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3785. Minimum Swaps to Avoid Forbidden Values

Description

You are given two integer arrays, nums and forbidden, each of length n.

You may perform the following operation any number of times (including zero):

  • Choose two distinct indices i and j, and swap nums[i] with nums[j].

Return the minimum number of swaps required such that, for every index i, the value of nums[i] is not equal to forbidden[i]. If no amount of swaps can ensure that every index avoids its forbidden value, return -1.

 

Example 1:

Input: nums = [1,2,3], forbidden = [3,2,1]

Output: 1

Explanation:

One optimal set of swaps:

  • Select indices i = 0 and j = 1 in nums and swap them, resulting in nums = [2, 1, 3].
  • After this swap, for every index i, nums[i] is not equal to forbidden[i].

Example 2:

Input: nums = [4,6,6,5], forbidden = [4,6,5,5]

Output: 2

Explanation:

One optimal set of swaps:
  • Select indices i = 0 and j = 2 in nums and swap them, resulting in nums = [6, 6, 4, 5].
  • Select indices i = 1 and j = 3 in nums and swap them, resulting in nums = [6, 5, 4, 6].
  • After these swaps, for every index i, nums[i] is not equal to forbidden[i].

Example 3:

Input: nums = [7,7], forbidden = [8,7]

Output: -1

Explanation:

It is not possible to make nums[i] different from forbidden[i] for all indices.

Example 4:

Input: nums = [1,2], forbidden = [2,1]

Output: 0

Explanation:

No swaps are required because nums[i] is already different from forbidden[i] for all indices, so the answer is 0.

 

Constraints:

  • 1 <= n == nums.length == forbidden.length <= 105
  • 1 <= nums[i], forbidden[i] <= 109

Solutions

Solution 1

Thinking

A conflict is an index with \(nums[i]=forbidden[i]\). If a value has no safe destination among those indices, the instance is impossible. Conflicts are resolved by swapping among themselves; the minimum number of swaps is determined by the number of conflicts (with the \(0\)/\(1\) cases handled separately).

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