[LeetCode]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.

解答：本题采用动态规划的方法，逐列扫描直至目标点



先计算第一行的路径权值f(0),f(1),f(2)，接着进行换行，再逐列比较选择路径，依次类推，最终到达目标点。

代码如下：

class Solution {
public:
int minPathSum(vector<vector<int> > &grid) {
int m = grid.size();
int n = grid[0].size();
if(m==1&&n==1)
return grid[0][0];
int minsum=grid[0][0];
vector<int> f;
f.resize(n);
f[0]=grid[0][0];
//设置一个迭代结构
for(int i=1;i<n;i++){
f[i]=grid[0][i]+f[i-1];
}
for(int i=1;i<m;i++){
f[0]+=grid[i][0];
for(int j=1;j<n;j++){
f[j]=min(f[j-1],f[j])+grid[i][j];
}
}

return f[n-1];
}
};