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Check if the array has an element which is equal to product of remaining elements
  • Difficulty Level : Basic
  • Last Updated : 16 Apr, 2019

Given an array of N elements, the task is to check if the array has an element which is equal to the product of all the remaining elements.

Examples:

Input: arr[] = {1, 2, 12, 3, 2}
Output: YES
12 is the product of all the remaining elements 
i.e. 1 * 2 * 3 * 2 = 12

Input: arr[] = {1, 2, 3}
Output: NO

Method-1:

  1. First, take the product of all the element of the array.
  2. Now traverse the whole array again.
  3. For any element a[i] check if it is equal to the product of all elements divided by that element.
  4. Print Yes if at least one such element is found.

Below is the implementation of the above approach:

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
bool CheckArray(int arr[], int n)
{
    int prod = 1;
  
    // Calculate the product of all the elements
    for (int i = 0; i < n; ++i)
        prod *= arr[i];
  
    // Return true if any such element is found
    for (int i = 0; i < n; ++i)
        if (arr[i] == prod / arr[i])
            return true;
  
    // If no element is found
    return false;
}
  
int main()
{
    int arr[] = { 1, 2, 12, 3, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    if (CheckArray(arr, n))
        cout << "YES";
  
    else
        cout << "NO";
  
    return 0;
}


Java




// Java implementation of the above approach
  
import java.io.*;
  
class GFG {
  
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
static boolean CheckArray(int arr[], int n)
{
    int prod = 1;
  
    // Calculate the product of all the elements
    for (int i = 0; i < n; ++i)
        prod *= arr[i];
  
    // Return true if any such element is found
    for (int i = 0; i < n; ++i)
        if (arr[i] == prod / arr[i])
            return true;
  
    // If no element is found
    return false;
}
  
  
  
    public static void main (String[] args) {
            int arr[] = { 1, 2, 12, 3, 2 };
    int n =arr.length;
  
    if (CheckArray(arr, n))
        System.out.println("YES");
  
    else
        System.out.println("NO");
  
    }
}
// This code is contributed by shs..


Python3




# Python 3 implementation of the above approach
  
# Function to Check if the array
# has an element which is equal to
# product of all the remaining elements
def CheckArray(arr, n):
    prod = 1
  
    # Calculate the product of all
    # the elements
    for i in range(0, n, 1):
        prod *= arr[i]
  
    # Return true if any such element 
    # is found
    for i in range(0, n, 1):
        if (arr[i] == prod / arr[i]):
            return True
  
    # If no element is found
    return False
  
# Driver code
if __name__ == '__main__':
    arr = [1, 2, 12, 3, 2
    n = len(arr)
  
    if (CheckArray(arr, n)):
        print("YES")
  
    else:
        print("NO")
  
# This code is contributed by 
# Surendra_Gangwar


C#




// C# implementation of the above approach
class GFG
{
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
static bool CheckArray(int[] arr, int n)
{
    int prod = 1;
  
    // Calculate the product of 
    // all the elements
    for (int i = 0; i < n; ++i)
        prod *= arr[i];
  
    // Return true if any such 
    // element is found
    for (int i = 0; i < n; ++i)
        if (arr[i] == prod / arr[i])
            return true;
  
    // If no element is found
    return false;
}
  
// Driver Code
public static void Main () 
{
    int[] arr = new int[] { 1, 2, 12, 3, 2 };
    int n = arr.Length;
      
    if (CheckArray(arr, n))
        System.Console.WriteLine("YES");
      
    else
        System.Console.WriteLine("NO");
}
}
  
// This code is contributed by mits


PHP




<?php
// PHP implementation of the above approach
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
function CheckArray($arr, $n)
{
    $prod = 1;
  
    // Calculate the product of 
    // all the elements
    for ($i = 0; $i < $n; ++$i)
        $prod *= $arr[$i];
  
    // Return true if any such element
    // is found
    for ($i = 0; $i < $n; ++$i)
        if ($arr[$i] == $prod / $arr[$i])
            return true;
  
    // If no element is found
    return false;
}
  
// Driver Code
$arr = array(1, 2, 12, 3, 2);
$n = sizeof($arr);
  
if (CheckArray($arr, $n))
    echo "YES";
else
    echo "NO";
  
// This code is contributed 
// by Akanksha Rai


Output:



YES

Method-2: The approach is to find the product of all the elements of the array and check if it is a perfect square or not. If it is a perfect square then check if the square root of the product exists in the array or not. If exists then print Yes else print No.

According to the problem statement, a * b = N
where b is the product of all the remaining elements of the array except a i.e arr[i]
And it is also mentioned that find the index such that a = b.
So, it simply means that a*a = N i.e. N is a perfect square. and a is its square root.

Below is the implementation of the above approach:

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
bool CheckArray(int arr[], int n)
{
    int prod = 1;
  
    // Storing frequency in map
    unordered_set<int> freq;
  
    // Calculate the product of all the elements
    for (int i = 0; i < n; ++i) {
        freq.insert(arr[i]);
        prod *= arr[i];
    }
  
    int root = sqrt(prod);
  
    // If the prod is a perfect square
    if (root * root == prod)
  
        // then check if its square root
        // exist in the array or not
        if (freq.find(root) != freq.end())
            return true;
  
    return false;
}
  
// Driver code
int main()
{
    int arr[] = { 1, 2, 12, 3, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
  
    if (CheckArray(arr, n))
        cout << "YES";
  
    else
        cout << "NO";
  
    return 0;
}


Java




import java.util.ArrayList;
  
// Java implementation of the above approach
class GFG {
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
    static boolean CheckArray(int arr[], int n) {
        int prod = 1;
  
        // Storing frequency in map
        ArrayList<Integer> freq = new ArrayList<>();
  
        // Calculate the product of all the elements
        for (int i = 0; i < n; ++i) {
            freq.add(arr[i]);
            prod *= arr[i];
        }
  
        int root = (int) Math.sqrt(prod);
  
        // If the prod is a perfect square
        if (root * root == prod) // then check if its square root
        // exist in the array or not
        {
            if (freq.contains(root) & freq.lastIndexOf(root) != (freq.size())) {
                return true;
            }
        }
  
        return false;
    }
// Driver code 
  
    public static void main(String[] args) {
  
        int arr[] = {1, 2, 12, 3, 2};
        int n = arr.length;
  
        if (CheckArray(arr, n)) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
  
    }
}
//This code is contributed by 29AjayKumar


Python3




# Python3 implementation of the above approach
   
import math
  
# Function to Check if the array
# has an element which is equal to
# product of all the remaining elements
def CheckArray( arr, n):
  
    prod = 1
   
    # Storing frequency in map
    freq = []
   
    # Calculate the product of all the elements
    for i in range(n) :
        freq.append(arr[i])
        prod *= arr[i]
   
    root = math.sqrt(prod)
   
    # If the prod is a perfect square
    if (root * root == prod):
   
        # then check if its square root
        # exist in the array or not
        if root in freq:
            return True
   
    return False
   
# Driver code
if __name__ == "__main__":
  
    arr = [1, 2, 12, 3, 2 ]
    n = len(arr)
   
    if (CheckArray(arr, n)):
        print ("YES")
   
    else:
        print ("NO")


C#




// C# implemenatation of above approach 
using System;
using System.Collections;
  
class GFG 
{
  
    // Function to Check if the array
    // has an element which is equal to
    // product of all the remaining elements
    static bool CheckArray(int []arr, int n)
    {
        int prod = 1;
  
        // Storing frequency in map
        ArrayList freq = new ArrayList();
  
        // Calculate the product of all the elements
        for (int i = 0; i < n; ++i) 
        {
            freq.Add(arr[i]);
            prod *= arr[i];
        }
  
        int root = (int) Math.Sqrt(prod);
  
        // If the prod is a perfect square
        if (root * root == prod) // then check if its square root
        // exist in the array or not
        {
            if (freq.Contains(root) & freq.LastIndexOf(root) != (freq.Count)) 
            {
                return true;
            }
        }
  
        return false;
    }
      
    // Driver code 
    public static void Main() 
    {
  
        int []arr = {1, 2, 12, 3, 2};
        int n = arr.Length;
  
        if (CheckArray(arr, n)) 
        {
            Console.WriteLine("YES");
        
        else 
        {
            Console.WriteLine("NO");
        }
    }
}
  
/* This code contributed by PrinciRaj1992 */


PHP




<?php
// PHP implementation of the above approach
  
// Function to Check if the array
// has an element which is equal to
// product of all the remaining elements
function CheckArray($arr, $n)
{
    $prod = 1;
  
    // Storing frequency in map
    $freq = array();
  
    // Calculate the product of all the elements
    for ($i = 0; $i < $n; ++$i)
    {
        array_push($freq, $arr[$i]);
        $prod *= $arr[$i];
    }
    $freq = array_unique($freq);
    $root = (int)(sqrt($prod));
  
    // If the prod is a perfect square
    if ($root * $root == $prod)
  
        // then check if its square root
        // exist in the array or not
        if (in_array($root, $freq))
            return true;
  
    return false;
}
  
// Driver code
$arr = array( 1, 2, 12, 3, 2 );
$n = count($arr);
  
if (CheckArray($arr, $n))
    echo "YES";
  
else
    echo "NO";
  
// This code is contributed by mits
?>


Output:

YES

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