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Gary and multiplication

Last Updated: 11 Oct, 2020
Difficulty: Easy


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Gary has recently learned about priority queues and is quite excited about them. He has asked his teacher for an interesting problem. So, his teacher came up with a simple problem.

The problem is that he now has an integer array 'ARR'. For every index i, he wants to find the product of the largest, second largest and the third largest integer in the range [0, i] given that array has 0 based indexing.

You have to return the list as required.

Note: Two numbers can be the same value-wise but they should be distinct index-wise.

If the array is [2, 3, 3, 4], the answer should be:-

18 (3 * 3 * 2)
36 (4 * 3 * 3) 
Input format:
The first line of input contains a single integer T, representing the number of test cases or queries to be run. 

Then the T test cases follow.

The first line of each test case contains an integer N, representing the number of elements in the array.

The second line contains N single space-separated integers X[0],X[1],X[2].... X[N-1] where X[i] is an element of the array.
Output format:
For each test case, return the required list. If there is no second largest or third largest number in the array X up to that index then print "-1", without the quotes.
You do not need to print anything. It has already been taken care of. Just implement the given function.
1 <= T <= 5
1 <= N <= 10^5 
1 <= X[i] <= 10^6 

Time limit: 1 sec

Approach 1

  1. The idea is to work with the max priority queue.
  2. Insert the elements of array ‘ARR’ one by one.
  3. Once you add the element, extract 3 elements from the max priority queue. They will, of course, be largest (the one extracted the first time), second largest (the one extracted the second time) and third largest (the one extracted the third time).
  4. It should be noted that while executing point 3, one should take care of the time when the size of the priority queue will be less than 2.
  5. Now, all you need to do is find the product of the three numbers and print the answer.
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