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## Monday, September 21, 2015

### LeetCode OJ - Unique Paths

Problem:

Please find the problem here.

Solution:

I have seen this problem so many time, typical dynamic programming solution would say the number of ways to reach a box is the sum of number of ways reaching its neighbor, then we figure this is simply the Pascal triangle, and therefore the solution is the binomial coefficients.

Code:

#include "stdafx.h"

// https://leetcode.com/problems/unique-paths/

#include "LEET_UNIQUE_PATHS.h"
#include <map>
#include <iostream>
#include <sstream>
#include <vector>
#include <string>
#include <algorithm>

using namespace std;

namespace _LEET_UNIQUE_PATHS
{
class Solution
{
public:
int uniquePaths(int m, int n)
{
if (m == 1 || n == 1)
{
return 1;
}
long long result = 1;
m--;
n--;
int u = m + n;
n = min(m, n); // be careful with the loop below - this minimum is required
for (int v = 1; v <= n; v++, u--)
{
result *= u;
result /= v;
}
return (int)result;
}
};
};

using namespace _LEET_UNIQUE_PATHS;

int LEET_UNIQUE_PATHS()
{
Solution s;
cout << s.uniquePaths(2, 100) << endl;
return 0;
}