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Count pairs of indices having sum of indices same as the sum of elements at those indices

  • Last Updated : 06 Aug, 2021

Given an array arr[] consisting of N integers, the task is to find the number of pairs (i, j) whose sum of indices is the same as the sum elements at the indices.

Examples:

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Input: arr[] = {0, 1, 7, 4, 3, 2}
Output: 1
Explanation: There exists only pair that satisfies the condition is {(0, 1)}.



Input: arr[] = {1, 6, 2, 4, 5, 6}
Output: 0

Naive Approach: The simple approach to solve the given problem is to generate all possible pairs of the given array and if the sum of any pairs is the same as the sum of its indices, then count this pair. After checking for all the pairs, print the total count obtained.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
void countPairs(int arr[], int N)
{
    // Stores the total count of pairs
    int answer = 0;
 
    // Iterate over the range
    for (int i = 0; i < N; i++) {
 
        // Iterate over the range
        for (int j = i + 1; j < N; j++) {
            if (arr[i] + arr[j] == i + j) {
                answer++;
            }
        }
    }
 
    // Print the total count
    cout << answer;
}
 
// Driver Code
int main()
{
    int arr[] = { 0, 1, 2, 3, 4, 5 };
    int N = sizeof(arr) / sizeof(arr[0]);
 
    countPairs(arr, N);
 
    return 0;
}

Java




// Java program for the above approach
class GFG{
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
public static void countPairs(int arr[], int N)
{
     
    // Stores the total count of pairs
    int answer = 0;
 
    // Iterate over the range
    for(int i = 0; i < N; i++)
    {
         
        // Iterate over the range
        for(int j = i + 1; j < N; j++)
        {
            if (arr[i] + arr[j] == i + j)
            {
                answer++;
            }
        }
    }
     
    // Print the total count
    System.out.println(answer);
}
 
// Driver Code
public static void main(String args[])
{
    int arr[] = { 0, 1, 2, 3, 4, 5 };
    int N = arr.length;
 
    countPairs(arr, N);
}
}
 
// This code is contributed by gfgking

Python3




# Python3 program for the above approach
 
# Function to find all possible pairs
# of the given array such that the sum
# of arr[i] + arr[j] is i + j
def countPairs(arr, N):
     
    # Stores the total count of pairs
    answer = 0
     
    # Iterate over the range
    for i in range(N):
         
        # Iterate over the range
        for j in range(i + 1, N):
            if arr[i] + arr[j] == i + j:
                answer += 1
                 
    # Print the total count            
    print(answer)
 
# Driver code
arr = [ 0, 1, 2, 3, 4, 5 ]
N = len(arr)
 
countPairs(arr, N)
 
# This code is contributed by Parth Manchanda

C#




// C# program for the above approach
using System;
 
class GFG{
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
static void countPairs(int[] arr, int N)
{
     
    // Stores the total count of pairs
    int answer = 0;
 
    // Iterate over the range
    for(int i = 0; i < N; i++)
    {
         
        // Iterate over the range
        for(int j = i + 1; j < N; j++)
        {
            if (arr[i] + arr[j] == i + j)
            {
                answer++;
            }
        }
    }
 
    // Print the total count
    Console.Write(answer);
}
 
// Driver Code
public static void Main(string[] args)
{
    int[] arr = { 0, 1, 2, 3, 4, 5 };
    int N = arr.Length;
     
    countPairs(arr, N);
}
}
 
// This code is contributed by target_2

Javascript




<script>
 
        // JavaScript program for the above approach
 
        // Function to find all possible pairs
        // of the given array such that the sum
        // of arr[i] + arr[j] is i + j
        function countPairs(arr, N)
        {
         
            // Stores the total count of pairs
            let answer = 0;
 
            // Iterate over the range
            for (let i = 0; i < N; i++) {
 
                // Iterate over the range
                for (let j = i + 1; j < N; j++) {
                    if (arr[i] + arr[j] == i + j) {
                        answer++;
                    }
                }
            }
 
            // Prlet the total count
            document.write(answer);
        }
 
        // Driver Code
        let arr = [0, 1, 2, 3, 4, 5];
        let N = arr.length;
 
        countPairs(arr, N);
         
// This code is contributed by Potta Lokesh
    </script>
Output: 
15

 

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

Efficient Approach: The above approach can also be optimized by using an unordered map to store the count of elements having (arr[i] – i) value in the array arr[]. Follow the steps below to solve the problem:

  • Initialize the variable, say answer as 0 to store the count of pairs in the array arr[].
  • Initialize an unordered map mp[] to store the frequency of an element in the array arr[] having value (arr[i] – i).
  • Iterate over the range [0, N] using the variable i and perform the following steps:
    • Initialize the variable keyValue as the value of (arr[i] – i).
    • Increase the value of keyValue in the unordered map mp[] by 1.
  • Iterate over the unordered map mp[] using the variable i and perform the following steps:
    • Initialize the variable size as i.second the value of the unordered map mp[].
    • Add the value of size*(size – 1)/2 to the variable answer.
  • After performing the above steps, print the value of the answer as the result.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
void countPairs(int arr[], int N)
{
    // Stores the total count of pairs
    int answer = 0;
 
    unordered_map<int, int> mp;
 
    // Iterate over the range [0, N]
    for (int i = 0; i < N; i++) {
        int keyValue = arr[i] - i;
        mp[keyValue]++;
    }
 
    // Iterate over the range [0, N]
    for (auto i : mp) {
        int size = i.second;
        answer += (size * (size - 1)) / 2;
    }
 
    // Print the answer
    cout << answer;
}
 
// Driver Code
int main()
{
    int arr[] = { 0, 1, 2, 3, 4, 5 };
    int N = sizeof(arr) / sizeof(arr[0]);
 
    countPairs(arr, N);
 
    return 0;
}

Java




/*package whatever //do not write package name here */
 
// Java program for the above approach
import java.io.*;
import java.util.*;
 
class GFG {
   
  // Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
    public static void countPairs(int[] arr, int n)
    {
       
          // Stores the total count of pairs
        int answer = 0;
        HashMap<Integer, Integer> mp
            = new HashMap<Integer, Integer>();
       
          // Iterate over the range [0, N]
        for (int i = 0; i < n; i++) {
            int value = arr[i] - i;
            if (mp.containsKey(value)) {
                mp.put(value, mp.get(value) + 1);
            }
            else {
                mp.put(value, 1);
            }
        }
       
          // Iterate over the range [0, N]
        for (Map.Entry<Integer, Integer> map :
             mp.entrySet()) {
            int temp = map.getValue();
            answer += temp * (temp - 1) / 2;
        }
       
          // Print the answer
        System.out.println(answer);
    }
   
  // Driver code
    public static void main(String[] args)
    {
        int[] arr = { 0, 1, 2, 3, 4, 5 };
        int n = 6;
        countPairs(arr, n);
    }
}
 
// This code is contributed by maddler.

Python3




# Python3 program for the above approach
 
# Function to find all possible pairs
# of the given array such that the sum
# of arr[i] + arr[j] is i + j
def countPairs(arr, N):
     
    # Stores the total count of pairs
    answer = 0
    mp = {}
     
    # Iterate over the range [0, N]
    for i in range(N):
        keyValue = arr[i] - i
        if keyValue in mp.keys():
            mp[keyValue] += 1
        else:
            mp[keyValue] = 1
             
    # Iterate over the range [0, N]
    for size in mp.values():
        answer += (size * (size - 1)) // 2
         
    print(answer)
 
# Driver code
arr = [ 0, 1, 2, 3, 4, 5 ]
N = len(arr)
 
countPairs(arr, N)
 
# This code is contributed by Parth Manchanda

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
static void countPairs(int []arr, int N)
{
    // Stores the total count of pairs
    int answer = 0;
     
    Dictionary<int,int> mp = new Dictionary<int,int>();
 
    // Iterate over the range [0, N]
    for (int i = 0; i < N; i++) {
        int keyValue = arr[i] - i;
        if(mp.ContainsKey(keyValue))
          mp[keyValue]++;
        else
          mp.Add(keyValue,1);
    }
 
    // Iterate over the range [0, N]
    foreach(KeyValuePair<int,int> entry in mp)
    {
        int size = entry.Value;
        answer += (size * (size - 1)) / 2;
    }
 
    // Print the answer
    Console.Write(answer);
}
 
// Driver Code
public static void Main()
{
    int []arr = {0, 1, 2, 3, 4, 5 };
    int N = arr.Length;
    countPairs(arr, N);
}
}
 
// This code is contributed by SURENDRA_GANGWAR.

Javascript




<script>
// Javascript program for the above approach
 
// Function to find all possible pairs
// of the given array such that the sum
// of arr[i] + arr[j] is i + j
function countPairs(arr, N) {
  // Stores the total count of pairs
  let answer = 0;
 
  let mp = new Map();
 
  // Iterate over the range [0, N]
  for (let i = 0; i < N; i++) {
    let keyValue = arr[i] - i;
 
    if (mp.has(keyValue)) {
      mp.set(keyValue, mp.get(keyValue) + 1);
    } else {
      mp.set(keyValue, 1);
    }
  }
 
  // Iterate over the range [0, N]
  for (let i of mp) {
    let size = i[1];
    answer += (size * (size - 1)) / 2;
  }
 
  // Print the answer
  document.write(answer);
}
 
// Driver Code
 
let arr = [0, 1, 2, 3, 4, 5];
let N = arr.length;
 
countPairs(arr, N);
 
// This code is contributed by _saurabh_jaiswal.
</script>
Output: 
15

 

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




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