# Sort Integers by Factor Value

Moderate
0/80
Average time to solve is 30m
Contributed by
1 upvote

## Problem statement

You have been given an array/list ‘ARR’ of integers consisting of ‘N’ integers. The factor value is the number of following operations it takes for the number to become 1.

The two operations are as follows:-

``````If ‘x’ is even then ‘x’ will become ‘x / 2’.

If ‘x’ is odd then ‘x’ will become ‘x * 3 + 1’.
``````

Your need to sort them in increasing order of factor value i.e. if two integers have the same factor value then sort in increasing order of their value. Your task is to return the ‘K-th’ value in the list after sorting.

Example:
``````Let’s say you have an array/list [1, 3, 4, 5] and ‘K’=2. The factor values are [0, 7, 2, 5] respectively. Finally, our array will look like [1, 4, 5, 3]. Since ‘K’ is 2 return 4.
``````
Detailed explanation ( Input/output format, Notes, Images )
Constraints:
``````1 <= T <= 10
1 <= N <= 1000
1 <= K <= N
1 <= ‘ARR[i]’ <= 10 ^ 4

Where ‘ARR[i]’ is an element of array/list ARR.

Time Limit: 1sec
``````
Sample Input 1:
``````2
4 4
1 2 3 4
2 1
13 12
``````
Sample Output 1:
``````3
12
``````

#### Sample Output 1 Explanation:

``````Test case 1:

The factor values of [1, 2, 3, 4] are [0, 1, 7, 2]. The array/list will become [1, 2, 4, 3] on sorting according to factor value.

Test case 2:

Both 12 and 13 have a factor value of 9. Since they have the same factor value we will sort them according to their value. Therefore on sorting ‘arr’ will be [12,13].

``````2
``````4