Find the GCD of all the non-prime numbers of given Array
Last Updated :
10 May, 2022
Given an array arr[] having N integers, the task is to find the GCD of all the numbers in the array which are not prime. If all the numbers are prime return -1.
Examples:
Input: N = 3, arr[ ] = {2, 3, 5}
Output: -1
Explanation: All the numbers are prime.
Hence answer will be -1.
Input: N = 6, arr[ ] = { 2, 4, 6, 12, 3, 5 }
Output: 2
Explanation: Non-prime numbers present in the array are 4, 6, and 12.
Their GCD is 2.
Approach: This problem can be solved by finding the prime numbers in the array using the Sieve of Eratosthenes.
Follow the below steps to solve the problem:
- Find all the prime numbers in the range of minimum of the array and maximum of the array using the sieve Of Eratosthenes.
- Now iterate through the given array and find the non-prime numbers.
- Take GCD of all the non-prime numbers.
Below is the implementation of the above approach:
C++
// C++ code to implement the approach
#include <bits/stdc++.h>
using namespace std;
vector<int> isPrime(100001, 1);
// Function to find the prime numbers
void sieve(int n)
{
// Mark 0 and 1 as non-prime
isPrime[0] = 0;
isPrime[1] = 0;
// Mark all multiples of 2 as
// non-prime
for (int i = 4; i <= n; i += 2)
isPrime[i] = 0;
// Mark all non-prime numbers
for (int i = 3; i * i <= n; i++) {
if (isPrime[i]) {
for (int j = i * i; j <= n;
j += i)
isPrime[j] = 0;
}
}
}
// Find the GCD of the non-prime numbers
int nonPrimeGCD(vector<int>& arr, int n)
{
int i = 0;
// Find all non-prime numbers till n
// using sieve of Eratosthenes
sieve(n);
// Find first non - prime number
// in the array
while (isPrime[arr[i]] and i < n)
i++;
// If not found return -1
if (i == n)
return -1;
// Initialize GCD as the first
// non prime number
int gcd = arr[i];
// Take gcd of all non-prime numbers
for (int j = i + 1; j < n; j++) {
if (!isPrime[arr[j]])
gcd = __gcd(gcd, arr[j]);
}
return gcd;
}
// Driver code
int main()
{
int N = 6;
vector<int> arr = { 2, 4, 6, 12, 3, 5 };
// Find non Prime GCD
cout << nonPrimeGCD(arr, N);
return 0;
}
// Java code to implement the approach
import java.io.*;
class GFG {
static int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
static int[] isPrime = new int[100001];
// Function to find the prime numbers
public static void sieve(int n)
{
for (int i = 0; i <= n; i++) {
isPrime[i] = 1;
}
// Mark 0 and 1 as non-prime
isPrime[0] = 0;
isPrime[1] = 0;
// Mark all multiples of 2 as
// non-prime
for (int i = 4; i <= n; i += 2)
isPrime[i] = 0;
// Mark all non-prime numbers
for (int i = 3; i * i <= n; i++) {
if (isPrime[i] != 0) {
for (int j = i * i; j <= n; j += i)
isPrime[j] = 0;
}
}
}
// Find the GCD of the non-prime numbers
public static int nonPrimeGCD(int arr[], int n)
{
int i = 0;
// Find all non-prime numbers till n
// using sieve of Eratosthenes
sieve(n);
// Find first non - prime number
// in the array
while (isPrime[arr[i]] != 0 && i < n)
i++;
// If not found return -1
if (i == n)
return -1;
// Initialize GCD as the first
// non prime number
int gg = arr[i];
// Take gcd of all non-prime numbers
for (int j = i + 1; j < n; j++) {
if (isPrime[arr[j]] == 0)
gg = gcd(gg, arr[j]);
}
return gg;
}
// Driver Code
public static void main(String[] args)
{
int N = 6;
int arr[] = { 2, 4, 6, 12, 3, 5 };
// Find non Prime GCD
System.out.print(nonPrimeGCD(arr, N));
}
}
// This code is contributed by Rohit Pradhan
# python3 code to implement the approach
import math
isPrime = [1 for _ in range(1000011)]
# Function for __gcd
def __gcd(a, b):
if b == 0:
return a
return __gcd(b, a % b)
# Function to find the prime numbers
def sieve(n):
global isPrime
# Mark 0 and 1 as non-prime
isPrime[0] = 0
isPrime[1] = 0
# Mark all multiples of 2 as
# non-prime
for i in range(4, n+1, 2):
isPrime[i] = 0
# Mark all non-prime numbers
for i in range(3, int(math.sqrt(n)) + 1):
if (isPrime[i]):
for j in range(i*i, n+1, i):
isPrime[j] = 0
# Find the GCD of the non-prime numbers
def nonPrimeGCD(arr, n):
i = 0
# Find all non-prime numbers till n
# using sieve of Eratosthenes
sieve(n)
# Find first non - prime number
# in the array
while (isPrime[arr[i]] and i < n):
i += 1
# If not found return -1
if (i == n):
return -1
# Initialize GCD as the first
# non prime number
gcd = arr[i]
# Take gcd of all non-prime numbers
for j in range(i+1, n):
if (not isPrime[arr[j]]):
gcd = __gcd(gcd, arr[j])
return gcd
# Driver code
if __name__ == "__main__":
N = 6
arr = [2, 4, 6, 12, 3, 5]
# Find non Prime GCD
print(nonPrimeGCD(arr, N))
# This code is contributed by rakeshsahni
// C# program for above approach
using System;
class GFG
{
static int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
static int[] isPrime = new int[100001];
// Function to find the prime numbers
public static void sieve(int n)
{
for (int i = 0; i <= n; i++) {
isPrime[i] = 1;
}
// Mark 0 and 1 as non-prime
isPrime[0] = 0;
isPrime[1] = 0;
// Mark all multiples of 2 as
// non-prime
for (int i = 4; i <= n; i += 2)
isPrime[i] = 0;
// Mark all non-prime numbers
for (int i = 3; i * i <= n; i++) {
if (isPrime[i] != 0) {
for (int j = i * i; j <= n; j += i)
isPrime[j] = 0;
}
}
}
// Find the GCD of the non-prime numbers
public static int nonPrimeGCD(int[] arr, int n)
{
int i = 0;
// Find all non-prime numbers till n
// using sieve of Eratosthenes
sieve(n);
// Find first non - prime number
// in the array
while (isPrime[arr[i]] != 0 && i < n)
i++;
// If not found return -1
if (i == n)
return -1;
// Initialize GCD as the first
// non prime number
int gg = arr[i];
// Take gcd of all non-prime numbers
for (int j = i + 1; j < n; j++) {
if (isPrime[arr[j]] == 0)
gg = gcd(gg, arr[j]);
}
return gg;
}
// Driver Code
public static void Main()
{
int N = 6;
int[] arr = { 2, 4, 6, 12, 3, 5 };
// Find non Prime GCD
Console.Write(nonPrimeGCD(arr, N));
}
}
// This code is contributed by code_hunt.
<script>
// JavaScript code to implement the approach
let isPrime = new Array(100001).fill(1)
// Function to find the prime numbers
function sieve(n)
{
// Mark 0 and 1 as non-prime
isPrime[0] = 0;
isPrime[1] = 0;
// Mark all multiples of 2 as
// non-prime
for (let i = 4; i <= n; i += 2)
isPrime[i] = 0;
// Mark all non-prime numbers
for (let i = 3; i * i <= n; i++) {
if (isPrime[i]) {
for (let j = i * i; j <= n;
j += i)
isPrime[j] = 0;
}
}
}
function GCD(x,y){
if (!y) {
return x;
}
return GCD(y, x % y);
}
// Find the GCD of the non-prime numbers
function nonPrimeGCD(arr,n)
{
let i = 0;
// Find all non-prime numbers till n
// using sieve of Eratosthenes
sieve(n);
// Find first non - prime number
// in the array
while (isPrime[arr[i]] && i < n)
i++;
// If not found return -1
if (i == n)
return -1;
// Initialize GCD as the first
// non prime number
let gcd = arr[i];
// Take gcd of all non-prime numbers
for (let j = i + 1; j < n; j++) {
if (!isPrime[arr[j]])
gcd = GCD(gcd, arr[j]);
}
return gcd;
}
// Driver code
let N = 6
let arr = [ 2, 4, 6, 12, 3, 5 ]
// Find non Prime GCD
document.write(nonPrimeGCD(arr, N))
// This code is contributed by shinjanpatra
</script>
Time Complexity: O(N * log(log( N )))
Auxiliary Space: O(N)
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