1. Description

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.

2. Example

[[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.

3. Explanation

4.Code

public class LeetCode0064 {
    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[][] 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 j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        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) {
        LeetCode0064 leetcode = new LeetCode0064();
        int[][] grid = new int[][] { { 1, 3, 1 }, { 1, 5, 1 }, { 4, 2, 1 } };
        System.out.println(leetcode.minPathSum(grid));
    }
}