Leetcode 931. Minimum Falling Path Sum

小白菜又菜2024-04-25 22:12

Problem

Given an n x n array of integers matrix, return the minimum sum of any falling path through matrix.

A falling path 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) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1).

Algorithm

Dynamic Programming (DP). Define the state dp $i$ $j$ as the minimum falling path to the point at (i-row, j-column). dp $i$ $j$ = min(dp $i-1$ $j-1$ , dp $i-1$ $j$ , dp $i-1$ $j+1$ ) + matrix $i$ $j$ .

Code

python3 复制代码

class Solution:
    def minFallingPathSum(self, matrix: List[List[int]]) -> int:
        r_size = len(matrix)
        if r_size == 1:
            return min(matrix[0])
        c_size = len(matrix[0])
        
        minSum = [[0] * c_size for r in range(r_size+1)]
        for r in range(1, r_size+1):
            print(r)
            for c in range(c_size):
                minSum[r][c] = minSum[r-1][c] + matrix[r-1][c]
                if c > 0 and minSum[r][c] > minSum[r-1][c-1] + matrix[r-1][c]:
                    minSum[r][c] = minSum[r-1][c-1] + matrix[r-1][c]
                if c < c_size-1 and minSum[r][c] > minSum[r-1][c+1] + matrix[r-1][c]:
                    minSum[r][c] = minSum[r-1][c+1] + matrix[r-1][c]
        
        return min(minSum[r_size])