What is the superpower of a number?

The Superpower is the highest power among the power of primes in the factorisation of a number n.

geeksforgeeks.org - Find the super power of a given Number - GeeksforGeeks

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Given an integer . The task is to find the superpower from the factorization of . The Superpower is the highest power among the power of primes in the factorisation of a number n.

Examples:

Input : n = 32 Output : 5 Input : n = 240 Output : 4 For finding the superpower of any given number , we have to complete the factorisation of n, and find out highest power among all of the prime factors. Note: Using Sieve for the purpose of storing list of primes is useful in terms of optimization.

Algorithm :

Iterate over primes and calculate the factorization of n.

For each prime among the stored list of primes and which is also a factor of n,

find its power and check it for super power.

Below is the implementation of the above approach:

C++

#include #define MAX 100000 using namespace std; bool prime[100002]; void SieveOfEratosthenes() { memset (prime, true , sizeof (prime)); for ( int p = 2; p * p <= MAX; p++) if (prime[p] == true ) for ( int i = p * 2; i <= MAX; i += p) prime[i] = false ; } int superpower( int n) { SieveOfEratosthenes(); int superPower = 0, factor = 0; int i = 2; while (n > 1 && i <= MAX) { if (prime[i]) { factor = 0; while (n % i == 0 && n > 1) { factor++; n = n / i; } if (superPower < factor) superPower = factor; } i++; } return superPower; } int main() { int n = 256; cout << superpower(n); return 0; } Java class GFG{ static int MAX= 100000 ; static boolean [] prime= new boolean [ 100002 ]; static void SieveOfEratosthenes() { for ( int p = 2 ; p * p <= MAX; p++) if (prime[p] == false ) for ( int i = p * 2 ; i <= MAX; i += p) prime[i] = true ; } static int superpower( int n) { SieveOfEratosthenes(); int superPower = 0 , factor = 0 ; int i = 2 ; while (n > 1 && i <= MAX) { if (!prime[i]) { factor = 0 ; while (n % i == 0 && n > 1 ) { factor++; n = n / i; } if (superPower < factor) superPower = factor; } i++; } return superPower; } public static void main(String[] args) { int n = 256 ; System.out.println(superpower(n)); } } Python3 MAX = 100000 ; prime = [ True ] * 100002 ; def SieveOfEratosthenes(): p = 2 ; while (p * p < = MAX ): if (prime[p] = = True ): i = p * 2 ; while (i < = MAX ): prime[i] = False ; i + = p; p + = 1 ; def superpower(n): SieveOfEratosthenes(); superPower = 0 ; factor = 0 ; i = 2 ; while (n > 1 and i < = MAX ): if (prime[i]): factor = 0 ; while (n % i = = 0 and n > 1 ): factor + = 1 ; n = int (n / i); if (superPower < factor): superPower = factor; i + = 1 ; return superPower; n = 256 ; print (superpower(n)); C#

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class GFG { static int MAX = 100000; static bool [] prime = new bool [100002]; static void SieveOfEratosthenes() { for ( int p = 2; p * p <= MAX; p++) if (prime[p] == false ) for ( int i = p * 2; i <= MAX; i += p) prime[i] = true ; } static int superpower( int n) { SieveOfEratosthenes(); int superPower = 0, factor = 0; int i = 2; while (n > 1 && i <= MAX) { if (!prime[i]) { factor = 0; while (n % i == 0 && n > 1) { factor++; n = n / i; } if (superPower < factor) superPower = factor; } i++; } return superPower; } static void Main() { int n = 256; System.Console.WriteLine(superpower(n)); } } PHP 1 && $i <= $MAX ) { if ( $prime [ $i ]) { $factor = 0; while ( $n % $i == 0 && $n > 1) { $factor ++; $n = $n / $i ; } if ( $superPower < $factor ) $superPower = $factor ; } $i ++; } return $superPower ; } $n = 256; echo superpower( $n ); ?> Javascript

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Output: 8

geeksforgeeks.org - Find the super power of a given Number - GeeksforGeeks

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