# Description

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.

The original problem is here.

The original code is here.

# My Solution

I solve this problem in C++, as below:

``````/*
*Minimum Path Sum
*Author: shuaijiang
*Email: zhaoshuaijiang8@gmail.com
*/
#include<iostream>
#include<vector>
#include[itex]
#include<stdlib.h>
using namespace std;

class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
int rowSize = grid.size();
if(rowSize<=0)
return 0;
vector<int> oneRow = grid[0];
int colSize = oneRow.size();

int **matrix = new int*[rowSize];
for(int i=0;i<rowSize;i++){
matrix[i] = new int[colSize];
for(int j=0;j<colSize;j++)
matrix[i][j] = 0;
}
matrix[0][0] = grid[0][0];
for(int i=1;i<colSize;i++)
matrix[0][i] = matrix[0][i-1] + grid[0][i];
for(int i=1;i<rowSize;i++)
matrix[i][0] = matrix[i-1][0] + grid[i][0];

for(int i=1;i<rowSize;i++){
for(int j=1;j<colSize;j++){
matrix[i][j] = grid[i][j] + min(matrix[i-1][j],matrix[i][j-1]);
}
}
return matrix[rowSize-1][colSize-1];
}
};
``````

# Note

To get the minimum path, I use a matrix to record the sum of every step. For every step, always choose the minimum step(down or right).