Minimum Operations to Make Array Values Equal to K

Problem Description

You are given an integer array nums and an integer k. An integer h is called valid if all values in the array that are strictly greater than h are identical. You are allowed to perform operations to set all elements in nums equal to k. Return the minimum number of operations required to achieve this, or -1 if it is impossible.

Key Insights

• A valid integer h must ensure that all numbers greater than h in the array are the same.
• If k is greater than the maximum value in nums, it's impossible to make all elements equal to k.
• The operations can be performed in decreasing order of valid integers starting from the largest distinct value in nums down to k.
• Each operation reduces the number of distinct values in nums, simplifying the problem in each step.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the distinct elements in nums. Space Complexity: O(n) - for storing distinct elements.

Solution

To solve the problem, we can follow these steps:

1. Identify the distinct elements in the array nums.
2. Sort these elements in descending order.
3. Iterate through the sorted list, performing operations to set elements greater than the current valid integer to that integer.
4. Count the number of operations until all elements are equal to k or determine if it's impossible.

We can use a list to store distinct values and a counter to track the number of operations.

Code Solutions