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4099. Minimum Operations to Sort With Locked Indices
Medium

You are given an integer array nums of length n, where nums is a of the integers in the range [1, n].

You are also given a locked of length n and an integer k.

  • locked[i] = 1 means index i is locked.
  • locked[i] = 0 means index i is unlocked.

You may perform the following operations in any order:

  • Swap: Choose an index i such that both indices i and i + 1 are currently unlocked, and swap nums[i] and nums[i + 1].
  • Unlock: Choose an index i such that locked[i] = 1 and permanently unlock it by setting locked[i] = 0.

You may perform any number of swap operations but at most k unlock operations.

Return the minimum total number of operations required to sort nums in order. If it is impossible, return -1.

 

Example 1:

Input: nums = [2,1,3,4], locked = [0,1,0,1], k = 1

Output: 2

Explanation:

  • Unlock index 1. The array locked becomes [0,0,0,1].
  • Swap nums[0] and nums[1]. The array nums becomes [1,2,3,4].

The total number of operations is 1 + 1 = 2.

Example 2:

Input: nums = [3,1,2], locked = [1,0,1], k = 2

Output: 4

Explanation:

  • Unlock indices 0 and 2. All indices are now unlocked.
  • Swap indices 0 and 1. The array nums becomes [1,3,2].
  • Swap indices 1 and 2. The array nums becomes [1,2,3].

The total number of operations is 2 + 2 = 4.

Example 3:

Input: nums = [2,3,1], locked = [1,0,0], k = 0

Output: -1

Explanation:

Index 0 is locked, so its value cannot be moved. Since k = 0, no indices can be unlocked. Therefore, sorting the array is impossible.

 

Constraints:

  • 1 <= n == nums.length == locked.length <= 2000
  • 1 <= nums[i] <= n
  • 0 <= locked[i] <= 1
  • nums is a permutation of the integers in the range [1, n].
  • 0 <= k <= n

 

Can you solve this in O(nlog(n))?
 
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