Count pairs from an array having product of their sum and difference equal to 0

Given an array arr[] of size N, the task is to count possible pairs of array elements (arr[i], arr[j]) such that (arr[i] + arr[j]) * (arr[i] – arr[j]) is 0.

Examples:

Input: arr[] = {2, -2, 1, 1}
Output : 2
Explanation:
(arr[0] + arr[1]) * (arr[0] – arr[1]) = 0
(arr[3] + arr[4]) * (arr[3] – arr[4]) = 0

Input: arr[] = {5, 9, -9, -9}
Output : 3

Approach: It can be observed that the equation (arr[i] + arr[j]) * (arr[i] – arr[j]) = 0 can be reduced to arr[i]2 = arr[j]2. Therefore, the task reduces to counting pairs having absolute value equal. Follow the steps below to solve the problem:  



  • Initialize an array hash[] to store the frequency of the absolute value of each array element.
  • Calculate the count of pairs by adding (hash[x] * (hash[x] – 1))/ 2 for every array distinct absolute values.

Below is the implementation of the above approach:

C++14

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
#define MAXN 100005
 
// Function to count required
// number of pairs
int countPairs(int arr[], int N)
{
    // Stores count of pairs
    int desiredPairs = 0;
 
    // Initialize hash with 0
    int hash[MAXN] = { 0 };
 
    // Count frequency of each element
    for (int i = 0; i < N; i++) {
        hash[abs(arr[i])]++;
    }
 
    // Calculate desired number of pairs
    for (int i = 0; i < MAXN; i++) {
        desiredPairs
            += ((hash[i]) * (hash[i] - 1)) / 2;
    }
 
    // Print desired pairs
    cout << desiredPairs;
}
 
// Driver Code
int main()
{
    // Given arr[]
    int arr[] = { 2, -2, 1, 1 };
 
    // Size of the array
    int N = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    countPairs(arr, N);
 
    return 0;
}

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Java

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// Java program for the above approach
import java.io.*;
import java.util.Arrays;
 
class GFG{
   
static int MAXN = 100005;
 
// Function to count required
// number of pairs
static void countPairs(int arr[], int N)
{
     
    // Stores count of pairs
    int desiredPairs = 0;
 
    // Initialize hash with 0
    int hash[] = new int[MAXN];
    Arrays.fill(hash, 0);
 
    // Count frequency of each element
    for(int i = 0; i < N; i++)
    {
        hash[Math.abs(arr[i])]++;
    }
 
    // Calculate desired number of pairs
    for(int i = 0; i < MAXN; i++)
    {
        desiredPairs += ((hash[i]) *
                         (hash[i] - 1)) / 2;
    }
 
    // Print desired pairs
    System.out.print(desiredPairs);
}  
   
// Driver Code
public static void main (String[] args)
{
     
    // Given arr[]
    int arr[] = { 2, -2, 1, 1 };
 
    // Size of the array
    int N = arr.length;
 
    // Function call
    countPairs(arr, N);
}
}
 
// This code is contributed by code_hunt

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Python3

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# Python3 program for
# the above approach
MAXN = 100005
 
# Function to count required
# number of pairs
def countPairs(arr, N):
 
    # Stores count of pairs
    desiredPairs = 0
 
    # Initialize hash with 0
    hash = [0] * MAXN
 
    # Count frequency of
    # each element
    for i in range(N):
        hash[abs(arr[i])] += 1
    
    # Calculate desired number
    # of pairs
    for i in range(MAXN):
        desiredPairs += ((hash[i]) *
                         (hash[i] - 1)) // 2
     
    # Print desired pairs
    print (desiredPairs)
 
# Driver Code
if __name__ == "__main__":
   
    # Given arr[]
    arr = [2, -2, 1, 1]
 
    # Size of the array
    N = len(arr)
 
    # Function Call
    countPairs(arr, N)
 
# This code is contributed by Chitranayal

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C#

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// C# program for the above approach
using System;
 
class GFG{
   
static int MAXN = 100005;
 
// Function to count required
// number of pairs
static void countPairs(int []arr, int N)
{
     
    // Stores count of pairs
    int desiredPairs = 0;
 
    // Initialize hash with 0
    int []hash = new int[MAXN];
 
    // Count frequency of each element
    for(int i = 0; i < N; i++)
    {
        hash[Math.Abs(arr[i])]++;
    }
 
    // Calculate desired number of pairs
    for(int i = 0; i < MAXN; i++)
    {
        desiredPairs += ((hash[i]) *
                         (hash[i] - 1)) / 2;
    }
 
    // Print desired pairs
    Console.Write(desiredPairs);
}  
   
// Driver Code
public static void Main(String[] args)
{
     
    // Given []arr
    int []arr = { 2, -2, 1, 1 };
 
    // Size of the array
    int N = arr.Length;
 
    // Function call
    countPairs(arr, N);
}
}
 
// This code is contributed by Amit Katiyar

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Output: 

2









 

Time Complexity: O(N)
Auxiliary Space: O(N) 

 

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