Given a integer N, with prime factorisation n1p1 * n2p2 …… The task is to check if the integer N is power-isolated or not.
An integer is said to be power-isolated if n1 * p1 * n2 * p2 ….. = N.
Examples:
Input: N = 12
Output: Power-isolated Integer.
Input: N = 18
Output: Not a power-isolated integer.
Approach: For an integer to be power-isolated the product of its prime factors and their power is equal to integer itself. So, for calculating same you have to find all prime factors of the given integer and their respective powers too. Later, calculate their product and check whether product is equal to the integer or not.
Algorithm:
- Find the prime factor with their factor and store them in key-value pair.
- Later calculate product of all factors and their powers.
- if product is equal to integer, print true else false.
Below is the implementation of the above algorithm:
C++
// C++ program to find whether a number// is power-isolated or not#include <bits/stdc++.h>using namespace std;void checkIfPowerIsolated(int num){ int input = num; int count = 0; int factor[num + 1] = { 0 }; // for 2 as prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // for odd prime factor for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) product = product * factor[i] * i; } // check result for power-isolation if (product == input) cout << "Power-isolated Integer\n"; else cout << "Not a Power-isolated Integer\n";}// Driver codeint main(){ checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35); return 0;}// This code is contributed by mits |
Java
// Java program to find whether a number// is power-isolated or notclass GFG { static void checkIfPowerIsolated(int num) { int input = num; int count = 0; int[] factor = new int[num + 1]; // for 2 as prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // for odd prime factor for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) product = product * factor[i] * i; } // check result for power-isolation if (product == input) System.out.print("Power-isolated Integer\n"); else System.out.print( "Not a Power-isolated Integer\n"); } // Driver code public static void main(String[] args) { checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35); }}// This code is contributed by Code_Mech. |
Python3
# Python3 program to find whether a number# is power-isolated or notdef checkIfPowerIsolated(num): input1 = num count = 0 factor = [0] * (num + 1) # for 2 as prime factor if(num % 2 == 0): while(num % 2 == 0): count += 1 num //= 2 factor[2] = count # for odd prime factor i = 3 while(i * i <= num): count = 0 while(num % i == 0): count += 1 num //= i if(count > 0): factor[i] = count i += 2 if(num > 1): factor[num] = 1 # calculate product of powers and prime factors product = 1 for i in range(0, len(factor)): if(factor[i] > 0): product = product * factor[i] * i # check result for power-isolation if (product == input1): print("Power-isolated Integer") else: print("Not a Power-isolated Integer")# Driver codecheckIfPowerIsolated(12)checkIfPowerIsolated(18)checkIfPowerIsolated(35)# This code is contributed by mits |
C#
// C# program to find whether a number// is power-isolated or notusing System;class GFG { static void checkIfPowerIsolated(int num) { int input = num; int count = 0; int[] factor = new int[num + 1]; // for 2 as prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // for odd prime factor for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) product = product * factor[i] * i; } // check result for power-isolation if (product == input) Console.Write("Power-isolated Integer\n"); else Console.Write("Not a Power-isolated Integer\n"); } // Driver code static void Main() { checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35); }}// This code is contributed by mits |
Javascript
<script>// Javascript program to find whether a number// is power-isolated or notfunction checkIfPowerIsolated(num){ let input = num; let count = 0; let factor = new Array(0); // for 2 as prime factor if(num % 2 == 0) { while(num % 2 == 0) { ++count; num/=2; } factor[2] = count; } // for odd prime factor for (let i = 3; i*i <= num; i += 2) { count = 0; while(num % i == 0) { ++count; num /= i; } if(count > 0) factor[i] = count; } if(num > 1) factor[num] = 1; // calculate product of powers and prime factors let product = 1; for(let i = 0; i < num + 1; i++) { if(factor[i] > 0) product = product * factor[i] * i; } // check result for power-isolation if (product == input) document.write("Power-isolated Integer" + "<br>"); else document.write("Not a Power-isolated Integer" + "<br>");}// Driver code checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35);// This code is contributed by Mayank Tyagi</script> |
PHP
<?php // PHP program to find whether a number// is power-isolated or notfunction checkIfPowerIsolated($num){ $input = $num; $count = 0; $factor= array(); // for 2 as prime factor if($num%2==0) { while($num%2==0) { ++$count; $num/=2; } $factor[2] = $count; } // for odd prime factor for ($i=3; $i*$i <= $num; $i+=2) { $count = 0; while($num%$i==0) { ++$count; $num /= $i; } if($count) $factor[$i] = $count; } if($num>1) $factor[$num] = 1; // calculate product of powers and prime factors $product = 1; foreach ($factor as $primefactor => $power) { $product = $product * $primefactor * $power; } // check result for power-isolation if ($product == $input) print_r("Power-isolated Integer\n"); else print_r("Not a Power-isolated Integer\n");}// driver code checkIfPowerIsolated(12);checkIfPowerIsolated(18);checkIfPowerIsolated(35);?> |
Output
Power-isolated Integer Not a Power-isolated Integer Power-isolated Integer
Time Complexity: O(num)
Auxiliary Space: O(num)
Approach 2 :
- Define a function named checkIfPowerIsolated that takes an integer num as input.
- Create a variable named input and assign the value of num to it.
- Create a variable named count and assign it a value of 0.
- Create an integer array named factor of size num + 1 and initialize all its elements to 0. This array will store the prime factors and their powers.
- Check if num is divisible by 2. If so, do the following:
a. Create a while loop that runs while num is even.
b. Divide num by 2 and increment the count variable by 1.
c. Store the value of count in the factor array at index 2. - Check for odd prime factors by creating a for loop that runs from 3 to the square root of num, incrementing by 2 each time. Do the following within this loop:
a. Reset the count variable to 0.
b. Create a while loop that runs while num is divisible by the current value of i.
c. Divide num by i and increment the count variable by 1.
d. Store the value of count in the factor array at index i.
e. If the count value is greater than 0, repeat steps b to d. - If num is greater than 1, store the value 1 in the factor array at index num.
- Create a variable named product and assign it a value of 1. This variable will store the product of the prime factors and their powers.
- Create a for loop that runs from 0 to num + 1. Do the following within this loop:
a. Check if the value at the current index of the factor array is greater than 0.
b. If so, multiply product by the value of i raised to the power of the value at the current index of the factor array. - Check if product is equal to input. If so, print “Power-isolated Integer”. If not, print “Not a Power-isolated Integer”.
C++
#include <bits/stdc++.h>using namespace std;void checkIfPowerIsolated(int num){ int input = num; int count = 0; int factor[num + 1] = { 0 }; // for 2 as prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // for odd prime factor for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) product = product * pow(i, factor[i]); } // check result for power-isolation if (product == input) cout << "Power-isolated Integer\n"; else cout << "Not a Power-isolated Integer\n";}// Driver codeint main(){ checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35); return 0;} |
Java
import java.util.Arrays;public class GFG { // Function to check if an integer is power-isolated public static void checkIfPowerIsolated(int num) { int input = num; int count = 0; int[] factor = new int[num + 1]; // Check for 2 as a prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // Check for odd prime factors for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) { factor[i] = count; } } if (num > 1) { factor[num] = 1; } // Calculate the product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) { product *= Math.pow(i, factor[i]); } } // Check if the result is a power-isolated integer if (product == input) { System.out.println("Power-isolated Integer"); } else { System.out.println("Not a Power-isolated Integer"); } } // Driver code public static void main(String[] args) { checkIfPowerIsolated(12); checkIfPowerIsolated(18); checkIfPowerIsolated(35); }} |
Python3
def checkIfPowerIsolated(num): input_num = num count = 0 factor = [0] * (num + 1) # for 2 as prime factor if num % 2 == 0: while num % 2 == 0: count += 1 num //= 2 factor[2] = count # for odd prime factor for i in range(3, int(num ** 0.5) + 1, 2): count = 0 while num % i == 0: count += 1 num //= i if count > 0: factor[i] = count if num > 1: factor[num] = 1 # calculate product of powers and prime factors product = 1 for i in range(num + 1): if factor[i] > 0: product *= i ** factor[i] # check result for power-isolation if product == input_num: print("Power-isolated Integer") else: print("Not a Power-isolated Integer")# Driver codecheckIfPowerIsolated(12)checkIfPowerIsolated(18)checkIfPowerIsolated(35) |
C#
using System;class GFG{ static void CheckIfPowerIsolated(int num) { int input = num; int count = 0; int[] factor = new int[num + 1]; // for 2 as a prime factor if (num % 2 == 0) { while (num % 2 == 0) { count++; num /= 2; } factor[2] = count; } // for odd prime factors for (int i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { count++; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors int product = 1; for (int i = 0; i < num + 1; i++) { if (factor[i] > 0) product *= (int)Math.Pow(i, factor[i]); } // check result for power-isolation if (product == input) Console.WriteLine("Power-isolated Integer"); else Console.WriteLine("Not a Power-isolated Integer"); } // Driver code static void Main() { CheckIfPowerIsolated(12); CheckIfPowerIsolated(18); CheckIfPowerIsolated(35); }} |
Javascript
function checkIfPowerIsolated(num){ let input = num; let count = 0; let factor = new Array(num + 1).fill(0); // for 2 as prime factor if (num % 2 == 0) { while (num % 2 == 0) { ++count; num /= 2; } factor[2] = count; } // for odd prime factor for (let i = 3; i * i <= num; i += 2) { count = 0; while (num % i == 0) { ++count; num /= i; } if (count > 0) factor[i] = count; } if (num > 1) factor[num] = 1; // calculate product of powers and prime factors let product = 1; for (let i = 0; i < num + 1; i++) { if (factor[i] > 0) product = product * Math.pow(i, factor[i]); } // check result for power-isolation if (product == input) console.log("Power-isolated Integer"); else console.log("Not a Power-isolated Integer");}// Driver codecheckIfPowerIsolated(12);checkIfPowerIsolated(18);checkIfPowerIsolated(35); |
Output
Power-isolated Integer Not a Power-isolated Integer Power-isolated Integer
Time Complexity: O(sqrt(n))
Auxiliary Space: O(n)
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