Check if elements of an array can be arranged satisfying the given condition

Given an array arr of N (even) integer elements. The task is to check if it is possible to reorder the elements of the array such that:

arr[2*i + 1] = 2 * A[2 * i] 

for i = 0 ... N-1. 

Print True if it is possible, otherwise print False.

Examples:

Input: arr[] = {4, -2, 2, -4}
Output: True
{-2, -4, 2, 4} is a valid arrangement, -2 * 2 = -4 and 2 * 2 = 4

Input: arr[] = {1, 2, 4, 16, 8, 4}
Output: False



Approach: The idea is that, if k is current minimum element in the array then it must pair with 2 * k as there does not exist any other element k / 2 to pair it with.
We check elements in ascending order. When we check an element k and it isn’t used, it must pair with 2 * k. We will attempt to arrange k followed by 2 * k however if we can’t, then the answer is False. In the end, if all the operations are successful, then print True.
We will store a count of each element to keep track of what we have not yet considered.

Below is the implementation of above approach:

C++

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// C++ implementation of the approach
#include<bits/stdc++.h>
using namespace std;
  
// Function to return true if the elements 
// can be arranged in the desired order
string canReorder(int A[],int n)
{
    map<int,int> m;
      
    for(int i=0;i<n;i++)
    m[A[i]]++;
      
    sort(A,A+n);
    int count = 0;
   
    for(int i=0;i<n;i++)
    {
        if (m[A[i]] == 0)
            continue;
   
        // If 2 * x is not found to pair
        if (m[2 * A[i]]){
              
        count+=2;
          
        // Remove an occurrence of x 
        // and an occurrence of 2 * x
        m[A[i]] -= 1;
        m[2 * A[i]] -= 1;
        }
    }
    if(count ==n)
    return "true";
    else
    return "false";
}
   
   
// Driver Code
int main()
{
int A[] = {4, -2, 2, -4};
int n= sizeof(A)/sizeof(int);
   
// Function call to print required answer
cout<<(canReorder(A,n));
  
return 0;
}
//contributed by Arnab Kundu

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Python

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# Python implementation of the approach
import collections
  
# Function to return true if the elements 
# can be arranged in the desired order
def canReorder(A):
  
    count = collections.Counter(A)
  
    for x in sorted(A, key = abs):
        if count[x] == 0:
            continue
  
        # If 2 * x is not found to pair
        if count[2 * x] == 0:
            return False
  
        # Remove an occurrence of x 
        # and an occurrence of 2 * x
        count[x] -= 1
        count[2 * x] -= 1
  
    return True
  
  
# Driver Code
A = [4, -2, 2, -4]
  
# Function call to print required answer
print(canReorder(A))

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Output:

True


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