Sync LeetCode submission Runtime - 75 ms (92.99%), Memory - 29.1 MB (73.61%)

Author: jimit105

2387-partition-array-such-that-maximum-difference-is-k/README.md

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+<p>You are given an integer array <code>nums</code> and an integer <code>k</code>. You may partition <code>nums</code> into one or more <strong>subsequences</strong> such that each element in <code>nums</code> appears in <strong>exactly</strong> one of the subsequences.</p>
+
+<p>Return <em>the <strong>minimum </strong>number of subsequences needed such that the difference between the maximum and minimum values in each subsequence is <strong>at most</strong> </em><code>k</code><em>.</em></p>
+
+<p>A <strong>subsequence</strong> is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> nums = [3,6,1,2,5], k = 2
+<strong>Output:</strong> 2
+<strong>Explanation:</strong>
+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.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> nums = [1,2,3], k = 1
+<strong>Output:</strong> 2
+<strong>Explanation:</strong>
+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].
+</pre>
+
+<p><strong class="example">Example 3:</strong></p>
+
+<pre>
+<strong>Input:</strong> nums = [2,2,4,5], k = 0
+<strong>Output:</strong> 3
+<strong>Explanation:</strong>
+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.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= k &lt;= 10<sup>5</sup></code></li>
+</ul>

2387-partition-array-such-that-maximum-difference-is-k/solution.py

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+# Approach: Sort + Greedy
+
+# Time: O(n log n)
+# Space: O(n)
+
+class Solution:
+    def partitionArray(self, nums: List[int], k: int) -> int:
+        nums.sort()
+        ans = 1
+        rec = nums[0]
+
+        for num in nums:
+            if num - rec > k:
+                ans += 1
+                rec = num
+        
+        return ans
+