1806. Minimum Number of Operations to Reinitialize a Permutation

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.

Rust Solution

struct Solution;

impl Solution {
    fn reinitialize_permutation(n: i32) -> i32 {
        if n == 2 {
            return 1;
        }
        let mut res = 0;
        let mut i = 1;
        while res == 0 || i != 1 {
            if i % 2 == 0 {
                i /= 2;
            } else {
                i = (n - 1 + i) / 2;
            }
            res += 1;
        }
        res
    }
}

#[test]
fn test() {
    let n = 2;
    let res = 1;
    assert_eq!(Solution::reinitialize_permutation(n), res);
    let n = 4;
    let res = 2;
    assert_eq!(Solution::reinitialize_permutation(n), res);
    let n = 6;
    let res = 4;
    assert_eq!(Solution::reinitialize_permutation(n), res);
}

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