64 Minimum Path Sum

Leetcode

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 1:

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

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

走到每个点点最小值为它的值加上上方和左方的最小值，无需关心它具体走那条路。

public int minPathSum(int[][] grid) {
    if(grid==null || grid.length==0 || grid[0].length==0) return 0;
    for(int i=1;i<grid[0].length;++i){
        grid[0][i]+=grid[0][i-1];
    }
    for(int i=1;i<grid.length;++i){
        grid[i][0]+=grid[i-1][0];
    }
    for(int i=1;i<grid.length;++i){
        for(int j=1;j<grid[i].length;++j){
            grid[i][j]+=Math.min(grid[i-1][j],grid[i][j-1]);
        }
    }
    return grid[grid.length-1][grid[0].length-1];
}