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

Note: m and n will be at most 100.

 

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