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design-skiplist.html
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<p>Design a <strong>Skiplist</strong> without using any built-in libraries.</p>
<p>A <strong>skiplist</strong> is a data structure that takes <code>O(log(n))</code> time to add, erase and search. Comparing with treap and red-black tree which has the same function and performance, the code length of Skiplist can be comparatively short and the idea behind Skiplists is just simple linked lists.</p>
<p>For example, we have a Skiplist containing <code>[30,40,50,60,70,90]</code> and we want to add <code>80</code> and <code>45</code> into it. The Skiplist works this way:</p>
<p><img alt="" src="https://assets.leetcode.com/uploads/2019/09/27/1506_skiplist.gif" style="width: 500px; height: 173px;" /><br />
<small>Artyom Kalinin [CC BY-SA 3.0], via <a href="https://commons.wikimedia.org/wiki/File:Skip_list_add_element-en.gif" target="_blank" title="Artyom Kalinin [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons">Wikimedia Commons</a></small></p>
<p>You can see there are many layers in the Skiplist. Each layer is a sorted linked list. With the help of the top layers, add, erase and search can be faster than <code>O(n)</code>. It can be proven that the average time complexity for each operation is <code>O(log(n))</code> and space complexity is <code>O(n)</code>.</p>
<p>See more about Skiplist: <a href="https://en.wikipedia.org/wiki/Skip_list" target="_blank">https://en.wikipedia.org/wiki/Skip_list</a></p>
<p>Implement the <code>Skiplist</code> class:</p>
<ul>
<li><code>Skiplist()</code> Initializes the object of the skiplist.</li>
<li><code>bool search(int target)</code> Returns <code>true</code> if the integer <code>target</code> exists in the Skiplist or <code>false</code> otherwise.</li>
<li><code>void add(int num)</code> Inserts the value <code>num</code> into the SkipList.</li>
<li><code>bool erase(int num)</code> Removes the value <code>num</code> from the Skiplist and returns <code>true</code>. If <code>num</code> does not exist in the Skiplist, do nothing and return <code>false</code>. If there exist multiple <code>num</code> values, removing any one of them is fine.</li>
</ul>
<p>Note that duplicates may exist in the Skiplist, your code needs to handle this situation.</p>
<p> </p>
<p><strong>Example 1:</strong></p>
<pre>
<strong>Input</strong>
["Skiplist", "add", "add", "add", "search", "add", "search", "erase", "erase", "search"]
[[], [1], [2], [3], [0], [4], [1], [0], [1], [1]]
<strong>Output</strong>
[null, null, null, null, false, null, true, false, true, false]
<strong>Explanation</strong>
Skiplist skiplist = new Skiplist();
skiplist.add(1);
skiplist.add(2);
skiplist.add(3);
skiplist.search(0); // return False
skiplist.add(4);
skiplist.search(1); // return True
skiplist.erase(0); // return False, 0 is not in skiplist.
skiplist.erase(1); // return True
skiplist.search(1); // return False, 1 has already been erased.</pre>
<p> </p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>0 <= num, target <= 2 * 10<sup>4</sup></code></li>
<li>At most <code>5 * 10<sup>4</sup></code> calls will be made to <code>search</code>, <code>add</code>, and <code>erase</code>.</li>
</ul>