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2717. Semi-Ordered Permutation

Easy

You are given a 0-indexed permutation of n integers nums.

A permutation is called semi-ordered if the first number equals 1 and the last number equals n. You can perform the below operation as many times as you want until you make nums a semi-ordered permutation:

Pick two adjacent elements in nums, then swap them. Return the minimum number of operations to make nums a semi-ordered permutation.

A permutation is a sequence of integers from 1 to n of length n containing each number exactly once.

Example 1:

Input: nums = [2,1,4,3]
Output: 2
Explanation: We can make the permutation semi-ordered using these sequence of operations: 
1 - swap i = 0 and j = 1. The permutation becomes [1,2,4,3].
2 - swap i = 2 and j = 3. The permutation becomes [1,2,3,4].
It can be proved that there is no sequence of less than two operations that make nums a semi-ordered permutation.

Example 2:

Input: nums = [2,4,1,3]
Output: 3
Explanation: We can make the permutation semi-ordered using these sequence of operations:
1 - swap i = 1 and j = 2. The permutation becomes [2,1,4,3].
2 - swap i = 0 and j = 1. The permutation becomes [1,2,4,3].
3 - swap i = 2 and j = 3. The permutation becomes [1,2,3,4].
It can be proved that there is no sequence of less than three operations that make nums a semi-ordered permutation.

Example 3:

Input: nums = [1,3,4,2,5]
Output: 0
Explanation: The permutation is already a semi-ordered permutation.

Constraints:

  • 2 <= nums.length == n <= 50
  • 1 <= nums[i] <= 50
  • nums is a permutation.

Solution

class Solution:
    def semiOrderedPermutation(self, nums: List[int]) -> int:
        n = len(nums)
        idx_1 = nums.index(1)
        idx_n = nums.index(n)

        return idx_1 + (n - 1 - idx_n) - int(idx_1 > idx_n)