n\n\n\n<li><strong>Complex Expressions<\/strong>: The algorithm handles arbitrarily complex expressions correctly, as long as they are valid postfix expressions.<\/li>\n\n\n\n<li><strong>Operator Associativity<\/strong>: The parentheses ensure that the original operation order is preserved, regardless of operator associativity.<\/li>\n\n\n\n<li><strong>Multi-Character Operands<\/strong>: The current implementation assumes single-character operands. For multi-character operands, additional tokenization would be needed.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"26-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"27-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We iterate through the input string once, processing each character exactly once.<\/li>\n\n\n\n<li>Each character is either pushed onto the stack once, or causes two pops and one push.<\/li>\n\n\n\n<li>String concatenation operations are generally O(1) for small strings.<\/li>\n\n\n\n<li>Overall, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"28-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the worst case, the stack might contain nearly all characters from the input.<\/li>\n\n\n\n<li>Additionally, as we build infix expressions with parentheses, the final expression can be larger than the input.<\/li>\n\n\n\n<li>Therefore, the space complexity is O(n), where n is the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"29-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>Understanding postfix to infix conversion has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compiler Design<\/strong>: Compilers often convert between different notations during the parsing and code generation stages.<\/li>\n\n\n\n<li><strong>Calculator Implementation<\/strong>: Many calculators that use postfix internally might need to display results in infix.<\/li>\n\n\n\n<li><strong>Expression Evaluation<\/strong>: Systems that evaluate expressions in postfix form may need to show intermediate steps in infix notation for debugging or user display.<\/li>\n\n\n\n<li><strong>Programming Language Tools<\/strong>: Debuggers and code analyzers might convert between notations to present information to developers.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"30-prefix-to-infix-conversion-explanation-\"><strong>Prefix to Infix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"31-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Prefix notation (also known as Polish notation) places operators before their operands. For example, the infix expression &#8220;a + b&#8221; is written as &#8220;+ a b&#8221; in prefix notation. Converting from prefix to infix requires a different approach than postfix to infix, but still leverages the power of stack-based parsing.<\/p>\n\n\n\n<p>The key insight for this conversion is that we need to process the prefix expression in reverse order (right to left). This is because in prefix notation, operators precede their operands, so when working right to left, we encounter the operands before their corresponding operators.<\/p>\n\n\n\n<p>The algorithm works as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scan the prefix expression from right to left<\/li>\n\n\n\n<li>When an operand is encountered, push it onto the stack<\/li>\n\n\n\n<li>When an operator is encountered, pop the top two elements from the stack (these are the operands)<\/li>\n\n\n\n<li>Combine these operands with the operator, surrounded by parentheses, to form a partial infix expression<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n\n\n\n<li>After processing the entire prefix expression, the stack will contain a single element &#8211; the complete infix expression<\/li>\n<\/ol>\n\n\n\n<p>The crucial difference from postfix conversion is the direction of traversal and the order of operands when forming expressions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"32-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def preToInfix(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 # Stack to store operands or partial infix expressions\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Process the prefix expression from right to left\n\u00a0 \u00a0 \u00a0 \u00a0 for char in s[::-1]:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operand (letter or digit), push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if char.isalnum():\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If character is an operator, pop two operands\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 # First operand\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 # Second operand\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Combine operands with the operator, surrounded by parentheses\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = f&quot;({operand1}{char}{operand2})&quot;\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Push the resulting expression back onto the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)\n\n\u00a0 \u00a0 \u00a0 \u00a0 # The final element in the stack is the complete infix expression\n\u00a0 \u00a0 \u00a0 \u00a0 return stack[-1]\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">preToInfix<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Stack to store operands or partial infix expressions<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Process the prefix expression from right to left<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> char <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> s[::-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operand (letter or digit), push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> char.isalnum():<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If character is an operator, pop two operands<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># First operand<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Second operand<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Combine operands with the operator, surrounded by parentheses<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = <\/span><span style=\"color: #569CD6\">f<\/span><span style=\"color: #CE9178\">&quot;(<\/span><span style=\"color: #569CD6\">{<\/span><span style=\"color: #D4D4D4\">operand1<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">char<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">operand2<\/span><span style=\"color: #569CD6\">}<\/span><span style=\"color: #CE9178\">)&quot;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Push the resulting expression back onto the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># The final element in the stack is the complete infix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"33-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation uses a single stack and processes each character in the prefix expression from right to left:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Stack Initialization<\/strong>: We create an empty list to serve as our stack for storing operands and intermediate expressions.<\/li>\n\n\n\n<li><strong>Character Processing<\/strong>:\n<ul class=\"wp-block-list\">\n<li>We use slice notation s[::-1] to iterate through the string in reverse order<\/li>\n\n\n\n<li>For each character:\n<ul class=\"wp-block-list\">\n<li>If it&#8217;s an alphanumeric character (operand), we push it directly onto the stack<\/li>\n\n\n\n<li>If it&#8217;s an operator, we:\n<ul class=\"wp-block-list\">\n<li>Pop the top element from the stack (first operand in infix notation)<\/li>\n\n\n\n<li>Pop the next element from the stack (second operand in infix notation)<\/li>\n\n\n\n<li>Combine them with the operator in the form &#8220;(operand1 operator operand2)&#8221;<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Final Result<\/strong>: After processing all characters, the stack will contain exactly one element &#8211; the complete infix expression.<\/li>\n<\/ol>\n\n\n\n<p>Note the order of popping operands: unlike in postfix conversion, the first operand popped corresponds to the first operand in the resulting infix expression. This is because when processing the prefix expression from right to left, we encounter operands in the reverse order than we would in a postfix expression processed from left to right.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"34-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the prefix expression &#8220;*+ab-cd&#8221; to infix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Initialize: stack = []<\/li>\n\n\n\n<li>Process (from right to left):\n<ul class=\"wp-block-list\">\n<li>&#8216;d&#8217;: Push to stack \u2192 stack = [&#8216;d&#8217;]<\/li>\n\n\n\n<li>&#8216;c&#8217;: Push to stack \u2192 stack = [&#8216;d&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>&#8216;-&#8216;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;c&#8217;, operand2 = &#8216;d&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;(c-d)&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;(c-d)&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>&#8216;b&#8217;: Push to stack \u2192 stack = [&#8216;(c-d)&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>&#8216;a&#8217;: Push to stack \u2192 stack = [&#8216;(c-d)&#8217;, &#8216;b&#8217;, &#8216;a&#8217;]<\/li>\n\n\n\n<li>&#8216;+&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;a&#8217;, operand2 = &#8216;b&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;(a+b)&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;(c-d)&#8217;, &#8216;(a+b)&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>&#8216;*&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;(a+b)&#8217;, operand2 = &#8216;(c-d)&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;((a+b)*(c-d))&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;((a+b)*(c-d))&#8217;]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Final result: &#8220;((a+b)*(c-d))&#8221;<\/li>\n<\/ol>\n\n\n\n<p>This infix expression correctly represents the computation encoded in the original prefix expression &#8220;<em>+ab-cd&#8221;, which means &#8220;(a+b)<\/em>(c-d)&#8221;.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"35-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would return an error for an empty input string. Input validation should be added.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Invalid Prefix Expression<\/strong>: If the input isn&#8217;t a valid prefix expression (e.g., not enough operands for operators), the algorithm will fail when attempting to pop from the stack.<\/li>\n\n\n\n<li><strong>Complex Expressions<\/strong>: The algorithm handles arbitrarily complex expressions correctly, as long as they are valid prefix expressions.<\/li>\n\n\n\n<li><strong>Operator Associativity<\/strong>: The parentheses ensure that the original operation order is preserved, regardless of operator associativity.<\/li>\n\n\n\n<li><strong>Multi-Character Operands<\/strong>: The current implementation assumes single-character operands. For multi-character operands, additional tokenization would be needed.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"36-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"37-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We iterate through the input string once, processing each character exactly once.<\/li>\n\n\n\n<li>String reversal takes O(n) time.<\/li>\n\n\n\n<li>Each character is either pushed onto the stack once, or causes two pops and one push.<\/li>\n\n\n\n<li>String concatenation operations are generally O(1) for small strings.<\/li>\n\n\n\n<li>Overall, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"38-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the worst case, the stack might contain nearly all characters from the input.<\/li>\n\n\n\n<li>Additionally, as we build infix expressions with parentheses, the final expression can be larger than the input.<\/li>\n\n\n\n<li>Therefore, the space complexity is O(n), where n is the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"39-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>Understanding prefix to infix conversion has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Programming Language Processing<\/strong>: Some languages like LISP use prefix notation, and tools might need to convert between notations.<\/li>\n\n\n\n<li><strong>Expression Evaluators<\/strong>: Systems that need to display prefix expressions in a more human-readable format.<\/li>\n\n\n\n<li><strong>Compiler Design<\/strong>: Compilers that work with different expression notations during various processing stages.<\/li>\n\n\n\n<li><strong>Mathematical Software<\/strong>: Tools that allow users to input expressions in different notations.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"40-postfix-to-prefix-conversion-explanation-\"><strong>Postfix to Prefix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"41-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Converting between different notations of mathematical expressions is a fundamental operation in compiler design and expression parsing. In this case, we&#8217;re converting from postfix notation (Reverse Polish Notation) to prefix notation (Polish Notation).<\/p>\n\n\n\n<p>Postfix notation places operators after their operands (e.g., &#8220;ab+&#8221;), while prefix notation places operators before their operands (e.g., &#8220;+ab&#8221;). Both notations eliminate the need for parentheses, unlike infix notation.<\/p>\n\n\n\n<p>The key insight for this conversion is that we can leverage the stack-based nature of postfix evaluation, but instead of computing values, we build prefix expression strings. When we encounter an operator in the postfix expression, we pop two operands from the stack, combine them with the operator in prefix form, and push the result back.<\/p>\n\n\n\n<p>The algorithm follows these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scan the postfix expression from left to right<\/li>\n\n\n\n<li>When an operand is encountered, push it onto the stack<\/li>\n\n\n\n<li>When an operator is encountered, pop the top two elements from the stack<\/li>\n\n\n\n<li>Create a new expression with the operator first, followed by the first operand, then the second operand<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n\n\n\n<li>After processing the entire postfix expression, the stack will contain a single element &#8211; the complete prefix expression<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"42-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def postToPre(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 # Stack to store operands or partial prefix expressions\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Process each character in postfix expression\n\u00a0 \u00a0 \u00a0 \u00a0 for char in s:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If the character is an operand, push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if char.isalnum():\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Pop two operands from the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 # Second operand (popped first)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 # First operand (popped second)\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Combine the operands with the operator in prefix form\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = f&quot;{char}{operand1}{operand2}&quot;\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Push the result back onto the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)\n\n\u00a0 \u00a0 \u00a0 \u00a0 # The final element in the stack is the prefix expression\n\u00a0 \u00a0 \u00a0 \u00a0 return stack[-1]\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">postToPre<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Stack to store operands or partial prefix expressions<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Process each character in postfix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> char <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> s:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If the character is an operand, push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> char.isalnum():<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Pop two operands from the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Second operand (popped first)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># First operand (popped second)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Combine the operands with the operator in prefix form<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = <\/span><span style=\"color: #569CD6\">f<\/span><span style=\"color: #CE9178\">&quot;<\/span><span style=\"color: #569CD6\">{<\/span><span style=\"color: #D4D4D4\">char<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">operand1<\/span><span style=\"color: #569CD6\">}{<\/span><span style=\"color: #D4D4D4\">operand2<\/span><span style=\"color: #569CD6\">}<\/span><span style=\"color: #CE9178\">&quot;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Push the result back onto the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># The final element in the stack is the prefix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"43-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation uses a single stack to process the postfix expression character by character:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Stack Initialization<\/strong>: We create an empty list to serve as our stack for storing operands and intermediate expressions.<\/li>\n\n\n\n<li><strong>Character Processing<\/strong>:\n<ul class=\"wp-block-list\">\n<li>For each character in the postfix expression:\n<ul class=\"wp-block-list\">\n<li>If it&#8217;s an alphanumeric character (an operand), we push it directly onto the stack<\/li>\n\n\n\n<li>If it&#8217;s an operator, we:\n<ul class=\"wp-block-list\">\n<li>Pop the top element from the stack (second operand)<\/li>\n\n\n\n<li>Pop the next element from the stack (first operand)<\/li>\n\n\n\n<li>Combine them with the operator in prefix form: &#8220;operator operand1 operand2&#8221;<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Final Result<\/strong>: After processing all characters, the stack will contain exactly one element &#8211; the complete prefix expression.<\/li>\n<\/ol>\n\n\n\n<p>The key aspects of this implementation are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Using isalnum() to identify operands (both letters and numbers)<\/li>\n\n\n\n<li>The order of popping operands matters: the second operand is popped first, and the first operand is popped second<\/li>\n\n\n\n<li>The new expression is formed with the operator first, followed by operand1 and operand2<\/li>\n\n\n\n<li>Unlike in the conversion to infix, we don&#8217;t need parentheses since prefix notation doesn&#8217;t require them<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"44-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the postfix expression &#8220;ab+cd-*&#8221; to prefix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Initialize: stack = []<\/li>\n\n\n\n<li>Process &#8216;a&#8217;: Push to stack \u2192 stack = [&#8216;a&#8217;]<\/li>\n\n\n\n<li>Process &#8216;b&#8217;: Push to stack \u2192 stack = [&#8216;a&#8217;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>Process &#8216;+&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;b&#8217;, operand1 = &#8216;a&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;+ab&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;+ab&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Process &#8216;c&#8217;: Push to stack \u2192 stack = [&#8216;+ab&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>Process &#8216;d&#8217;: Push to stack \u2192 stack = [&#8216;+ab&#8217;, &#8216;c&#8217;, &#8216;d&#8217;]<\/li>\n\n\n\n<li>Process &#8216;-&#8216;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;d&#8217;, operand1 = &#8216;c&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;-cd&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;+ab&#8217;, &#8216;-cd&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Process &#8216;*&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand2 = &#8216;-cd&#8217;, operand1 = &#8216;+ab&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;*+ab-cd&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;*+ab-cd&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Final result: &#8220;*+ab-cd&#8221;<\/li>\n<\/ol>\n\n\n\n<p>This prefix expression correctly represents the computation encoded in the original postfix expression &#8220;ab+cd-<em>&#8220;, which means &#8220;(a+b)<\/em>(c-d)&#8221; in infix notation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"45-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would attempt to access an empty stack, causing an error. Input validation should be added.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Invalid Postfix Expression<\/strong>: If the input isn&#8217;t a valid postfix expression (e.g., not enough operands for operators), the algorithm will fail when attempting to pop from the stack.<\/li>\n\n\n\n<li><strong>Complex Expressions<\/strong>: The algorithm handles arbitrarily complex expressions correctly, as long as they are valid postfix expressions.<\/li>\n\n\n\n<li><strong>Multi-Character Operands<\/strong>: The current implementation assumes single-character operands. For multi-character operands, additional tokenization would be needed.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"46-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"47-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We iterate through the input string once, processing each character exactly once.<\/li>\n\n\n\n<li>Each character is either pushed onto the stack once, or causes two pops and one push.<\/li>\n\n\n\n<li>String concatenation operations are generally O(1) for small strings.<\/li>\n\n\n\n<li>Overall, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"48-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the worst case, the stack might contain nearly all characters from the input.<\/li>\n\n\n\n<li>Therefore, the space complexity is O(n), where n is the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"49-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>Understanding postfix to prefix conversion has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compiler Design<\/strong>: Compilers often convert between different notations during parsing and code generation.<\/li>\n\n\n\n<li><strong>Expression Evaluators<\/strong>: Systems that work with multiple notation formats need conversion capabilities.<\/li>\n\n\n\n<li><strong>Programming Language Tools<\/strong>: Some languages use different notations natively, requiring conversion for interoperability.<\/li>\n\n\n\n<li><strong>Educational Tools<\/strong>: Teaching aids for computer science students learning about different expression notations.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\" id=\"50-prefix-to-postfix-conversion-explanation-\"><strong>Prefix to Postfix Conversion Explanation<\/strong><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"51-approachintuition-\"><strong>Approach\/Intuition<\/strong><\/h2>\n\n\n\n<p>Converting from prefix notation to postfix notation involves transforming expressions from a format where operators precede their operands (e.g., &#8220;+ab&#8221;) to one where operators follow their operands (e.g., &#8220;ab+&#8221;). Both notations are parenthesis-free and unambiguous, making them valuable in computer science for expression evaluation.<\/p>\n\n\n\n<p>The key insight for this conversion is that we need to process the prefix expression in reverse order (right to left). This approach works because:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>In prefix notation, operators come before operands<\/li>\n\n\n\n<li>When reading right to left, we encounter operands before their operators<\/li>\n\n\n\n<li>By using a stack and processing in reverse, we can build the postfix expression incrementally<\/li>\n<\/ol>\n\n\n\n<p>The algorithm follows these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Scan the prefix expression from right to left<\/li>\n\n\n\n<li>When an operand is encountered, push it onto the stack<\/li>\n\n\n\n<li>When an operator is encountered, pop the top two elements from the stack (these are operands)<\/li>\n\n\n\n<li>Create a new expression with the first operand, then the second operand, then the operator<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n\n\n\n<li>After processing the entire prefix expression, the stack will contain a single element &#8211; the complete postfix expression<\/li>\n<\/ol>\n\n\n\n<p>This approach elegantly handles the structural differences between prefix and postfix notations.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"52-code-\"><strong>Code<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.5rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#1E1E1E\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" data-code=\"class Solution:\n\u00a0 \u00a0 def preToPost(self, s):\n\u00a0 \u00a0 \u00a0 \u00a0 # Stack to store operands or partial postfix expressions\n\u00a0 \u00a0 \u00a0 \u00a0 stack = []\n\n\u00a0 \u00a0 \u00a0 \u00a0 # Traverse the prefix expression from right to left using index\n\u00a0 \u00a0 \u00a0 \u00a0 n = len(s)\n\u00a0 \u00a0 \u00a0 \u00a0 for i in range(n - 1, -1, -1):\u00a0 # Reverse iteration using index\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 char = s[i]\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # If the character is an operand, push it to the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 if char.isalnum():\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 else:\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Pop two operands from the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 # First operand\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 # Second operand\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Combine the operands with the operator in postfix form\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = operand1 + operand2 + char\n\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 # Push the result back onto the stack\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)\n\n\u00a0 \u00a0 \u00a0 \u00a0 # The final element in the stack is the postfix expression\n\u00a0 \u00a0 \u00a0 \u00a0 return stack[-1]\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">Solution<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 <\/span><span style=\"color: #569CD6\">def<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">preToPost<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">self<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">s<\/span><span style=\"color: #D4D4D4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Stack to store operands or partial postfix expressions<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 stack = []<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Traverse the prefix expression from right to left using index<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 n = <\/span><span style=\"color: #DCDCAA\">len<\/span><span style=\"color: #D4D4D4\">(s)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">for<\/span><span style=\"color: #D4D4D4\"> i <\/span><span style=\"color: #C586C0\">in<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">range<\/span><span style=\"color: #D4D4D4\">(n - <\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">, -<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">):\u00a0 <\/span><span style=\"color: #6A9955\"># Reverse iteration using index<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 char = s[i]<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># If the character is an operand, push it to the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> char.isalnum():<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(char)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Pop two operands from the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand1 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># First operand<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 operand2 = stack.pop()\u00a0 <\/span><span style=\"color: #6A9955\"># Second operand<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Combine the operands with the operator in postfix form<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 new_expr = operand1 + operand2 + char<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># Push the result back onto the stack<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 stack.append(new_expr)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #6A9955\"># The final element in the stack is the postfix expression<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">\u00a0 \u00a0 \u00a0 \u00a0 <\/span><span style=\"color: #C586C0\">return<\/span><span style=\"color: #D4D4D4\"> stack[-<\/span><span style=\"color: #B5CEA8\">1<\/span><span style=\"color: #D4D4D4\">]<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"53-code-explanation-\"><strong>Code Explanation<\/strong><\/h2>\n\n\n\n<p>The implementation uses a single stack and processes the prefix expression from right to left:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Stack Initialization<\/strong>: We create an empty list to serve as our stack for storing operands and intermediate expressions.<\/li>\n\n\n\n<li><strong>Character Processing<\/strong>:\n<ul class=\"wp-block-list\">\n<li>We iterate through the string in reverse order using range(n-1, -1, -1)<\/li>\n\n\n\n<li>For each character:\n<ul class=\"wp-block-list\">\n<li>If it&#8217;s an alphanumeric character (an operand), we push it directly onto the stack<\/li>\n\n\n\n<li>If it&#8217;s an operator, we:\n<ul class=\"wp-block-list\">\n<li>Pop the top element from the stack (first operand)<\/li>\n\n\n\n<li>Pop the next element from the stack (second operand)<\/li>\n\n\n\n<li>Combine them with the operator in postfix form: &#8220;operand1 operand2 operator&#8221;<\/li>\n\n\n\n<li>Push this new expression back onto the stack<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Final Result<\/strong>: After processing all characters, the stack will contain exactly one element &#8211; the complete postfix expression.<\/li>\n<\/ol>\n\n\n\n<p>The key aspects of this implementation are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Using isalnum() to identify operands (both letters and numbers)<\/li>\n\n\n\n<li>Processing the string from right to left (crucial for correct conversion)<\/li>\n\n\n\n<li>The order of operands in the formed expression: operand1 + operand2 + operator<\/li>\n\n\n\n<li>Using string concatenation to build the postfix expression incrementally<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"54-dry-run-example-\"><strong>Dry Run Example<\/strong><\/h2>\n\n\n\n<p>Let&#8217;s trace through the conversion of the prefix expression &#8220;*+ab-cd&#8221; to postfix:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Initialize: stack = []<\/li>\n\n\n\n<li>Process (from right to left):\n<ul class=\"wp-block-list\">\n<li>&#8216;d&#8217;: Push to stack \u2192 stack = [&#8216;d&#8217;]<\/li>\n\n\n\n<li>&#8216;c&#8217;: Push to stack \u2192 stack = [&#8216;d&#8217;, &#8216;c&#8217;]<\/li>\n\n\n\n<li>&#8216;-&#8216;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;c&#8217;, operand2 = &#8216;d&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;cd-&#8220;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;cd-&#8216;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>&#8216;b&#8217;: Push to stack \u2192 stack = [&#8216;cd-&#8216;, &#8216;b&#8217;]<\/li>\n\n\n\n<li>&#8216;a&#8217;: Push to stack \u2192 stack = [&#8216;cd-&#8216;, &#8216;b&#8217;, &#8216;a&#8217;]<\/li>\n\n\n\n<li>&#8216;+&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;a&#8217;, operand2 = &#8216;b&#8217;<\/li>\n\n\n\n<li>Create new expression: &#8220;ab+&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;cd-&#8216;, &#8216;ab+&#8217;]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>&#8216;*&#8217;:\n<ul class=\"wp-block-list\">\n<li>Pop two operands: operand1 = &#8216;ab+&#8217;, operand2 = &#8216;cd-&#8216;<\/li>\n\n\n\n<li>Create new expression: &#8220;ab+cd-*&#8221;<\/li>\n\n\n\n<li>Push to stack \u2192 stack = [&#8216;ab+cd-*&#8217;]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Final result: &#8220;ab+cd-*&#8221;<\/li>\n<\/ol>\n\n\n\n<p>This postfix expression correctly represents the computation encoded in the original prefix expression &#8220;<em>+ab-cd&#8221;, which means &#8220;(a+b)<\/em>(c-d)&#8221; in infix notation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"55-edge-cases-to-consider-\"><strong>Edge Cases to Consider<\/strong><\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Empty Input<\/strong>: The algorithm would attempt to access an empty stack, causing an error. Input validation should be added.<\/li>\n\n\n\n<li><strong>Single Operand<\/strong>: For input like &#8220;a&#8221;, the output would just be &#8220;a&#8221;, which is correct.<\/li>\n\n\n\n<li><strong>Invalid Prefix Expression<\/strong>: If the input isn&#8217;t a valid prefix expression (e.g., not enough operands for operators), the algorithm will fail when attempting to pop from the stack.<\/li>\n\n\n\n<li><strong>Complex Expressions<\/strong>: The algorithm handles arbitrarily complex expressions correctly, as long as they are valid prefix expressions.<\/li>\n\n\n\n<li><strong>Multi-Character Operands<\/strong>: The current implementation assumes single-character operands. For multi-character operands, additional tokenization would be needed.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"56-time-and-space-complexity-\"><strong>Time and Space Complexity<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"57-time-complexity-on-\"><strong>Time Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>We iterate through the input string once, processing each character exactly once.<\/li>\n\n\n\n<li>Each character is either pushed onto the stack once, or causes two pops and one push.<\/li>\n\n\n\n<li>String concatenation operations are generally O(1) for small strings.<\/li>\n\n\n\n<li>Overall, the time complexity is linear in the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"58-space-complexity-on-\"><strong>Space Complexity: O(n)<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the worst case, the stack might contain nearly all characters from the input.<\/li>\n\n\n\n<li>The final postfix expression will be roughly the same size as the input prefix expression.<\/li>\n\n\n\n<li>Therefore, the space complexity is O(n), where n is the length of the input string.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"59-applications-\"><strong>Applications<\/strong><\/h2>\n\n\n\n<p>The ability to convert between prefix and postfix notations has several practical applications:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compiler Design<\/strong>: Compilers often convert between different notations during different phases of compilation.<\/li>\n\n\n\n<li><strong>Expression Evaluators<\/strong>: Systems that support multiple input formats may need to convert to a standard internal format.<\/li>\n\n\n\n<li><strong>Calculator Implementations<\/strong>: Calculators might use one notation internally but need to display or accept input in different formats.<\/li>\n\n\n\n<li><strong>Programming Language Tools<\/strong>: Tools for languages that natively use prefix notation (like LISP) or postfix notation might need conversion capabilities.<\/li>\n<\/ol>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/codeanddebug.in\/course\/zero-to-hero-python-dsa\" target=\"_blank\" rel=\"noreferrer noopener\">Join our Advance DSA COURSE<\/a><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><em>For any changes to the article, kindly email at <a href=\"mailto:code@codeanddebug.in\" target=\"_blank\" rel=\"noreferrer noopener\">code@codeanddebug.in<\/a> or contact us at <a href=\"tel:+91-9712928220\" target=\"_blank\" rel=\"noreferrer noopener\">+91-9712928220<\/a>.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Postfix, prefix, and infix are three common notations used to write arithmetic expressions. In\u00a0infix notation, the operator is placed between operands (e.g., A + B), and is the most familiar to humans.\u00a0Prefix notation\u00a0(Polish notation) places the operator before the operands (e.g., + A B), while\u00a0postfix notation\u00a0(Reverse Polish notation) places the operator after the operands (e.g.,<\/p>\n","protected":false},"author":1,"featured_media":857,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4],"tags":[8,37],"class_list":{"0":"post-856","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-structures-and-algorithm","8":"category-beginner","9":"tag-easy","10":"tag-stack-and-queues"},"featured_image_src":"https:\/\/codeanddebug.in\/blog\/wp-content\/uploads\/2025\/08\/infix-postfix-prefix-conversions-featured-image.png","author_info":{"display_name":"codeanddebug","author_link":"https:\/\/codeanddebug.in\/blog\/author\/codeanddebug\/"},"_links":{"self":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/856","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/comments?post=856"}],"version-history":[{"count":1,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/856\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/posts\/856\/revisions\/858"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/media\/857"}],"wp:attachment":[{"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/media?parent=856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/categories?post=856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/codeanddebug.in\/blog\/wp-json\/wp\/v2\/tags?post=856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}