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:

[[1,3,1],
 [1,5,1],
 [4,2,1]]

Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.

題意：找到數(shù)組中的最短路徑

思路：動態(tài)規(guī)劃

java代碼：

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