【leetcode每日刷题】【DP】64. 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.

使用动态规划的方式：

初始化 dp[0][0] = grid[0][0];

状态转移  dp[i][j] = Math.min(dp[i-1][j]+grid[i][j], dp[i][j-1]+grid[i][j]);

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