Count all possible paths from top left to bottom right of a Matrix without crossing the diagonal | Java Program to implement the above approach ; Function to calculate Binomial Coefficient C ( n , r ) ; C ( n , r ) = C ( n , n - r ) ; [ n * ( n - 1 ) * -- - * ( n - r + 1 ) ] / [ r * ( r - 1 ) * -- -- * 1 ] ; Function to calculate the total possible paths ; Update n to n - 1 as ( N - 1 ) catalan number is the result ; Stores 2 nCn ; Stores Nth Catalan number ; Stores the required answer ; Driver Code
import java . util . * ; class GFG { static int binCoff ( int n , int r ) { int val = 1 ; int i ; if ( r > ( n - r ) ) { r = ( n - r ) ; } for ( i = 0 ; i < r ; i ++ ) { val *= ( n - i ) ; val /= ( i + 1 ) ; } return val ; } static int findWays ( int n ) { n -- ; int a , b , ans ; a = binCoff ( 2 * n , n ) ; b = a / ( n + 1 ) ; ans = b ; return ans ; } public static void main ( String [ ] args ) { int n = 4 ; System . out . print ( findWays ( n ) ) ; } }