LeetCode

题目：

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.

思路：

动态规划，和unique paths一样

package dp;

public class MinimumPathSum {

    public int minPathSum(int[][] grid) {
        int m;
        int n;
        if (grid == null || (m = grid.length) == 0 || (n = grid[0].length) == 0) return 0;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i = 1; i < m; ++i) dp[i][0] = dp[i - 1][0] + grid[i][0];
        for (int i = 1; i < n; ++i) dp[0][i] = dp[0][i - 1] + grid[0][i];
        for (int i = 1; i < m; ++i) {
            for (int j = 1; j < n; ++j) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        
        return dp[m - 1][n - 1];
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[][] grid = { {4,3,1},
                {2,1,3},
                {8,1,3}
              };
        MinimumPathSum m = new MinimumPathSum();
        System.out.println(m.minPathSum(grid));
    }

}