Leetcode 64. Minimum Path Sum

64. Minimum Path Sum

• Total Accepted: 76284
• Total Submissions:214404
• Difficulty: Medium

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：优化的部分可以参考Leetcode 62. Unique Paths

代码：
方法一：未优化。

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m=grid.size();
        int n=grid[0].size();
        int i,j;
        for(i=1;i<m;i++){
            grid[i][0]+=grid[i-1][0];
        }
        for(j=1;j<n;j++){
            grid[0][j]+=grid[0][j-1];
        }
        for(i=1;i<m;i++){
            for(j=1;j<n;j++){
                grid[i][j]+=grid[i-1][j]<grid[i][j-1]?grid[i-1][j]:grid[i][j-1];
            }
        }
        return grid[m-1][n-1];
    }
};

方法二：已优化。

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m=grid.size();
        int n=grid[0].size();
        int i,j;
        vector<int> cur(n,0);
        cur[0]=grid[0][0];
        for(j=1;j<n;j++){
            cur[j]=grid[0][j]+cur[j-1];
        }
        for(i=1;i<m;i++){
            cur[0]+=grid[i][0];
            for(j=1;j<n;j++){
                cur[j]=grid[i][j]+(cur[j-1]>cur[j]?cur[j]:cur[j-1]);
            }
        }
        return cur[n-1];
    }
};