[LeetCode ] Minimum Path Sum

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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:

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

dp入门题，dp[i][j] = a[i][j] + min(dp[i+1][j],dp[i][j+1])，注意边界处理。

class Solution {
    public int minPathSum(int[][] grid) {
        int n,m;
        n = grid.length;
        m = grid[0].length;
        int dp[][] = new int[n][m];
        for(int i = n - 1; i >= 0; i--) {
            for(int j = m - 1; j >= 0; j--) {
                if(i == n - 1 && j == m - 1) dp[i][j] = grid[i][j];
                else if(i == n - 1) dp[i][j] = grid[i][j] + dp[i][j + 1];
                else if(j == m - 1) dp[i][j] = grid[i][j] + dp[i + 1][j];
                else dp[i][j] = grid[i][j] + Math.min(dp[i + 1][j],dp[i][j + 1]);
            }
        }
        return dp[0][0];
    } 
}