62 - Unique Paths

#medium

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 109.

Example 1:

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

Example 2:
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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

class Solution {
public:
    int uniquePaths(int m, int n) {
        if ( m == 1 && n == 1 ) return 1;
        vector<vector<int>> dp( m, vector<int>(n, 0));
        dp[0][0] = 0;
        for ( int i = 0; i < m; i++ ) dp[i][0] = 1;
        for ( int j = 0; j < n; j++ ) dp[0][j] = 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];
    }
};