|
| 1 | +""" |
| 2 | +Problem Link: https://leetcode.com/problems/minimum-falling-path-sum/ |
| 3 | + |
| 4 | +Given an n x n array of integers matrix, return the minimum sum of any falling path through matrix. |
| 5 | +A falling path starts at any element in the first row and chooses the element in the next row that |
| 6 | +is either directly below or diagonally left/right. Specifically, the next element from position |
| 7 | +(row, col) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1). |
| 8 | + |
| 9 | +Example 1: |
| 10 | +Input: matrix = [[2,1,3],[6,5,4],[7,8,9]] |
| 11 | +Output: 13 |
| 12 | +Explanation: There are two falling paths with a minimum sum as shown. |
| 13 | + |
| 14 | +Example 2: |
| 15 | +Input: matrix = [[-19,57],[-40,-5]] |
| 16 | +Output: -59 |
| 17 | +Explanation: The falling path with a minimum sum is shown. |
| 18 | + |
| 19 | +Constraints: |
| 20 | +n == matrix.length == matrix[i].length |
| 21 | +1 <= n <= 100 |
| 22 | +-100 <= matrix[i][j] <= 100 |
| 23 | +""" |
| 24 | +class Solution: |
| 25 | + def minFallingPathSum(self, matrix: List[List[int]]) -> int: |
| 26 | + if len(matrix) == 1: |
| 27 | + return min(matrix[0]) |
| 28 | + |
| 29 | + dp = matrix[0].copy() |
| 30 | + min_path = float('inf') |
| 31 | + |
| 32 | + for row in range(1, len(matrix)): |
| 33 | + temp = [] |
| 34 | + for col in range(len(matrix[0])): |
| 35 | + min_val = dp[col] + matrix[row][col] |
| 36 | + if col - 1 >= 0: |
| 37 | + min_val = min(min_val, matrix[row][col] + dp[col-1]) |
| 38 | + if col + 1 < len(matrix[0]): |
| 39 | + min_val = min(min_val, matrix[row][col] + dp[col+1]) |
| 40 | + |
| 41 | + temp.append(min_val) |
| 42 | + |
| 43 | + if row == len(matrix) - 1: |
| 44 | + min_path = min(min_path, temp[col]) |
| 45 | + |
| 46 | + dp = temp |
| 47 | + |
| 48 | + return min_path |
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