[LeetCode] Minimum Path Sum

Minimum Path Sum

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.

解题思路：

这道题找到从左上角到右下角最小路径长度。每个方格有一个值，路径只能往右走或者往下走。

用DP算法。

d[i][j]表示从0,0到i,j的最短路径长度。那么有递推公式：

d[i][j] = grid[i][j]+min(d[i-1][j], d[i][j-1])。

还得注意边界条件。

下面是程序代码：

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