64. Minimum Path Sum

一个m*n矩阵,里面数字皆为非负整数,从左上到右下,问路径所经过的数的值之和的最小值

"""
64. Minimum Path Sum
Medium

996

25

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Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example:

Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
"""

到点(i,j)的值等于到(i,j-1),到(i-1,j)两个数的较小值加上该点的值

class Solution:
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m, n = len(grid), len(grid[0])
        mat = [[0 for i in range(n)]for j in range(m)]
        mat[0][0] = grid[0][0]
        for j in range(1, n):
            mat[0][j] = mat[0][j-1] + grid[0][j]
        for i in range(1, m):
            mat[i][0] = mat[i-1][0] + grid[i][0]
        for i in range(1, m):
            for j in range(1, n):
                mat[i][j] = min(mat[i-1][j], mat[i][j-1]) + grid[i][j]
        return mat[m-1][n-1]