Question

2499. Minimum Total Cost to Make Arrays Unequal

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Description

You are given two 0-indexed integer arrays nums1 and nums2, of equal length n.

In one operation, you can swap the values of any two indices of nums1. The cost of this operation is the sum of the indices.

Find the minimum total cost of performing the given operation any number of times such that nums1[i] != nums2[i] for all 0 <= i <= n - 1 after performing all the operations.

Return _the minimum total cost such that _nums1 and nums2_ satisfy the above condition_. In case it is not possible, return -1.

 

Example 1:

Input: nums1 = [1,2,3,4,5], nums2 = [1,2,3,4,5]
Output: 10
Explanation: 
One of the ways we can perform the operations is:
- Swap values at indices 0 and 3, incurring cost = 0 + 3 = 3. Now, nums1 = [4,2,3,1,5]
- Swap values at indices 1 and 2, incurring cost = 1 + 2 = 3. Now, nums1 = [4,3,2,1,5].
- Swap values at indices 0 and 4, incurring cost = 0 + 4 = 4. Now, nums1 =[5,3,2,1,4].
We can see that for each index i, nums1[i] != nums2[i]. The cost required here is 10.
Note that there are other ways to swap values, but it can be proven that it is not possible to obtain a cost less than 10.

Example 2:

Input: nums1 = [2,2,2,1,3], nums2 = [1,2,2,3,3]
Output: 10
Explanation: 
One of the ways we can perform the operations is:
- Swap values at indices 2 and 3, incurring cost = 2 + 3 = 5. Now, nums1 = [2,2,1,2,3].
- Swap values at indices 1 and 4, incurring cost = 1 + 4 = 5. Now, nums1 = [2,3,1,2,2].
The total cost needed here is 10, which is the minimum possible.

Example 3:

Input: nums1 = [1,2,2], nums2 = [1,2,2]
Output: -1
Explanation: 
It can be shown that it is not possible to satisfy the given conditions irrespective of the number of operations we perform.
Hence, we return -1.

 

Constraints:

• n == nums1.length == nums2.length
• 1 <= n <= 105
• 1 <= nums1[i], nums2[i] <= n

Solutions

Solution 1

class Solution:
  def minimumTotalCost(self, nums1: List[int], nums2: List[int]) -> int:
    ans = same = 0
    cnt = Counter()
    for i, (a, b) in enumerate(zip(nums1, nums2)):
      if a == b:
        same += 1
        ans += i
        cnt[a] += 1

    m = lead = 0
    for k, v in cnt.items():
      if v * 2 > same:
        m = v * 2 - same
        lead = k
        break
    for i, (a, b) in enumerate(zip(nums1, nums2)):
      if m and a != b and a != lead and b != lead:
        ans += i
        m -= 1
    return -1 if m else ans

class Solution {
  public long minimumTotalCost(int[] nums1, int[] nums2) {
    long ans = 0;
    int same = 0;
    int n = nums1.length;
    int[] cnt = new int[n + 1];
    for (int i = 0; i < n; ++i) {
      if (nums1[i] == nums2[i]) {
        ans += i;
        ++same;
        ++cnt[nums1[i]];
      }
    }
    int m = 0, lead = 0;
    for (int i = 0; i < cnt.length; ++i) {
      int t = cnt[i] * 2 - same;
      if (t > 0) {
        m = t;
        lead = i;
        break;
      }
    }
    for (int i = 0; i < n; ++i) {
      if (m > 0 && nums1[i] != nums2[i] && nums1[i] != lead && nums2[i] != lead) {
        ans += i;
        --m;
      }
    }
    return m > 0 ? -1 : ans;
  }
}

class Solution {
public:
  long long minimumTotalCost(vector<int>& nums1, vector<int>& nums2) {
    long long ans = 0;
    int same = 0;
    int n = nums1.size();
    int cnt[n + 1];
    memset(cnt, 0, sizeof cnt);
    for (int i = 0; i < n; ++i) {
      if (nums1[i] == nums2[i]) {
        ans += i;
        ++same;
        ++cnt[nums1[i]];
      }
    }
    int m = 0, lead = 0;
    for (int i = 0; i < n + 1; ++i) {
      int t = cnt[i] * 2 - same;
      if (t > 0) {
        m = t;
        lead = i;
        break;
      }
    }
    for (int i = 0; i < n; ++i) {
      if (m > 0 && nums1[i] != nums2[i] && nums1[i] != lead && nums2[i] != lead) {
        ans += i;
        --m;
      }
    }
    return m > 0 ? -1 : ans;
  }
};

func minimumTotalCost(nums1 []int, nums2 []int) (ans int64) {
  same, n := 0, len(nums1)
  cnt := make([]int, n+1)
  for i, a := range nums1 {
    b := nums2[i]
    if a == b {
      same++
      ans += int64(i)
      cnt[a]++
    }
  }
  var m, lead int
  for i, v := range cnt {
    if t := v*2 - same; t > 0 {
      m = t
      lead = i
      break
    }
  }
  for i, a := range nums1 {
    b := nums2[i]
    if m > 0 && a != b && a != lead && b != lead {
      ans += int64(i)
      m--
    }
  }
  if m > 0 {
    return -1
  }
  return ans
}