Coding/UniquePaths.java at master · anshulsaxena-93/Coding · GitHub

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/*
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?

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

Constraints:

1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.
*/

class Solution {
    public int uniquePaths(int m, int n) {
        return count(m,n);
    }

    private int count(int m,int n){

        int dp[][] = new int[m+1][n+1];

        for(int i=0; i<=m; i++){
            dp[i][0] = 0;
            dp[i][1] = 1;
        }

        for(int j=0; j<=n; j++){
            dp[0][j] = 0;
            dp[1][j] = 1;
        }

        for(int i=2; i<=m; i++){
            for(int j=2; j<=n; j++){
                dp[i][j] = dp[i-1][j] + dp[i][j-1];
            }
        }

        return dp[m][n];
    }
}