Count pairs (i, j) from arrays arr[] & brr[] such that arr[i] – brr[j] = arr[j] – brr[i]

Given two arrays arr[] and brr[] consisting of N integers, the task is to count the number of pairs (i, j) from both the array such that (arr[i] – brr[j]) and (arr[j] – brr[i]) are equal. 

Examples:

Input: A[] = {1, 2, 3, 2, 1}, B[] = {1, 2, 3, 2, 1} 
Output: 2 
Explanation: The pairs satisfying the condition are: 

1. (1, 5): arr[1] – brr[5] = 1 – 1 = 0, arr[5[ – brr[1] = 1 – 1 = 0
2. (2, 4): arr[2] – brr[4] = 2 – 2 = 0, arr[4] – brr[2] = 2 – 2 = 0

Input: A[] = {1, 4, 20, 3, 10, 5}, B[] = {9, 6, 1, 7, 11, 6} 
Output: 4 

Naive Approach: The simplest approach to solve the problem is to generate all pairs from two given arrays and check for the required condition. For every pair for which the condition is found to be true, increase count of such pairs. Finally, print the count obtained. 

Time Complexity: O(N²) 
Auxiliary Space: O(1)

Efficient Approach: The idea is to transform the given expression (a[i] – b[j] = a[j] – b[i]) into the form (a[i] + b[i] = a[j] + b[j]) and then calculate pairs satisfying the condition. Below are the steps:

1. Transform the expression, a[i] – b[j] = a[j] – b[i] ==> a[i] + b[i] = a[j] +b[j]. The general form of expression becomes to count the sum of values at each corresponding index of the two arrays for any pair (i, j).
2. Initialize an auxiliary array c[] to store the corresponding sum c[i] = a[i] + b[i] at each index i.
3. Now the problem reduces to find the number of possible pairs having same c[i] value.
4. Count the frequency of each element in the array c[] and If any c[i] frequency value is greater than one then it can make a pair.
5. Count the number of valid pairs in the above steps using formula:

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to count the pairs such that
// given condition is satisfied
int CountPairs(int* a, int* b, int n)
{
    // Stores the sum of element at
    // each corresponding index
    int C[n];

    // Find the sum of each index
    // of both array
    for (int i = 0; i < n; i++) {
        C[i] = a[i] + b[i];
    }

    // Stores frequency of each element
    // present in sumArr
    map<int, int> freqCount;

    for (int i = 0; i < n; i++) {
        freqCount[C[i]]++;
    }

    // Initialize number of pairs
    int NoOfPairs = 0;

    for (auto x : freqCount) {
        int y = x.second;

        // Add possible valid pairs
        NoOfPairs = NoOfPairs
                    + y * (y - 1) / 2;
    }

    // Return Number of Pairs
    cout << NoOfPairs;
}

// Driver Code
int main()
{
    // Given array arr[] and brr[]
    int arr[] = { 1, 4, 20, 3, 10, 5 };

    int brr[] = { 9, 6, 1, 7, 11, 6 };

    // Size of given array
    int N = sizeof(arr) / sizeof(arr[0]);

    // Function calling
    CountPairs(arr, brr, N);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
import java.io.*;

class GFG{

// Function to find the minimum number
// needed to be added so that the sum
// of the digits does not exceed K
static void CountPairs(int a[], int b[], int n)
{

    // Stores the sum of element at
    // each corresponding index
    int C[] = new int[n];

    // Find the sum of each index
    // of both array
    for(int i = 0; i < n; i++)
    {
        C[i] = a[i] + b[i];
    }

    // Stores frequency of each element
    // present in sumArr
    // map<int, int> freqCount;
    HashMap<Integer,
            Integer> freqCount = new HashMap<>();

    for(int i = 0; i < n; i++)
    {
        if (!freqCount.containsKey(C[i]))
            freqCount.put(C[i], 1);
        else
            freqCount.put(C[i],
            freqCount.get(C[i]) + 1);
    }

    // Initialize number of pairs
    int NoOfPairs = 0;

    for(Map.Entry<Integer,
                  Integer> x : freqCount.entrySet())
    {
        int y = x.getValue();

        // Add possible valid pairs
        NoOfPairs = NoOfPairs +
                  y * (y - 1) / 2;
    }

    // Return Number of Pairs
   System.out.println(NoOfPairs);
}

// Driver Code
public static void main(String args[])
{

    // Given array arr[] and brr[]
    int arr[] = { 1, 4, 20, 3, 10, 5 };
    int brr[] = { 9, 6, 1, 7, 11, 6 };

    // Size of given array
    int N = arr.length;

    // Function calling
    CountPairs(arr, brr, N);
}
}

// This code is contributed by bikram2001jha

Python3

# Python3 program for the above approach

# Function to count the pairs such that
# given condition is satisfied
def CountPairs(a, b, n):

    # Stores the sum of element at
    # each corresponding index
    C = [0] * n

    # Find the sum of each index
    # of both array
    for i in range(n):
        C[i] = a[i] + b[i]

    # Stores frequency of each element
    # present in sumArr
    freqCount = dict()

    for i in range(n):
        if C[i] in freqCount.keys():
            freqCount[C[i]] += 1
        else:
            freqCount[C[i]] = 1

    # Initialize number of pairs
    NoOfPairs = 0

    for x in freqCount:
        y = freqCount[x]

        # Add possible valid pairs
        NoOfPairs = (NoOfPairs + y *
                       (y - 1) // 2)

    # Return Number of Pairs
    print(NoOfPairs)

# Driver Code

# Given array arr[] and brr[]
arr = [ 1, 4, 20, 3, 10, 5 ]
brr = [ 9, 6, 1, 7, 11, 6 ]

# Size of given array
N = len(arr)

# Function calling
CountPairs(arr, brr, N)

# This code is contributed by code_hunt

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG{

// Function to find the minimum number
// needed to be added so that the sum
// of the digits does not exceed K
static void CountPairs(int []a, int []b,
                       int n)
{

    // Stores the sum of element at
    // each corresponding index
    int []C = new int[n];

    // Find the sum of each index
    // of both array
    for(int i = 0; i < n; i++)
    {
        C[i] = a[i] + b[i];
    }

    // Stores frequency of each element
    // present in sumArr
    // map<int, int> freqCount;
    Dictionary<int,
               int> freqCount = new Dictionary<int,
                                               int>();

    for(int i = 0; i < n; i++)
    {
        if (!freqCount.ContainsKey(C[i]))
            freqCount.Add(C[i], 1);
        else
            freqCount[C[i]] = freqCount[C[i]] + 1;
    }

    // Initialize number of pairs
    int NoOfPairs = 0;

    foreach(KeyValuePair<int,
                         int> x in freqCount)
    {
        int y = x.Value;

        // Add possible valid pairs
        NoOfPairs = NoOfPairs +
                  y * (y - 1) / 2;
    }

    // Return Number of Pairs
    Console.WriteLine(NoOfPairs);
}

// Driver Code
public static void Main(String []args)
{

    // Given array []arr and brr[]
    int []arr = { 1, 4, 20, 3, 10, 5 };
    int []brr = { 9, 6, 1, 7, 11, 6 };

    // Size of given array
    int N = arr.Length;

    // Function calling
    CountPairs(arr, brr, N);
}
}

// This code is contributed by Amit Katiyar

Javascript

<script>

// JavaScript program for the above approach

// Function to count the pairs such that
// given condition is satisfied
function CountPairs(a,b, n)
{
    // Stores the sum of element at
    // each corresponding index
    var C = Array(n);

    // Find the sum of each index
    // of both array
    for (var i = 0; i < n; i++) {
        C[i] = a[i] + b[i];
    }

    // Stores frequency of each element
    // present in sumArr
    var freqCount = new Map();

    for (var i = 0; i < n; i++) {
        if(freqCount.has(C[i]))
            freqCount.set(C[i], freqCount.get(C[i])+1)
        else
            freqCount.set(C[i], 1)
    }

    // Initialize number of pairs
    var NoOfPairs = 0;

    freqCount.forEach((value, key) => {

        var y = value;

        // Add possible valid pairs
        NoOfPairs = NoOfPairs
                    + y * (y - 1) / 2;
    });

    // Return Number of Pairs
    document.write( NoOfPairs);
}

// Driver Code

// Given array arr[] and brr[]
var arr = [1, 4, 20, 3, 10, 5];
var brr = [ 9, 6, 1, 7, 11, 6 ];

// Size of given array
var N = arr.length;

// Function calling
CountPairs(arr, brr, N);

</script>

Output:

4

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