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# Length of longest Powerful number subsequence in an Array

• Last Updated : 16 Apr, 2021

Given an array arr[] containing non-negative integers of length N, the task is to print the length of the longest subsequence of Powerful numbers in the array.

A number n is said to be Powerful Number if, for every prime factor p of it, p2 also divides it.

Examples:

Input: arr[] = { 3, 4, 11, 2, 9, 21 }
Output:
Explanation:
Longest Powerful number Subsequence is {4, 9} and hence the answer is 2.
Input: arr[] = { 6, 4, 10, 13, 9, 25 }
Output:
Explanation:
Longest Powerful number Subsequence is {4, 9, 25} and hence the answer is 3.

Approach: To solve the problem mentioned above, we have to follow the steps given below:

• Traverse the given array and for each element in the array, check if it is Powerful number or not.
• If the element is a Powerful number, it will be in Longest Powerful number Subsequence.
• Hence increment the required length of Longest Powerful number Subsequence by 1
• Return the final length after reaching the size of the array.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the length of``// Longest Powerful Subsequence in an Array` `#include ``using` `namespace` `std;` `// Function to check if the number is powerful``bool` `isPowerful(``int` `n)``{``    ``// First divide the number repeatedly by 2``    ``while` `(n % 2 == 0) {``        ``int` `power = 0;``        ``while` `(n % 2 == 0) {``            ``n /= 2;``            ``power++;``        ``}` `        ``// Check if only 2^1 divides n,``        ``// then return false``        ``if` `(power == 1)``            ``return` `false``;``    ``}` `    ``// Check if n is not a power of 2``    ``// then this loop will execute``    ``// repeat above process``    ``for` `(``int` `factor = 3;``         ``factor <= ``sqrt``(n);``         ``factor += 2) {` `        ``// Find highest power of "factor"``        ``// that divides n``        ``int` `power = 0;``        ``while` `(n % factor == 0) {``            ``n = n / factor;``            ``power++;``        ``}` `        ``// If only factor^1 divides n,``        ``// then return false``        ``if` `(power == 1)``            ``return` `false``;``    ``}` `    ``// n must be 1 now``    ``// if it is not a prime number.``    ``// Since prime numbers``    ``// are not powerful, we return``    ``// false if n is not 1.``    ``return` `(n == 1);``}` `// Function to find the longest subsequence``// which contain all powerful numbers``int` `longestPowerfulSubsequence(``    ``int` `arr[], ``int` `n)``{``    ``int` `answer = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(isPowerful(arr[i]))``            ``answer++;``    ``}` `    ``return` `answer;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 6, 4, 10, 13, 9, 25 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << longestPowerfulSubsequence(arr, n)``         ``<< endl;` `    ``return` `0;``}`

## Java

 `// Java program to find the length of``// Longest Powerful Subsequence in an Array``class` `GFG{` `// Function to check if the number is powerful``static` `boolean` `isPowerful(``int` `n)``{` `    ``// First divide the number repeatedly by 2``    ``while` `(n % ``2` `== ``0``)``    ``{``        ``int` `power = ``0``;``        ``while` `(n % ``2` `== ``0``)``        ``{``            ``n /= ``2``;``            ``power++;``        ``}` `        ``// Check if only 2^1 divides n,``        ``// then return false``        ``if` `(power == ``1``)``            ``return` `false``;``    ``}` `    ``// Check if n is not a power of 2``    ``// then this loop will execute``    ``// repeat above process``    ``for``(``int` `factor = ``3``;``            ``factor <= Math.sqrt(n);``            ``factor += ``2``)``    ``{` `       ``// Find highest power of "factor"``       ``// that divides n``       ``int` `power = ``0``;``       ``while` `(n % factor == ``0``)``       ``{``           ``n = n / factor;``           ``power++;``       ``}``       ` `       ``// If only factor^1 divides n,``       ``// then return false``       ``if` `(power == ``1``)``       ``return` `false``;``        ` `    ``}` `    ``// n must be 1 now``    ``// if it is not a prime number.``    ``// Since prime numbers``    ``// are not powerful, we return``    ``// false if n is not 1.``    ``return` `(n == ``1``);``}` `// Function to find the longest subsequence``// which contain all powerful numbers``static` `int` `longestPowerfulSubsequence(``int` `arr[],``                                      ``int` `n)``{``    ``int` `answer = ``0``;` `    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``       ``if` `(isPowerful(arr[i]))``       ``answer++;``    ``}``    ` `    ``return` `answer;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``6``, ``4``, ``10``, ``13``, ``9``, ``25` `};``    ``int` `n = arr.length;` `    ``System.out.print(longestPowerfulSubsequence(arr,``                                                ``n) + ``"\n"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to find the length of``# Longest Powerful Subsequence in an Array``import` `math` `# Function to check if the number is powerful``def` `isPowerful(n):` `    ``# First divide the number repeatedly by 2``    ``while` `(n ``%` `2` `=``=` `0``):``        ``power ``=` `0``        ` `        ``while` `(n ``%` `2` `=``=` `0``):``            ``n ``/``/``=` `2``            ``power ``+``=` `1``        ` `        ``# Check if only 2^1 divides n,``        ``# then return false``        ``if` `(power ``=``=` `1``):``            ``return` `False``    ` `    ``# Check if n is not a power of 2``    ``# then this loop will execute``    ``# repeat above process``    ``for` `factor ``in` `range``(``3``, ``int``(math.sqrt(n)) ``+` `1``, ``2``):` `        ``# Find highest power of "factor"``        ``# that divides n``        ``power ``=` `0``        ``while` `(n ``%` `factor ``=``=` `0``):``            ``n ``=` `n ``/``/` `factor``            ``power ``+``=` `1``        ` `        ``# If only factor^1 divides n,``        ``# then return false``        ``if` `(power ``=``=` `1``):``            ``return` `False``    ` `    ``# n must be 1 now``    ``# if it is not a prime number.``    ``# Since prime numbers``    ``# are not powerful, we return``    ``# false if n is not 1.``    ``return` `(n ``=``=` `1``)` `# Function to find the longest subsequence``# which contain all powerful numbers``def` `longestPowerfulSubsequence(arr, n):``    ` `    ``answer ``=` `0` `    ``for` `i ``in` `range``(n):``        ``if` `(isPowerful(arr[i])):``            ``answer ``+``=` `1``    ` `    ``return` `answer` `# Driver code``arr ``=` `[ ``6``, ``4``, ``10``, ``13``, ``9``, ``25` `]` `n ``=` `len``(arr)` `print``(longestPowerfulSubsequence(arr, n))` `# This code is contributed by sanjoy_62`

## C#

 `// C# program to find the length of``// longest Powerful Subsequence in``// an array``using` `System;``class` `GFG{` `// Function to check if the``// number is powerful``static` `bool` `isPowerful(``int` `n)``{` `    ``// First divide the number``    ``// repeatedly by 2``    ``while` `(n % 2 == 0)``    ``{``        ``int` `power = 0;``        ``while` `(n % 2 == 0)``        ``{``            ``n /= 2;``            ``power++;``        ``}` `        ``// Check if only 2^1 divides``        ``// n, then return false``        ``if` `(power == 1)``            ``return` `false``;``    ``}` `    ``// Check if n is not a power of 2``    ``// then this loop will execute``    ``// repeat above process``    ``for``(``int` `factor = 3;``            ``factor <= Math.Sqrt(n);``            ``factor += 2)``    ``{``       ` `       ``// Find highest power of "factor"``       ``// that divides n``       ``int` `power = 0;``       ``while` `(n % factor == 0)``       ``{``           ``n = n / factor;``           ``power++;``       ``}``       ` `       ``// If only factor^1 divides n,``       ``// then return false``       ``if` `(power == 1)``           ``return` `false``;``    ``}``    ` `    ``// n must be 1 now``    ``// if it is not a prime number.``    ``// Since prime numbers``    ``// are not powerful, we return``    ``// false if n is not 1.``    ``return` `(n == 1);``}` `// Function to find the longest subsequence``// which contain all powerful numbers``static` `int` `longestPowerfulSubsequence(``int` `[]arr,``                                      ``int` `n)``{``    ``int` `answer = 0;` `    ``for``(``int` `i = 0; i < n; i++)``    ``{``       ``if` `(isPowerful(arr[i]))``           ``answer++;``    ``}``    ``return` `answer;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 6, 4, 10, 13, 9, 25 };``    ``int` `n = arr.Length;` `    ``Console.Write(longestPowerfulSubsequence(arr,``                                             ``n) + ``"\n"``);``}``}` `// This code is contributed by gauravrajput1`

## Javascript

 ``
Output:
`3`

Time Complexity: O(N*√N)
Auxiliary Space Complexity: O(1)

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