Unique Paths

 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.


 


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 solve(int i,int j,int m,int n, int [][] dp)
    {
        if(i==m-1 && j==n-1)
        {
            return 1;
        }

          // Out of bounds
        if (i >= m || j >= n) {
            return 0;
        }
        if(dp[i][j] !=-1)
        {
            return dp[i][j];
        }
        int right=solve(i,j+1,m,n,dp);
        int down=solve(i+1,j,m,n,dp);

        return dp[i][j]=right+down;
       
    }
    public int uniquePaths(int m, int n) {
        int [][] dp= new int[m][n];

          // Initialize all cells to -1 (uncomputed)
        for (int row = 0; row < m; row++) {
            for (int col = 0; col < n; col++) {
                dp[row][col] = -1;
            }
        }
        return solve(0,0,m,n,dp);
    }
}

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