# [Solved] The power of an integer x is defined as the number of steps needed to transform x into 1 using the following steps: if x is even then x = x / 2

Table of Contents

## Question

The power of an integer `x` is defined as the number of steps needed to transform `x` into `1` using the following steps:

• if `x` is even then `x = x / 2`
• if `x` is odd then `x = 3 * x + 1`

For example, the power of `x = 3` is `7` because `3` needs `7` steps to become `1` (`3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1`).

Given three integers `lo``hi` and `k`. The task is to sort all integers in the interval `[lo, hi]` by the power value in ascending order, if two or more integers have the same power value sort them by ascending order.

Return the `kth` integer in the range `[lo, hi]` sorted by the power value.

Notice that for any integer `x` `(lo <= x <= hi)` it is guaranteed that `x` will transform into `1` using these steps and that the power of `x` is will fit in a 32-bit signed integer.

Example 1:

```Input: lo = 12, hi = 15, k = 2
Output: 13
Explanation: The power of 12 is 9 (12 --> 6 --> 3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1)
The power of 13 is 9
The power of 14 is 17
The power of 15 is 17
The interval sorted by the power value [12,13,14,15]. For k = 2 answer is the second element which is 13.
Notice that 12 and 13 have the same power value and we sorted them in ascending order. Same for 14 and 15.
```

Example 2:

```Input: lo = 7, hi = 11, k = 4
Output: 7
Explanation: The power array corresponding to the interval [7, 8, 9, 10, 11] is [16, 3, 19, 6, 14].
The interval sorted by power is [8, 10, 11, 7, 9].
The fourth number in the sorted array is 7.
```

Constraints:

• `1 <= lo <= hi <= 1000`
• `1 <= k <= hi - lo + 1`

## Python Solution

```def power(x):
c = 0
while x!=1:
if x%2==0:
c+=1
x//=2
else:
c+=1
x = 3*x +1
return c

class Solution:
def getKth(self, lo: int, hi: int, k: int) -> int:
return sorted(range(lo,hi+1),key=power)[k-1]```