[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.

 

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 Array Dynamic Programming

 

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     找矩阵左上到右下的最短路径，标准的动态规划。

1. 初始化统计矩阵的最上行，最右列。
2. 从上往下，从左到右填写每格。
3. 输出结果

#include <iostream>
#include <vector>
using namespace std;


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

int main()
{
    vector<vector<int> > grid({{1,2,3},{4,5,6},{7,8,9}});
    Solution sol;
    cout<<sol.minPathSum(grid)<<endl;
    for(int i=0;i<grid.size();i++){
        for(int j=0;j<grid[i].size();j++)
            cout<<grid[i][j]<<" ";
        cout<<endl;
    }
    return 0;
}