Carol Broj
Isprobajte na GfG Practice 
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#practiceLinkDiv { display: none !important; } Carolov broj je cijeli broj oblika 4 n - 2 (n+1) - 1. Ekvivalentna formula je (2 n -1) 2 - 2.
Zanimljiva nekretnina:
Za n > 2 binarna reprezentacija n-tog Carolovog broja je n-2 uzastopne jedinice s jednom nulom u sredini i n + 1 uzastopna jedinica. Primjer n = 4 broj pjesme je 223, a binarni broj od 223 je 11011111 ovdje n-2 = 4-2 = 2 uzastopne jedinice na početku, zatim pojedinačna 0 u sredini i zatim n + 1 = 4 + 1 = 5 uzastopnih jedinica nakon toga.
Zadat je broj n zadatak je pronaći n-ti Carolov broj. Prvih nekoliko brojeva pjesama je -1 7 47 223 959... itd.
Primjeri:
Input : n = 2 Output: 7 Input : n = 4 Output: 223Recommended Practice Carol Numbers Probajte! C++
// C++ program to find n'th Carol number #include using namespace std ; // Function to find n'th carol number int carol ( int n ) { int result = pow ( 2 n ) - 1 ; return result * result - 2 ; } // Driver program to ru the case int main () { int n = 4 ; cout < < carol ( n ); return 0 ; }
Python3 # Python program to find n'th Carol number def carol ( n ): # a**b is a ^ b in python result = ( 2 ** n ) - 1 return result * result - 2 # driver program to run the case n = 4 print ( carol ( n ))
Java /* Java program to find n'th Carol number */ class GFG { static int carol ( int n ) { double tmp = Math . pow ( 2 n ) - 1 ; return ( int ) tmp ; } public static void main ( String [] args ) { int n = 4 ; System . out . println ( carol ( n )); } }
C# /* C# program to find n'th Carol number */ using System ; class GFG { static int carol ( int n ) { int result = ( int ) Math . Pow ( 2 n ) - 1 ; return result * result - 2 ; } // Driver code public static void Main () { int n = 4 ; Console . WriteLine ( carol ( n )); } } // This code is contributed by vt_m.
PHP // PHP program to find // n'th Carol number // Function to find // n'th carol number function carol ( $n ) { $result = pow ( 2 $n ) - 1 ; return $result * $result - 2 ; } // Driver Code $n = 4 ; echo carol ( $n ); // This code is contributed by ajit ?>
JavaScript < script > /* Javascript program to find n'th Carol number */ function carol ( n ) { let result = Math . pow ( 2 n ) - 1 ; return result * result - 2 ; } let n = 4 ; document . write ( carol ( n )); < /script>
Izlaz:
223
Vremenski kompleks y: O(log n) za pow funkciju
Pomoćni prostor: O(1)
