Print all triplets with sum S in given sorted Linked List

Given a sorted singly linked list as list of N distinct nodes (no two nodes have the same data) and an integer S. The task is to find all distinct triplets in the list that sum up to given integer S.

Examples:

Input: list = 1->2->4->5->6->8->9,  S = 15
Output: [(1, 5, 9), (1, 6, 8), (2, 4, 9), (2 ,5, 8), (4, 5, 6)]
Explanation: These are the only distinct triplets which have sum equal to S i.e 15. Note that (2, 4, 9) and (9, 4, 2) both triplets have sum 15 but they are not distinct as all the elements of the triplets are same.

Input: list = 1->2->4->5->6->8->9,  S = 17
Output: [(2, 6, 9), (4, 5, 8)]

Naive approach: 

 The idea is to use three nested loop and after that Generate all triplets and find the distinct triplets having sum equal to S.

Algorithm

• Initialize a variable called “triplets” as an empty list.
• Traverse the linked list with three nested loops to generate all possible triplets.
• For each triplet, check if the sum of the values is equal to S and if the triplet is distinct  
• If both conditions are true, append the triplet to the “triplets” list.
• Return the “triplets” list.

Implementation of the above approach

C++

#include <iostream>
#include <tuple>
#include <vector>
using namespace std;

// define the Node class
class Node {
public:
    int data;
    Node* next;
    Node(int data)
    {
        this->data = data;
        this->next = NULL;
    }
};

// function to find triplets in the linked list
vector<tuple<int, int, int> > findTriplets(Node* head,
                                           int S)
{
    vector<tuple<int, int, int> >
        triplets; // initialize empty vector to store
                  // triplets
    Node* ptr1
        = head; // pointer to traverse the linked list
    while (ptr1 != NULL) {
        Node* ptr2 = ptr1->next; // pointer to traverse the
                                 // remaining part of the
                                 // linked list
        while (ptr2 != NULL) {
            Node* ptr3 = ptr2->next; // pointer to traverse
                                     // the remaining part
                                     // of the linked list
            while (ptr3 != NULL) {
                if (ptr1->data + ptr2->data + ptr3->data
                    == S) { // check if sum of values is
                            // equal to S
                    if (ptr1->data != ptr2->data
                        && ptr1->data != ptr3->data
                        && ptr2->data != ptr3->data) {
                        // check if triplet is distinct
                        // (i.e., all elements are unique)
                        tuple<int, int, int> triplet
                            = make_tuple(ptr1->data,
                                         ptr2->data,
                                         ptr3->data);
                        triplets.push_back(
                            triplet); // add triplet to the
                                      // vector
                    }
                }
                ptr3 = ptr3->next; // move ptr3 to its next
                                   // node
            }
            ptr2 = ptr2->next; // move ptr2 to its next node
        }
        ptr1 = ptr1->next; // move ptr1 to its next node
    }
    return triplets; // return the vector of triplets
}

// main function to test the code
int main()
{
    Node* head = new Node(1);
    head->next = new Node(2);
    head->next->next = new Node(4);
    head->next->next->next = new Node(5);
    head->next->next->next->next = new Node(6);
    head->next->next->next->next->next = new Node(8);
    head->next->next->next->next->next->next = new Node(9);
    int S = 15;
    vector<tuple<int, int, int> > triplets
        = findTriplets(head, S);
    for (auto triplet : triplets) {
        cout << "(" << get<0>(triplet) << ", "
             << get<1>(triplet) << ", " << get<2>(triplet)
             << ")" << endl;
    }
    return 0;
}

Output

(1, 5, 9)
(1, 6, 8)
(2, 4, 9)
(2, 5, 8)
(4, 5, 6)

Time Complexity: O(N³)
Auxiliary Space: O(N³)

Efficient Approach: Use the concept of hashing to efficiently solve the problem. Follow the steps mentioned below

1. Create a hash array to store the scanned node data.
2. Insert head node value into the hash array.
3. Now start traversing the linked list using nested loops, and in each iteration:
   • Subtract the data of both the nodes from the given integer ‘S’ to find the value which makes the triplet.
   • Now find that value in the hash array.
   • If that value is present in the hash array(i. e. triplet is found), then store the triplet in a list as a possible answer.
4. Return the list.

Below is the implementation of the above approach:

C++

// C++ code to find
// all distinct triplets having sum S
#include <bits/stdc++.h>
using namespace std;

// Structure of node of singly linked list
struct Node {
    int data;
    Node* next;
    Node(int x)
    {
        data = x;
        next = NULL;
    }
};

// Inserting new node
// at the  beginning of the linked list
void push(struct Node** head_ref,
          int new_data)
{
    // Create a new node with the given data.
    struct Node* new_node
      = new Node(new_data);

    // Make the new node point to the head.
    new_node->next = (*head_ref);

    // Make the new node as the head node.
    (*head_ref) = new_node;
}

// Function to print triplets
// in a sorted singly linked list
// whose sum is equal to given value 'S'
vector<vector<int>>
  printTriplets(struct Node* head, int S)
{
    // Declare unordered map
    // to store the scanned value
    unordered_map<int, bool> mp;

    // Vector to store the triplets
    vector<vector<int>> v;

    // Declare two pointers 'p' and 'q'
    // for traversing singly linked list
    struct Node* p;
    struct Node* q;

    // Insert 1st node data into map
    // and start traversing from next node
    mp[head->data] = true;

    // Outer loop terminates
    // when last node reached
    for (p = head->next; p->next != NULL;
         p = p->next) {

        // Inner loop terminates
        // when second pointer become NULL
        for (q = p->next; q != NULL;
             q = q->next) {

            // Temporary vector
            // to store the current triplet
            vector<int> temp;
            int second = p->data;
            int third = q->data;

            // find the number required
            // to make triplet by subtracting
            // node1 and node2 data from S
            // and store it.
            int first = S - second - third;

            // Search if that value
            // is present in the map or not
            if (mp.find(first)
                != mp.end()) {

                // If 'first' is present
                // in map, make a triplet of
                // first,second & third
                temp.push_back(mp.find(first)->first);
                temp.push_back(second);
                temp.push_back(third);

                // Push current triplet
                // stored in 'temp' to
                // vector 'v'
                v.push_back(temp);
            }
        }

        // Insert current node data into map
        mp[p->data] = true;
    }

    // Return a vector of triplets.
    return v;
}

// Driver code
int main()
{
    int S = 15;

    // Create an empty singly linked list
    struct Node* head = NULL;
    vector<vector<int> > ans;

    // Insert values in sorted order
    push(&head, 9);
    push(&head, 8);
    push(&head, 6);
    push(&head, 5);
    push(&head, 4);
    push(&head, 2);
    push(&head, 1);

    // Call printTriplets function
    // to find all triplets in
    // the linked list
    ans = printTriplets(head, S);

    // Sort and  display
    // all possible triplets
    sort(ans.begin(), ans.end());
    for (int i = 0; i < ans.size(); i++) {
        for (int j = 0;
             j < ans[i].size(); j++) {
            cout << ans[i][j] << " ";
        }
        cout << "\n";
    }
    return 0;
}

Java

// Java code to find
// all distinct triplets having sum S
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;

class GFG
{

    // Structure of node of singly linked list
    static class Node {
        int data;
        Node next;

        public Node(int x) {
            data = x;
            next = null;
        }
    };

    // Function to print triplets
    // in a sorted singly linked list
    // whose sum is equal to given value 'S'
    public static ArrayList<ArrayList<Integer>> printTriplets(Node head, int S) {
        // Declare unordered map
        // to store the scanned value
        HashMap<Integer, Boolean> mp = new HashMap<Integer, Boolean>();

        // Vector to store the triplets
        ArrayList<ArrayList<Integer>> v = new ArrayList<ArrayList<Integer>>();

        // Declare two pointers 'p' and 'q'
        // for traversing singly linked list
        Node p;
        Node q;

        // Insert 1st node data into map
        // and start traversing from next node
        mp.put(head.data, true);

        // Outer loop terminates
        // when last node reached
        for (p = head.next; p.next != null; p = p.next) {

            // Inner loop terminates
            // when second pointer become null
            for (q = p.next; q != null; q = q.next) {

                // Temporary vector
                // to store the current triplet
                ArrayList<Integer> temp = new ArrayList<Integer>();
                int second = p.data;
                int third = q.data;

                // find the number required
                // to make triplet by subtracting
                // node1 and node2 data from S
                // and store it.
                int first = S - second - third;

                // Search if that value
                // is present in the map or not
                if (mp.containsKey(first)) {

                    // If 'first' is present
                    // in map, make a triplet of
                    // first,second & third
                    temp.add(first);
                    temp.add(second);
                    temp.add(third);

                    // Push current triplet
                    // stored in 'temp' to
                    // vector 'v'
                    v.add(temp);
                }
            }

            // Insert current node data into map
            mp.put(p.data, true);
        }

        // Return a vector of triplets.
        return v;
    }

    // Driver code
    public static void main(String args[]) {
        int S = 15;

        // Create an empty singly linked list
        Node head = null;
        ArrayList<ArrayList<Integer>> ans = new ArrayList<ArrayList<Integer>>();

        // Insert values in sorted order
        head = new Node(9);
        head.next = new Node(8);
        head.next.next = new Node(6);
        head.next.next.next = new Node(5);
        head.next.next.next.next = new Node(4);
        head.next.next.next.next.next = new Node(2);
        head.next.next.next.next.next.next = new Node(1);

        // Call printTriplets function
        // to find all triplets in
        // the linked list
        ans = printTriplets(head, S);

        // Sort and display
        // all possible triplets
        for (ArrayList<Integer> x : ans) {
            Collections.sort(x);
        }

        Collections.sort(ans, new Comparator<ArrayList<Integer>>() {
            @Override
            public int compare(ArrayList<Integer> o1, ArrayList<Integer> o2) {
                return o2.get(0) - (o1.get(0));
            }
        });
        Collections.reverse(ans);

        for (int i = 0; i < ans.size(); i++) {
            for (int j = 0; j < ans.get(i).size(); j++) {
                System.out.print(ans.get(i).get(j) + " ");
            }
            System.out.println("");
        }
    }
}

// This code is contributed by gfgking.

Python3

# Python code to find all distinct triplets having sum S

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

def printTriplets(head, S):
    # Declare a dictionary
    # to store the scanned value
    mp = {}

    # List to store the triplets
    v = []

    # Declare two pointers 'p' and 'q'
    # for traversing singly linked list
    p = head
    q = head.next

    # Insert 1st node data into map
    # and start traversing from next node
    mp[head.data] = True

    # Outer loop terminates
    # when last node reached
    while q:
        if q:
            # Inner loop terminates
            # when second pointer become None
            r = q.next
            while r:
                # Temporary list
                # to store the current triplet
                temp = []
                second = q.data
                third = r.data

                # find the number required
                # to make triplet by subtracting
                # node1 and node2 data from S
                # and store it.
                first = S - second - third

                # Search if that value
                # is present in the map or not
                if first in mp:
                    # If 'first' is present
                    # in map, make a triplet of
                    # first,second & third
                    temp.append(first)
                    temp.append(second)
                    temp.append(third)
                    v.append(temp)
                r = r.next
            if q:
                mp[q.data] = True
            q = q.next

    # Return a list of triplets.
    return v

# Driver code
if __name__ == '__main__':
    S = 15

    # Create an empty singly linked list
    head = Node(9)
    head.next = Node(8)
    head.next.next = Node(6)
    head.next.next.next = Node(5)
    head.next.next.next.next = Node(4)
    head.next.next.next.next.next = Node(2)
    head.next.next.next.next.next.next = Node(1)

    # Call printTriplets function
    # to find all triplets in
    # the linked list
    ans = printTriplets(head, S)

    # Sort and display
    # all possible triplets
    for i in ans:
        i.sort()
    ans.sort(key=lambda x: (x[0], x[1], x[2]))
    for i in ans:
        for j in i:
              print(j, end = ' ')
        print()

# This code is contributed by lokeshmvs21.

C#

// C# code to find all distinct
// triplets having sum S

using System;
using System.Collections.Generic;
using System.Linq;

public class GFG {

    // Structure of node of singly linked list
    class Node {
        public int data;
        public Node next;

        public Node(int x)
        {
            data = x;
            next = null;
        }
    }

    // Function to print triplets
    // in a sorted singly linked list
    // whose sum is equal to given value 'S'
    static List<List<int> > PrintTriplets(Node head, int S)
    {
        // Declare unordered map
        // to store the scanned value
        var mp = new Dictionary<int, bool>();

        // Vector to store the triplets
        var v = new List<List<int> >();

        // Declare two pointers 'p' and 'q'
        // for traversing singly linked list
        Node p;
        Node q;

        // Insert 1st node data into map
        // and start traversing from next node
        mp.Add(head.data, true);

        // Outer loop terminates
        // when last node reached
        for (p = head.next; p.next != null; p = p.next) {
            // Inner loop terminates
            // when second pointer become null
            for (q = p.next; q != null; q = q.next) {
                // Temporary vector
                // to store the current triplet
                var temp = new List<int>();
                int second = p.data;
                int third = q.data;

                // find the number required
                // to make triplet by subtracting
                // node1 and node2 data from S
                // and store it.
                int first = S - second - third;

                // Search if that value
                // is present in the map or not
                if (mp.ContainsKey(first)) {
                    // If 'first' is present
                    // in map, make a triplet of
                    // first,second & third
                    temp.Add(first);
                    temp.Add(second);
                    temp.Add(third);

                    // Push current triplet
                    // stored in 'temp' to
                    // vector 'v'
                    v.Add(temp);
                }
            }

            // Insert current node data into map
            mp.Add(p.data, true);
        }

        // Return a vector of triplets.
        return v;
    }

    static public void Main()
    {

        // Code
        int S = 15;

        // Create an empty singly linked list
        Node head = null;
        var ans = new List<List<int> >();

        // Insert values in sorted order
        head = new Node(9);
        head.next = new Node(8);
        head.next.next = new Node(6);
        head.next.next.next = new Node(5);
        head.next.next.next.next = new Node(4);
        head.next.next.next.next.next = new Node(2);
        head.next.next.next.next.next.next = new Node(1);

        // Call printTriplets function
        // to find all triplets in
        // the linked list
        ans = PrintTriplets(head, S);

        // Sort and display
        // all possible triplets
        foreach(var x in ans) { x.Sort(); }

        ans = ans.OrderBy(x = > x[0])
                  .ThenBy(x = > x[1])
                  .ThenBy(x = > x[2])
                  .ToList();

        for (int i = 0; i < ans.Count; i++) {
            for (int j = 0; j < ans[i].Count; j++) {
                Console.Write(ans[i][j] + " ");
            }
            Console.WriteLine();
        }
    }
}

// This code is contributed by lokesh.

Javascript

<script>

      // JavaScript Program to implement
      // the above approach

      // Structure of node of singly linked list
      class Node {

          constructor(x) {
              this.data = x;
              this.next = null;
          }
      };

      // Function to print triplets
      // in a sorted singly linked list
      // whose sum is equal to given value 'S'
      function printTriplets(head, S)
      {

          // Declare unordered map
          // to store the scanned value
          let mp = new Map();

          // Vector to store the triplets
          let v = [];

          // Declare two pointers 'p' and 'q'
          // for traversing singly linked list
          let p;
          let q;

          // Insert 1st node data into map
          // and start traversing from next node
          mp.set(head.data, true);

          // Outer loop terminates
          // when last node reached
          for (p = head.next; p.next != null;
              p = p.next) {

              // Inner loop terminates
              // when second pointer become null
              for (q = p.next; q != null;
                  q = q.next) {

                  // Temporary vector
                  // to store the current triplet
                  let temp = [];
                  let second = p.data;
                  let third = q.data;

                  // find the number required
                  // to make triplet by subtracting
                  // node1 and node2 data from S
                  // and store it.
                  let first = S - second - third;

                  // Search if that value
                  // is present in the map or not
                  if (mp.has(first)) {

                      // If 'first' is present
                      // in map, make a triplet of
                      // first,second & third
                      temp.push(first);
                      temp.push(second);
                      temp.push(third);

                      // Push current triplet
                      // stored in 'temp' to
                      // vector 'v'
                      v.push(temp);
                  }
              }

              // Insert current node data into map
              mp.set(p.data, true);
          }

          // Return a vector of triplets.
          return v;
      }

      // Driver code
      let S = 15;

      // Create an empty singly linked list
      let head = null;
      let ans = [];

      // Insert values in sorted order
      head = new Node(9)
      head.next = new Node(8)
      head.next.next = new Node(6)
      head.next.next.next = new Node(5)
      head.next.next.next.next = new Node(4)
      head.next.next.next.next.next = new Node(2)
      head.next.next.next.next.next.next = new Node(1)

      // Call printTriplets function
      // to find all triplets in
      // the linked list
      ans = printTriplets(head, S);

      // Sort and  display
      // all possible triplets
      for (let i = 0; i < ans.length; i++) {

          ans[i].sort(function (a, b) { return a - b })
      }
      ans.sort()
      for (let i = 0; i < ans.length; i++) {
          for (let j = 0;
              j < ans[i].length; j++) {
              document.write(ans[i][j] + " ");
          }
          document.write('<br>')
      }

  // This code is contributed by Potta Lokesh
  </script>

Output

1 5 9 
1 6 8 
2 4 9 
2 5 8 
4 5 6 

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