#### Unique Paths

S
```/** Author : Siddhant Swarup Mallick
* Github : https://github.com/siddhant2002
*/

/**
* 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?
*/

/** Program description - To find the number of unique paths possible */

package com.thealgorithms.dynamicprogramming;

import java.util.*;

public class UniquePaths {
public static boolean uniquePaths(int m , int n , int ans) {
int []dp = new int[n];
Arrays.fill(dp,1);
for (int i=1; i<m; i++)
{
for (int j=1; j<n; j++)
{
dp[j] += dp[j-1];

}
}
return dp[n-1]==ans;
}
// The above method runs in O(n) time
public static boolean uniquePaths2(int m , int n , int ans) {
int dp[][] = new int[m][n];
for (int i=0; i<m; i++)
{
dp[i] = 1;
}
for (int j=0; j<n; j++)
{
dp[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]==ans;
}
// The above mthod takes O(m*n) time
}
/**
* OUTPUT :
* Input - m = 3, n = 7
* Output: it returns either true if expected answer matches with the predicted answer else it returns false
* 1st approach Time Complexity : O(n)
* Auxiliary Space Complexity : O(n)
* Input - m = 3, n = 7
* Output: it returns either true if expected answer matches with the predicted answer else it returns false
* 2nd approach Time Complexity : O(m*n)
* Auxiliary Space Complexity : O(m*n)
*/
```  