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.

 

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

int minPathSum(vector<vector<int> > &grid) {
	
	int length = grid[0].size();
	int rows   = grid.size();

	vector<vector<int>>cost(rows,vector<int>(length,0));
	cost[0][0]= grid[0][0];
	for (int i = 1;i!=rows;++i)
		cost[i][0] = cost[i-1][0]+grid[i][0];
	for (int j =1;j!=length;++j)
		cost[0][j] = cost[0][j-1]+grid[0][j];
	for (int i = 1;i!=rows;++i){
		for (int j = 1;j!=length;++j){
			cost[i][j] =  min(cost[i-1][j],cost[i][j-1])+grid[i][j];
		}
	}
	return cost[rows-1][length-1];

}