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"content": "<p>Given an <code>n x n</code> integer matrix <code>grid</code>, return <em>the minimum sum of a <strong>falling path with non-zero shifts</strong></em>.</p>\n\n<p>A <strong>falling path with non-zero shifts</strong> is a choice of exactly one element from each row of <code>grid</code> such that no two elements chosen in adjacent rows are in the same column.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/08/10/falling-grid.jpg\" style=\"width: 244px; height: 245px;\" />\n<pre>\n<strong>Input:</strong> arr = [[1,2,3],[4,5,6],[7,8,9]]\n<strong>Output:</strong> 13\n<strong>Explanation:</strong> \nThe possible falling paths are:\n[1,5,9], [1,5,7], [1,6,7], [1,6,8],\n[2,4,8], [2,4,9], [2,6,7], [2,6,8],\n[3,4,8], [3,4,9], [3,5,7], [3,5,9]\nThe falling path with the smallest sum is [1,5,7], so the answer is 13.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[7]]\n<strong>Output:</strong> 7\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>1 <= n <= 200</code></li>\n\t<li><code>-99 <= grid[i][j] <= 99</code></li>\n</ul>\n",
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"Use dynamic programming.",
"Let dp[i][j] be the answer for the first i rows such that column j is chosen from row i.",
"Use the concept of cumulative array to optimize the complexity of the solution."
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