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53 lines
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53 lines
2.6 KiB
HTML
<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>
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<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>
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<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>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [3,6,1,2,5], k = 2
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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We can partition nums into the two subsequences [3,1,2] and [6,5].
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The difference between the maximum and minimum value in the first subsequence is 3 - 1 = 2.
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The difference between the maximum and minimum value in the second subsequence is 6 - 5 = 1.
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Since two subsequences were created, we return 2. It can be shown that 2 is the minimum number of subsequences needed.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3], k = 1
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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We can partition nums into the two subsequences [1,2] and [3].
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The difference between the maximum and minimum value in the first subsequence is 2 - 1 = 1.
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The difference between the maximum and minimum value in the second subsequence is 3 - 3 = 0.
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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].
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,2,4,5], k = 0
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<strong>Output:</strong> 3
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<strong>Explanation:</strong>
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We can partition nums into the three subsequences [2,2], [4], and [5].
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The difference between the maximum and minimum value in the first subsequences is 2 - 2 = 0.
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The difference between the maximum and minimum value in the second subsequences is 4 - 4 = 0.
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The difference between the maximum and minimum value in the third subsequences is 5 - 5 = 0.
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Since three subsequences were created, we return 3. It can be shown that 3 is the minimum number of subsequences needed.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>0 <= nums[i] <= 10<sup>5</sup></code></li>
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<li><code>0 <= k <= 10<sup>5</sup></code></li>
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</ul>
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