[leetcode] Minimum Path Sum

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.

https://oj.leetcode.com/problems/minimum-path-sum/

思路：二维DP。 len[i][j] = min(len[i-1][j], len[i][j-1]) +grid[i][j];

 

public class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0)
            return 0;
        int m = grid.length;
        int n = grid[0].length;
        int[][] len = new int[m][n];

        int i;
        int sum = 0;
        for (i = 0; i < m; i++) {
            sum += grid[i][0];
            len[i][0] = sum;
        }
        sum = 0;
        for (i = 0; i < n; i++) {
            sum += grid[0][i];
            len[0][i] = sum;
        }
        int j;
        for (i = 1; i < m; i++) {
            for (j = 1; j < n; j++) {
                if (len[i][j] == 0) {
                    len[i][j] = (len[i - 1][j] < len[i][j - 1] ? len[i - 1][j]
                            : len[i][j - 1]) + grid[i][j];
                }

            }

        }

        return len[m - 1][n - 1];
    }

    public static void main(String[] args) {
        int[][] grid = { { 1 } };
        System.out.println(new Solution().minPathSum(grid));
    }
}