{"id":836,"date":"2025-08-04T12:53:52","date_gmt":"2025-08-04T07:23:52","guid":{"rendered":"https:\/\/codeanddebug.in\/blog\/?p=836"},"modified":"2025-08-04T12:53:53","modified_gmt":"2025-08-04T07:23:53","slug":"minimum-falling-path-sum","status":"publish","type":"post","link":"https:\/\/codeanddebug.in\/blog\/minimum-falling-path-sum\/","title":{"rendered":"Minimum Falling Path Sum | Leetcode 931 | Variable Starting and Ending Points"},"content":{"rendered":"\n

Given an n x n<\/code> array of integers matrix<\/code>, return the minimum sum<\/strong> of any falling path<\/strong> through<\/em> matrix<\/code>.<\/p>\n\n\n\n

A falling path<\/strong> starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left\/right. Specifically, the next element from position (row, col)<\/code> will be (row + 1, col - 1)<\/code>, (row + 1, col)<\/code>, or (row + 1, col + 1)<\/code>.<\/p>\n\n\n\n

Here’s the [Problem Link<\/span><\/mark><\/a><\/strong>] to begin with.<\/p>\n\n\n\n

Example 1:<\/strong><\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output:<\/strong> 13
Explanation:<\/strong> There are two falling paths with a minimum sum as shown.<\/pre>\n\n\n\n
Example 2:<\/strong><\/p>\n\n\n\n
\"\"\/<\/figure>\n\n\n\n
Input:<\/strong> matrix = [[-19,57],[-40,-5]]
Output:<\/strong> -59
Explanation:<\/strong> The falling path with a minimum sum is shown.<\/pre>\n\n\n\n
Constraints:<\/strong><\/p>\n\n\n\n