Count of binary strings of length N having equal count of 0 ' s ▁ and ▁ 1' s and count of 1 ' s ▁ â ‰ ¥ ▁ count ▁ of ▁ 0' s in each prefix substring | C ++ Program to implement the above approach ; Function to calculate and returns the value of Binomial Coefficient C ( n , k ) ; Since C ( n , k ) = C ( n , n - k ) ; Calculate the value of [ n * ( n - 1 ) * -- - * ( n - k + 1 ) ] / [ k * ( k - 1 ) * -- - * 1 ] ; Function to return the count of all binary strings having equal count of 0 ' s ▁ and ▁ 1' s and each prefix substring having frequency of 1 ' s ▁ > = ▁ frequencies ▁ of ▁ 0' s ; If N is odd ; No such strings possible ; Otherwise ; Calculate value of 2 nCn ; Return 2 nCn / ( n + 1 ) ; Driver Code
#include <bits/stdc++.h> NEW_LINE using namespace std ; unsigned long int binomialCoeff ( unsigned int n , unsigned int k ) { unsigned long int res = 1 ; if ( k > n - k ) k = n - k ; for ( int i = 0 ; i < k ; ++ i ) { res *= ( n - i ) ; res /= ( i + 1 ) ; } return res ; } unsigned long int countStrings ( unsigned int N ) { if ( N % 2 == 1 ) return 0 ; else { N /= 2 ; unsigned long int c = binomialCoeff ( 2 * N , N ) ; return c / ( N + 1 ) ; } } int main ( ) { int N = 6 ; cout << countStrings ( N ) << " ▁ " ; return 0 ; }