Gary and multiplication

Easy

0/40

Average time to solve is 20m

15 upvotes

Asked in companies

Problem statement

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.

Example:

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

-1 
-1
18 (3 * 3 * 2)
36 (4 * 3 * 3)

Detailed explanation ( Input/output format, Notes, Images )

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.

Note:

You do not need to print anything. It has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 5
1 <= N <= 10^5 
1 <= X[i] <= 10^6 

Time limit: 1 sec

Sample input 1:

1
4  
2 3 1 4

Sample output 1:

-1 -1 6 24

Explanation

-1 (no second largest as well as third largest element is present)
-1 (no third largest element is present)
6 (3 * 2 * 1)
24 (4 * 3 * 2)

Sample input 2:

1
6 
1 5 7 3 9 12

Sample output 2:

1 -1 35 105 315 756

Hint 1

Hint 2

It is very clear from the question that it is a priority queue question. All we need to do is work on the first largest, second largest and third largest elements which makes it clear that the max priority queue will come to play.

Approaches (2)

Approach 1

Approach 2

Priority Queue

The idea is to work with the max priority queue.
Insert the elements of array ‘ARR’ one by one.
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).
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.
Now, all you need to do is find the product of the three numbers and print the answer.

Time Complexity

O(N * log N), where N is the size of the array.

In the worst case, we will be inserting all N elements in the priority queue O(N) and for each element, we will require only the top 3 elements from the priority queue (N * 3logN). Thus the overall time complexity will be O(N * logN).

Space Complexity

O(N), where N is the size of the array.

In the worst case, we are using a priority queue to store N elements.

(100% EXP penalty)

Gary and multiplication

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