grid_unique_paths.cpp

/*
A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. 
The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?
Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
*/
class Solution {
public:
    int uniquePaths(int m, int n) {
        int dp[m][n];
        for(int i=0;i<n;i++)
            dp[0][i]=1;
        for(int i=0;i<m;i++)
            dp[i][0]=1;
        for(int i=1;i<m;i++)
        {
            for(int j=1;j<n;j++)
            {
                dp[i][j]=dp[i-1][j]+dp[i][j-1];
            }
        }
        return dp[m-1][n-1];
    }
};