Hey students! If you’re diving\u00a0into recursion\u00a0and backtracking, the\u00a0“Subsets” problem\u00a0(also known as\u00a0generating the\u00a0power set or\u00a0all subsequences) is\u00a0a perfect starting\u00a0point. It’s like\u00a0deciding what\u00a0to pack for a\u00a0trip, for each\u00a0item, you choose\u00a0to take it or\u00a0leave it, and\u00a0all combinations\u00a0are possible. <\/p>\n\n\n\n
Here’s the [Problem Link<\/span><\/mark><\/a><\/strong>] to begin with.<\/p>\n\n\n\n Today, we’ll\u00a0focus on solving\u00a0it using\u00a0backtracking<\/strong>,\u00a0a technique that’s\u00a0super useful\u00a0for exploring\u00a0all possibilities. I’ll explain\u00a0it in simple\u00a0terms, step by\u00a0step, so even\u00a0beginners can\u00a0follow along. Let’s get started!<\/p>\n\n\n\n Given an integer array The solution set must not<\/strong> contain duplicate subsets. Return the solution in any order<\/strong>.<\/p>\n\n\n\n Example 1:<\/strong><\/p>\n\n\n\n Example 2:<\/strong><\/p>\n\n\n\n Constraints:<\/strong><\/p>\n\n\n\n Backtracking is like exploring a maze where you try different paths, and if you hit a dead end, you go back (backtrack) and try another way. For subsets, think of it as making choices for each element in the array: “Do I include this number in my current subset or not?” We start from the first element, make a choice to include it (add it to our subset and move to the next), then backtrack by removing it and trying the “exclude” choice. This builds a tree of decisions, and each complete path gives us one subset. It’s perfect for generating all combinations without duplicates!<\/p>\n\n\n\n This way, we systematically explore all 2^n possibilities (for n elements).<\/p>\n\n\n\nnums<\/code> of unique<\/strong> elements, return all possible<\/em> subsets<\/em> (the power set)<\/em>.<\/p>\n\n\n\nInput:<\/strong> nums = [1,2,3]
Output:<\/strong> [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]<\/pre>\n\n\n\nInput:<\/strong> nums = [0]
Output:<\/strong> [[],[0]]<\/pre>\n\n\n\n\n
1 <= nums.length <= 10<\/code><\/li>\n\n\n\n-10 <= nums[i] <= 10<\/code><\/li>\n\n\n\nnums<\/code>\u00a0are\u00a0unique<\/strong>.<\/li>\n<\/ul>\n\n\n
\n\n\n\nSolution: Backtracking Approach<\/h2>\n\n\n\n
Intuition<\/h3>\n\n\n\n
Detailed Approach<\/h3>\n\n\n\n
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solve<\/code>\u00a0that takes the current index in the array, the current subset being built, the original array, and the result list.<\/li>\n\n\n\nCode<\/h3>\n\n\n\n