1806. Minimum Number of Operations to Reinitialize a Permutation

Description

You are given an even integer n​​​​​​. You initially have a permutation perm of size n​​ where perm[i] == i​ (0-indexed)​​​​.

In one operation, you will create a new array arr, and for each i:

• If i % 2 == 0, then arr[i] = perm[i / 2].
• If i % 2 == 1, then arr[i] = perm[n / 2 + (i - 1) / 2].

You will then assign arr​​​​ to perm.

Return the minimum non-zero number of operations you need to perform on perm to return the permutation to its initial value.

 

Example 1:

Input: n = 2
Output: 1
Explanation: perm = [0,1] initially.
After the 1st operation, perm = [0,1]
So it takes only 1 operation.

Example 2:

Input: n = 4
Output: 2
Explanation: perm = [0,1,2,3] initially.
After the 1st operation, perm = [0,2,1,3]
After the 2nd operation, perm = [0,1,2,3]
So it takes only 2 operations.

Example 3:

Input: n = 6
Output: 4

 

Constraints:

• 2 <= n <= 1000
• n​​​​​​ is even.

 

Solutions

Solution: simulation

• Time complexity: O(n)
• Space complexity: O(1)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const reinitializePermutation = function (n) {
  const BASE_INDEX = 1;
  let result = 1;
  let index = n / 2 + (BASE_INDEX - 1) / 2;

  while (index !== BASE_INDEX) {
    index = index % 2 ? n / 2 + (index - 1) / 2 : index / 2;
    result += 1;
  }
  return result;
};