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// Source : https://oj.leetcode.com/problems/minimum-path-sum/
// Author : Hao Chen
// Date : 2014-06-21
/*****************************************************************************************************
*
* 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.
*
* Example:
*
* Input:
* [
* [1,3,1],
* [1,5,1],
* [4,2,1]
* ]
* Output: 7
* Explanation: Because the path 1→3→1→1→1 minimizes the sum.
*
******************************************************************************************************/
#include <limits.h>
#include <iostream>
#include <vector>
using namespace std;
int minPathSum(vector<vector<int>>& grid) {
for (int i=0; i<grid.size(); i++) {
for (int j=0; j<grid[0].size(); j++) {
if (i==0 && j==0) continue;
else if (i==0) grid[0][j] += grid[0][j-1];
else if (j==0) grid[i][0] += grid[i-1][j];
else grid[i][j] += min( grid[i-1][j], grid[i][j-1]);
}
}
return grid[grid.size()-1][grid[0].size()-1];
}
int main()
{
int a[6][2]={{7,2},{6,6},{8,6},{8,7},{5,0},{6,0}};
vector< vector<int> > grid;
for(int i=0; i<6; i++){
vector<int> v;
for(int j=0; j<2; j++){
v.push_back(a[i][j]);
}
grid.push_back(v);
}
cout << "minPathSum=" << minPathSum(grid) << endl;
return 0;
}
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