Count of triplets from the given Array such that sum of any two elements is the third element

Given an unsorted array arr, the task is to find the count of the distinct triplets in which the sum of any two elements is the third element.

Examples:

Input: arr[] = {1, 3, 4, 15, 19} 
Output: 2 
Explanation:
In the given array there are two triplets such that the sum of the two elements is equal to the third element: {{1, 3, 4}, {4, 15, 19}}

Input: arr[] = {7, 2, 5, 4, 3, 6, 1, 9, 10, 12} 
Output: 18 

Approach:

• Sort the given array
• Create a Hash map for the array to check that a particular element is present or not.
• Iterate over the Array with two Loops to select any two elements at different positions and check that the sum of those two elements is present in the hash map in O(1) time.
• If the sum of the two elements is present in the hash map, then increment the count of the triplets.

Below is the implementation of the above approach:  

C++

// C++ Implementation to find the
// Count the triplets in which sum
// of two elements is the third element
#include <bits/stdc++.h>

using namespace std;

// Function to find the count
// the triplets in which sum
// of two elements is the third element
int triplets(vector<int>arr)
{

    // Dictionary to check a element is
    // present or not in array
    map<int, int> k;
    map<pair<int, int>, int> mpp;

    // List to check for
    // duplicates of Triplets
    vector<vector<int >> ssd;

    // Set initial count to zero
    int count = 0;

    // Sort the array
    sort(arr.begin(),arr.end());

    int i = 0;
    while (i < arr.size())
    {

        // Add all the values as key
        // value pairs to the dictionary
        if (k.find(arr[i]) == k.end())
            k[arr[i]] = 1;

        i += 1;
    }

    // Loop to choose two elements
    int j = 0;
    while (j < arr.size() - 1)
    {

        int q = j + 1;
        while (q < arr.size())
        {

            // Check for the sum and duplicate
            if ( k.find(arr[j] + arr[q]) != k.end() and
                mpp[{arr[j], arr[q]}] != arr[j] + arr[q])
            {

                count += 1;

                ssd.push_back({arr[j], arr[q], arr[j] + arr[q]});
                mpp[{arr[j], arr[q]}] = arr[j] + arr[q];
            }

            q += 1;
        }
        j += 1;
    }
    return count;
}


// Driver Code
int main()
{
    vector<int>arr = {7, 2, 5, 4, 3, 6, 1, 9, 10, 12};
    int count = triplets(arr);
    printf("%d",count);
    return 0;
}

// This code is contributed by mohit kumar 29

Java

// Java implementation to find the
// Count the triplets in which sum
// of two elements is the third element
import java.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;

class GFG{

// Function to find the count the triplets
// in which sum of two elements is the third element
public static int triplets(ArrayList<Integer> arr)
{

      // Dictionary to check a element is
       // present or not in array
    HashSet<Integer> k = new HashSet<>();

      // List to check for
    // duplicates of Triplets
    HashSet<ArrayList<Integer>> ssd = new HashSet<>();

      // Set initial count to zero
    int count = 0;

    // Sort the array
    Collections.sort(arr);

    int i = 0;

      // Add all the values as key
    // value pairs to the dictionary
    while (i < arr.size())
    {
        if (!k.contains(arr.get(i)))
        {
            k.add(arr.get(i));
        }
        i += 1;
    }
    int j = 0;

    // Loop to choose two elements
    while (j < arr.size() - 1)
    {
        int q = j + 1;

          // Check for the sum and duplicate
        while (q < arr.size())
        {
            ArrayList<Integer> trip = new ArrayList<>();
            trip.add(arr.get(j));
            trip.add(arr.get(q));
            trip.add(arr.get(j) + arr.get(q));

            if (k.contains(arr.get(j) + arr.get(q)) &&
                !ssd.contains(trip))
            {
                count += 1;
                ArrayList<Integer> nums = new ArrayList<>();
                nums.add(arr.get(j));
                nums.add(arr.get(q));
                nums.add(arr.get(j) + arr.get(q));
                ssd.add(nums);
            }
            q += 1;
        }
        j += 1;
    }
    return count;
}

// Driver Code
public static void main(String[] args)
{
    ArrayList<Integer> arr = new ArrayList<>();
    arr.add(7);
    arr.add(2);
    arr.add(5);
    arr.add(4);
    arr.add(3);
    arr.add(6);
    arr.add(1);
    arr.add(9);
    arr.add(10);
    arr.add(12);

    int count = triplets(arr);

    System.out.println(count);
}
}

// This code is contributed by aditya7409

Python3

# Python3 Implementation to find the
# Count the triplets in which sum
# of two elements is the third element

# Function to find the count
# the triplets in which sum
# of two elements is the third element
def triplets(arr):

    # Dictionary to check a element is
    # present or not in array
    k = set()

    # List to check for
    # duplicates of Triplets
    ssd = []

    # Set initial count to zero
    count = 0

    # Sort the array
    arr.sort()

    i = 0
    while i < len(arr):

        # Add all the values as key
        # value pairs to the dictionary
        if arr[i] not in k:
            k.add(arr[i])

        i += 1

    # Loop to choose two elements
    j = 0
    while j < len(arr) - 1:

        q = j + 1
        while q < len(arr):

            # Check for the sum and duplicate
            if arr[j] + arr[q] in k and\
               [arr[j], arr[q], arr[j] + arr[q]] not in ssd:

                count += 1

                ssd.append([arr[j], arr[q], arr[j] + arr[q]])

            q += 1
        j += 1

    return count


# Driver Code
if __name__ == "__main__":
    arr = [7, 2, 5, 4, 3, 6, 1, 9, 10, 12]
    count = triplets(arr)
    print(count)

C#

// C# Implementation to find the
// Count the triplets in which sum
// of two elements is the third element
using System;
using System.Collections.Generic;
class GFG {

  // Function to find the count
  // the triplets in which sum
  // of two elements is the third element
  static int triplets(List<int> arr)
  {

    // Dictionary to check a element is
    // present or not in array
    Dictionary<int, int> k = new Dictionary<int, int>();
    Dictionary<Tuple<int, int>, int> mpp = new Dictionary<Tuple<int, int>, int>();

    // List to check for
    // duplicates of Triplets
    List<List<int>> ssd = new List<List<int>>();

    // Set initial count to zero
    int count = 0;

    // Sort the array
    arr.Sort();

    int i = 0;
    while (i < arr.Count)
    {

      // Add all the values as key
      // value pairs to the dictionary
      if (!k.ContainsKey(arr[i]))
        k[arr[i]] = 1;

      i += 1;
    }

    // Loop to choose two elements
    int j = 0;
    while (j < arr.Count - 1)
    {
      int q = j + 1;
      while (q < arr.Count)
      {

        // Check for the sum and duplicate
        if(!k.ContainsKey(arr[j] + arr[q]))
        {
          q += 1;
          continue;
        }
        if (mpp.ContainsKey(new Tuple<int,int>(arr[j], arr[q])) &&
            mpp[new Tuple<int,int>(arr[j], arr[q])] != (arr[j] + arr[q]))
        {
          count += 1;
          ssd.Add(new List<int>(new int[]{arr[j], arr[q], arr[j] + arr[q]}));
          mpp[new Tuple<int,int>(arr[j], arr[q])] = arr[j] + arr[q];
        }
        else{
          count += 1;
          ssd.Add(new List<int>(new int[]{arr[j], arr[q], arr[j] + arr[q]}));
          mpp[new Tuple<int,int>(arr[j], arr[q])] = arr[j] + arr[q];
        }
        q += 1;
      }
      j += 1;
    }
    return count;
  }

  // Driver code
  static void Main()
  {
    List<int> arr = new List<int>(new int[]{7, 2, 5, 4, 3, 6, 1, 9, 10, 12});
    int count = triplets(arr);
    Console.Write(count);
  }
}

// This code is contributed by divyeshrabadiya07

Javascript

<script>
// Javascript implementation to find the
// Count the triplets in which sum
// of two elements is the third element

// Function to find the count the triplets
// in which sum of two elements is the third element
function triplets(arr)
{

    // Dictionary to check a element is
    // present or not in array
    let k = new Set();

    // List to check for
    // duplicates of Triplets
    let ssd = new Set();

    // Set initial count to zero
    let count = 0;

    // Sort the array
    arr.sort((a, b) => a - b);

    let i = 0;

      // Add all the values as key
    // value pairs to the dictionary
    while (i < arr.length)
    {
        if (!k.has(arr[i]))
        {
            k.add(arr[i]);
        }
        i += 1;
    }
    let j = 0;

    // Loop to choose two elements
    while (j < arr.length - 1)
    {
        let q = j + 1;

        // Check for the sum and duplicate
        while (q < arr.length)
        {
            let trip = new Array();
            trip.push(arr[j]);
            trip.push(arr[q]);
            trip.push(arr[j] + arr[q]);

            if (k.has(arr[j] + arr[q]) &&
                !ssd.has(trip))
            {
                count += 1;
                let nums = new Array();
                nums.push(arr[j]);
                nums.push(arr[q]);
                nums.push(arr[j] + arr[q]);
                ssd.add(nums);
            }
            q += 1;
        }
        j += 1;
    }
    return count;
}

// Driver Code

    let arr = new Array();
    arr.push(7);
    arr.push(2);
    arr.push(5);
    arr.push(4);
    arr.push(3);
    arr.push(6);
    arr.push(1);
    arr.push(9);
    arr.push(10);
    arr.push(12);

    let count = triplets(arr);

    document.write(count);


// This code is contributed by gfgking
</script>

Output:

18

Time Complexity: O(N²*logN)

Auxiliary Space: O(3*N²)