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];}