Partition Array Such That Maximum Difference Is K

Problem Description

You are given an integer array nums and an integer k. You may partition nums into one or more subsequences such that each element in nums appears in exactly one of the subsequences. Return the minimum number of subsequences needed such that the difference between the maximum and minimum values in each subsequence is at most k.

Key Insights

• The problem requires partitioning an array into subsequences with constraints on the maximum difference between elements within each subsequence.
• A sorted version of the array can help in efficiently determining valid subsequences.
• A greedy approach can be used, where we try to include as many elements as possible into a single subsequence until the difference constraint is violated.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array. Space Complexity: O(1) - as we are using constant space for additional variables.

Solution

To solve the problem, we can follow these steps:

1. Sort the array to bring elements closer together that can be part of the same subsequence.
2. Initialize a counter for the number of subsequences needed.
3. Iterate through the sorted array and keep track of the minimum and maximum values in the current subsequence.
4. Whenever the difference between the maximum and minimum exceeds k, increment the subsequence counter and start a new subsequence.
5. Continue until all elements are accounted for.

The main data structure used here is an array for sorting, and we utilize a greedy algorithm to minimize the number of subsequences.

Code Solutions