Partition Array Such That Maximum Difference Is K
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.
A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
Example 1:
Input: nums = [3,6,1,2,5], k = 2
Output: 2
Explanation: We can partition nums into the two subsequences [3,1,2] and [6,5]. The difference between the maximum and minimum value in the first subsequence is 3 - 1 = 2. The difference between the maximum and minimum value in the second subsequence is 6 - 5 = 1. Since two subsequences were created, we return 2. It can be shown that 2 is the minimum number of subsequences needed.Example 2:
Input: nums = [1,2,3], k = 1
Output: 2
Explanation: We can partition nums into the two subsequences [1,2] and [3]. The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1. The difference between the maximum and minimum value in the second subsequence is 3 - 3 = 0. Since two subsequences were created, we return 2. Another optimal solution is to partition nums into [1] and [2,3].Example 3:
Input: nums = [2,2,4,5], k = 0
Output: 3
Explanation: We can partition nums into the three subsequences [2,2], [4], and [5]. The difference between the maximum and minimum value in the first subsequence is 2 - 2 = 0. The difference between the maximum and minimum value in the second subsequence is 4 - 4 = 0. The difference between the maximum and minimum value in the third subsequence is 5 - 5 = 0. Since three subsequences were created, we return 3. It can be shown that 3 is the minimum number of subsequences needed.Constraints:
1 <= nums.length <= 10^5
The key idea is greedy grouping after sorting the array: build each subsequence from consecutive values as long as the difference between the current minimum and maximum stays within k. Once adding the next number would exceed k, start a new subsequence. This turns the problem into counting how many valid groups are needed in one left-to-right pass over the sorted array. The standard solution runs in O(n log n) time due to sorting and uses constant or near-constant extra space depending on the sort implementation.
