Number of Permutations such that no Three Terms forms Increasing Subsequence | Returns value of Binomial Coefficient C ( n , k ) ; Since C ( n , k ) = C ( n , n - k ) ; Calculate value of [ n * ( n - 1 ) * -- - * ( n - k + 1 ) ] [ k * ( k - 1 ) * -- - * 1 ] ; A Binomial coefficient based function to find nth catalan number in O ( n ) time ; Calculate value of 2 nCn ; return 2 nCn / ( n + 1 ) ; Driver code
def binomialCoeff ( n , k ) : NEW_LINE INDENT res = 1 NEW_LINE if k > n - k : NEW_LINE INDENT k = n - k NEW_LINE DEDENT for i in range ( k ) : NEW_LINE INDENT res = res * ( n - i ) NEW_LINE res = res // ( i + 1 ) NEW_LINE DEDENT return res NEW_LINE DEDENT def catalan ( n ) : NEW_LINE INDENT c = binomialCoeff ( 2 * n , n ) NEW_LINE return c // ( n + 1 ) NEW_LINE DEDENT n = 3 NEW_LINE print ( catalan ( n ) ) NEW_LINE