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Check if the given array contains all the divisors of some integer

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  • Last Updated : 30 May, 2022

Given an integer array arr[], the task is to check if that array contains all the divisor of some integer.
Examples: 
 

Input: arr[] = { 2, 3, 1, 6} 
Output: Yes 
The array contains all the divisors of 6
Input: arr[] = { 12, 2, 5, 3, 6, 4, 1} 
Output: No 
 

 

Approach: If the array contains all the divisors of a particular integer say X then the maximum element in the array arr[] is the integer X. Now, find the maximum element of the array arr[] and calculate all of its divisors and store it in a vector b. If array arr[] and vector b are equal then the array contains all the divisors of a particular integer, otherwise no.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function that returns true if arr[]
// contains all the divisors of some integer
bool checkDivisors(int a[], int n)
{
 
    // Maximum element from the array
    int X = *max_element(a, a + n);
 
    // Vector to store divisors
    // of the maximum element i.e. X
    vector<int> b;
 
    // Store all the divisors of X
    for (int i = 1; i * i <= X; i++) {
        if (X % i == 0) {
            b.push_back(i);
            if (X / i != i)
                b.push_back(X / i);
        }
    }
 
    // If the lengths of a[]
    // and b are different
    // return false
    if (b.size() != n)
        return false;
 
    // Sort a[] and b
    sort(a, a + n);
    sort(b.begin(), b.end());
 
    for (int i = 0; i < n; i++) {
 
        // If divisors are not
        // equal return false
        if (b[i] != a[i])
            return false;
    }
 
    return true;
}
 
// Driver code
int main()
{
    int arr[] = { 8, 1, 2, 12, 48,
                  6, 4, 24, 16, 3 };
 
    int N = sizeof(arr) / sizeof(arr[0]);
 
    if (checkDivisors(arr, N))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.*;
 
class GFG
{
 
// returns th maximum element of the array
static int max_element(int a[] )
{
    int m = a[0];
    for(int i = 0; i < a.length; i++)
    m = Math.max(a[i], m);
    return m;
}
 
// Function that returns true if arr[]
// contains all the divisors of some integer
static boolean checkDivisors(int a[], int n)
{
 
    // Maximum element from the array
    int X = max_element(a);
 
    // Vector to store divisors
    // of the maximum element i.e. X
    Vector<Integer> b=new Vector<Integer>();
 
    // Store all the divisors of X
    for (int i = 1; i * i <= X; i++)
    {
        if (X % i == 0)
        {
            b.add(i);
            if (X / i != i)
                b.add(X / i);
        }
    }
 
    // If the lengths of a[]
    // and b are different
    // return false
    if (b.size() != n)
        return false;
 
    // Sort a[] and b
    Arrays.sort(a);
    Collections.sort(b);
 
    for (int i = 0; i < n; i++)
    {
 
        // If divisors are not
        // equal return false
        if (b.get(i) != a[i])
            return false;
    }
 
    return true;
}
 
// Driver code
public static void main(String args[])
{
    int arr[] = { 8, 1, 2, 12, 48,
                6, 4, 24, 16, 3 };
 
    int N = arr.length;
 
    if (checkDivisors(arr, N))
        System.out.println("Yes");
    else
        System.out.println("No");
 
}
}
 
// This code is contributed by Arnab Kundu

Python3




# Python 3 implementation of the approach
from math import sqrt
 
# Function that returns true if arr[]
# contains all the divisors of some integer
def checkDivisors(a,n):
    # Maximum element from the array
    X = max(a)
 
    # Vector to store divisors
    # of the maximum element i.e. X
    b = []
 
    # Store all the divisors of X
    for i in range(1,int(sqrt(X))+1):
        if (X % i == 0):
            b.append(i)
            if (X // i != i):
                b.append(X // i)
 
    # If the lengths of a[]
    # and b are different
    # return false
    if (len(b) != n):
        return False
 
    # Sort a[] and b
    a.sort(reverse = False)
    b.sort(reverse = False)
 
    for i in range(n):
        # If divisors are not
        # equal return false
        if (b[i] != a[i]):
            return False
    return True
 
# Driver code
if __name__ == '__main__':
    arr = [8, 1, 2, 12, 48,6, 4, 24, 16, 3]
 
    N = len(arr)
 
    if (checkDivisors(arr, N)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by
# Surendra_Gangwar

C#




// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG
{
 
// returns th maximum element of the array
static int max_element(int []a )
{
    int m = a[0];
    for(int i = 0; i < a.Length; i++)
    m = Math.Max(a[i], m);
    return m;
}
 
// Function that returns true if arr[]
// contains all the divisors of some integer
static bool checkDivisors(int []a, int n)
{
 
    // Maximum element from the array
    int X = max_element(a);
 
    // Vector to store divisors
    // of the maximum element i.e. X
    List<int> b = new List<int>();
 
    // Store all the divisors of X
    for (int i = 1; i * i <= X; i++)
    {
        if (X % i == 0)
        {
            b.Add(i);
            if (X / i != i)
                b.Add(X / i);
        }
    }
 
    // If the lengths of a[]
    // and b are different
    // return false
    if (b.Count != n)
        return false;
 
    // Sort a[] and b
    Array.Sort(a);
    b.Sort();
 
    for (int i = 0; i < n; i++)
    {
 
        // If divisors are not
        // equal return false
        if (b[i] != a[i])
            return false;
    }
 
    return true;
}
 
// Driver code
public static void Main(String []args)
{
    int []arr = { 8, 1, 2, 12, 48,
                6, 4, 24, 16, 3 };
 
    int N = arr.Length;
 
    if (checkDivisors(arr, N))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
 
}
}
 
// This code is contributed by Princi Singh

Javascript




<script>
// Javascript implementation of the approach
 
// Function that returns true if arr[]
// contains all the divisors of some integer
function checkDivisors(a, n)
{
 
    // Maximum element from the array
    let X = Math.max(...a);
 
    // Vector to store divisors
    // of the maximum element i.e. X
    let b = [];
 
    // Store all the divisors of X
    for (let i = 1; i * i <= X; i++) {
        if (X % i == 0) {
            b.push(i);
            if (parseInt(X / i) != i)
                b.push(parseInt(X / i));
        }
    }
 
    // If the lengths of a[]
    // and b are different
    // return false
    if (b.length != n)
        return false;
 
    // Sort a[] and b
    a.sort((x,y) => x - y);
    b.sort((x,y) => x - y);
 
    for (let i = 0; i < n; i++) {
 
        // If divisors are not
        // equal return false
        if (b[i] != a[i])
            return false;
    }
 
    return true;
}
 
// Driver code
    let arr = [ 8, 1, 2, 12, 48,
                  6, 4, 24, 16, 3 ];
 
    let N = arr.length;
 
    if (checkDivisors(arr, N))
        document.write("Yes");
    else
        document.write("No");
 
</script>

Output: 

Yes

 

Time Complexity: O((n * log n) + max(arr)), where max(arr) is the largest element of the array arr.

Auxiliary Space: O(max(arr))


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