62. Unique Paths

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?

Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

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
Example 2:

Input: m = 7, n = 3
Output: 28

class Solution {
public:
    int uniquePaths(int m, int n) {
      int a[m][n];    
      for(int i=0;i<m;i++)
              a[i][0]=1;
           
         for(int i=0;i<n;i++)
              a[0][i]=1;
           
 
        for(int i=1;i<m;i++)
            for(int j=1;j<n;j++)
                       a[i][j]=a[i][j-1]+a[i-1][j];
        
        return a[m-1][n-1];
        
        
    }
};