unique_paths.cpp

/*
    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) {
        int mat[m][n];
        for(int  i = 0; i < m; i++){
            mat[i][0] = 1;
        }
        for(int i = 0; i < n; i++){
            mat[0][i] = 1;
        }
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                mat[i][j] = mat[i - 1][j] + mat[i][j - 1];
            }
        }
        return mat[m-1][n-1];
    }
};