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1{2  "id": 2387,3  "name": "partition-array-such-that-maximum-difference-is-k",4  "difficulty": "Medium",5  "link": "https://leetcode.com/problems/partition-array-such-that-maximum-difference-is-k/",6  "date": "2022-05-29",7  "task_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`_._ 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. Note that another optimal solution is to partition nums into the two subsequences [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 subsequences is 2 - 2 = 0. The difference between the maximum and minimum value in the second subsequences is 4 - 4 = 0. The difference between the maximum and minimum value in the third subsequences 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 <= 105` `0 <= nums[i] <= 105` `0 <= k <= 105`",8  "test_case": [9    {10      "label": "Example 1",11      "input": "nums = [3,6,1,2,5], k = 2",12      "output": "2 "13    },14    {15      "label": "Example 2",16      "input": "nums = [1,2,3], k = 1",17      "output": "2 "18    },19    {20      "label": "Example 3",21      "input": "nums = [2,2,4,5], k = 0",22      "output": "3 "23    }24  ],25  "constraints": [26    "1 <= nums.length <= 105",27    "0 <= nums[i] <= 105",28    "0 <= k <= 105"29  ],30  "python_template": "class Solution(object):\n    def partitionArray(self, nums, k):\n        \"\"\"\n        :type nums: List[int]\n        :type k: int\n        :rtype: int\n        \"\"\"\n        ",31  "java_template": "class Solution {\n    public int partitionArray(int[] nums, int k) {\n        \n    }\n}",32  "metadata": {33    "func_name": "partitionArray"34  }35}