Largest triplet product in a stream

Given a stream of integers represented as arr[]. For each index i from 0 to n-1, print the multiplication of largest, second largest, third largest element of the subarray arr[0…i]. If i < 2 print -1. 

Examples: 

Input : arr[] = {1, 2, 3, 4, 5}
Output :-1
        -1
         6
         24
         60
Explanation : for i = 2 only three elements 
are there {1, 2, 3} so answer is 6. For i = 3
largest three elements are {2, 3, 4} their
product is 2*3*4 = 24 ....so on            

We will use priority queue here. 

1. Insert arr[i] in the priority queue
2. As the top element in priority queue is largest so pop it and store it as x. Now the top element in the priority queue will be the second largest element in subarray arr[0…i] pop it and store as y. Now the top element is third largest element in subarray arr[0…i] so pop it and store it as z.
3. Print x*y*z
4. Reinsert x, y, z.

Below is the implementation of the above approach:

C++

// C++ implementation of largest triplet
// multiplication
#include <bits/stdc++.h>
using namespace std;

// Prints the product of three largest numbers
// in subarray arr[0..i]
void LargestTripletMultiplication(int arr[], int n)
{
    // call a priority queue
    priority_queue<int> q;

    // traversing the array
    for (int i = 0; i < n; i++) {
        // pushing arr[i] in the array
        q.push(arr[i]);

        // if less than three elements are present
        // in array print -1
        if (q.size() < 3)
            cout << "-1" << endl;
        else {
            // pop three largest elements
            int x = q.top();
            q.pop();
            int y = q.top();
            q.pop();
            int z = q.top();
            q.pop();

            // Reinsert x, y, z in priority_queue
            int ans = x * y * z;
            cout << ans << endl;
            q.push(x);
            q.push(y);
            q.push(z);
        }
    }
    return;
}

// Driver Function
int main()
{
    int arr[] = { 1, 2, 3, 4, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);
    LargestTripletMultiplication(arr, n);
    return 0;
}

Java

// Java implementation of largest triplet
// multiplication
import java.util.Collections;
import java.util.PriorityQueue;

class GFG {

    // Prints the product of three largest numbers
    // in subarray arr[0..i]
    static void LargestTripletMultiplication(int arr[], int n)
    {
        // call a priority queue
        PriorityQueue<Integer> q = new PriorityQueue(Collections.reverseOrder());

        // traversing the array
        for (int i = 0; i < n; i++) {
            // pushing arr[i] in array
            q.add(arr[i]);

            // if less than three elements are present
            // in array print -1
            if (q.size() < 3)
                System.out.println("-1");
            else {
                // pop three largest elements
                int x = q.poll();
                int y = q.poll();
                int z = q.poll();

                // Reinsert x, y, z in priority_queue
                int ans = x * y * z;
                System.out.println(ans);
                q.add(x);
                q.add(y);
                q.add(z);
            }
        }
    }

    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, 4, 5 };
        int n = arr.length;
        LargestTripletMultiplication(arr, n);
    }
}

// This code is contributed by shubham96301

Python3

# Python3 implementation of largest triplet
# multiplication
from queue import PriorityQueue

# Prints the product of three largest
# numbers in subarray arr[0..i]
def LargestTripletMultiplication(arr, n):

    # Call a priority queue
    q = PriorityQueue()

    # Traversing the array
    for i in range(n):

        # Pushing -arr[i] in array
        # to get max PriorityQueue
        q.put(-arr[i])

        # If less than three elements
        # are present in array print -1
        if (q.qsize() < 3):
            print(-1)
        else:

            # pop three largest elements
            x = q.get()
            y = q.get()
            z = q.get()

            # Reinsert x, y, z in
            # priority_queue
            ans = x * y * z

            print(-ans)

            q.put(x);
            q.put(y);
            q.put(z);

# Driver Code
if __name__ == '__main__':

    arr = [ 1, 2, 3, 4, 5 ]
    n = len(arr)

    LargestTripletMultiplication(arr, n)

# This code is contributed by math_lover

C#

// C# implementation of largest triplet
// multiplication
using System;
using System.Collections.Generic;
public class GFG {

  // Prints the product of three largest numbers
  // in subarray arr[0..i]
  static void LargestTripletMultiplication(int []arr, int n)
  {
    // call a priority queue
    List<int> q = new List<int>();

    // traversing the array
    for (int i = 0; i < n; i++)
    {

      // pushing arr[i] in array
      q.Add(arr[i]);
      q.Sort();
      q.Reverse();

      // if less than three elements are present
      // in array print -1
      if (q.Count < 3)
        Console.WriteLine("-1");
      else
      {

        // pop three largest elements
        int x = q[0];
        int y = q[1];
        int z = q[2];
        q.RemoveRange(0, 3);

        // Reinsert x, y, z in priority_queue
        int ans = x * y * z;
        Console.WriteLine(ans);
        q.Add(x);
        q.Add(y);
        q.Add(z);
      }
    }
  }

  // Driver code
  public static void Main(String[] args)
  {
    int []arr = { 1, 2, 3, 4, 5 };
    int n = arr.Length;
    LargestTripletMultiplication(arr, n);
  }
}


// This code is contributed by Rajput-Ji

Javascript

<script>
// javascript implementation of largest triplet
// multiplication
    // Prints the product of three largest numbers
    // in subarray arr[0..i]
    function LargestTripletMultiplication(arr , n) {
        // call a priority queue
        var q = [];

        // traversing the array
        for (i = 0; i < n; i++) {
            // pushing arr[i] in array
            q.push(arr[i]);
q.sort();

            // if less than three elements are present
            // in array print -1
            if (q.length < 3)
                document.write("-1<br/>");
            else {
                // pop three largest elements
                q.sort();

                var x = q.pop();
                var y = q.pop();
                var z = q.pop();

                // Reinsert x, y, z in priority_queue
                var ans = x * y * z;
                document.write(ans+"<br/>");
                q.push(x);
                q.push(y);
                q.push(z);
                q.sort();
                q.reverse();
            }
        }
    }

    // Driver code

        var arr = [ 1, 2, 3, 4, 5 ];
        var n = arr.length;
        LargestTripletMultiplication(arr, n);

// This code contributed by umadevi9616
</script>

Output

-1
-1
6
24
60

Time Complexity: O(N * log N ).
Auxiliary Space: O(N), N is the length of the array.

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