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<h1 id="61-hash-table">6.1 &nbsp; Hash table<a class="headerlink" href="#61-hash-table" title="Permanent link">&para;</a></h1>
<p>A <u>hash table</u> achieves efficient element querying by establishing a mapping between keys and values. Specifically, when we input a <code>key</code> into the hash table, we can retrieve the corresponding <code>value</code> in <span class="arithmatex">\(O(1)\)</span> time.</p>
<p>As shown in Figure 6-1, given <span class="arithmatex">\(n\)</span> students, each with two pieces of data: "name" and "student number". If we want to implement a query feature that returns the corresponding name when given a student number, we can use the hash table shown in Figure 6-1.</p>
<p><a class="glightbox" href="../hash_map.assets/hash_table_lookup.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Abstract representation of a hash table" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></a></p>
<p align="center"> Figure 6-1 &nbsp; Abstract representation of a hash table </p>
<p>Apart from hash tables, arrays and linked lists can also be used to implement querying functions. Their efficiency is compared in Table 6-1.</p>
<ul>
<li><strong>Adding elements</strong>: Simply add the element to the end of the array (or linked list), using <span class="arithmatex">\(O(1)\)</span> time.</li>
<li><strong>Querying elements</strong>: Since the array (or linked list) is unordered, it requires traversing all the elements, using <span class="arithmatex">\(O(n)\)</span> time.</li>
<li><strong>Deleting elements</strong>: First, locate the element, then delete it from the array (or linked list), using <span class="arithmatex">\(O(n)\)</span> time.</li>
</ul>
<p align="center"> Table 6-1 &nbsp; Comparison of element query efficiency </p>
<div class="center-table">
<table>
<thead>
<tr>
<th></th>
<th>Array</th>
<th>Linked List</th>
<th>Hash Table</th>
</tr>
</thead>
<tbody>
<tr>
<td>Find Element</td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td>Add Element</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td>Delete Element</td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
</tbody>
</table>
</div>
<p>Observations reveal that <strong>the time complexity for adding, deleting, and querying in a hash table is <span class="arithmatex">\(O(1)\)</span></strong>, which is highly efficient.</p>
<h2 id="611-common-operations-of-hash-table">6.1.1 &nbsp; Common operations of hash table<a class="headerlink" href="#611-common-operations-of-hash-table" title="Permanent link">&para;</a></h2>
<p>Common operations of a hash table include initialization, querying, adding key-value pairs, and deleting key-value pairs, etc. Example code is as follows:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># Initialize hash table</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">hmap</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">=</span> <span class="p">{}</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Add operation</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Xiao Ha&quot;</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Xiao Luo&quot;</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Xiao Suan&quot;</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Xiao Fa&quot;</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Xiao Ya&quot;</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># Query operation</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># Input key into hash table, get value</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">name</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="c1"># Delete operation</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">hmap</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">10583</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Xiao Ha&quot;</span><span class="p">;</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Xiao Luo&quot;</span><span class="p">;</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Xiao Suan&quot;</span><span class="p">;</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Xiao Fa&quot;</span><span class="p">;</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Xiao Ya&quot;</span><span class="p">;</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">map</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ha&quot;</span><span class="p">);</span><span class="w"> </span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Luo&quot;</span><span class="p">);</span><span class="w"> </span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Suan&quot;</span><span class="p">);</span><span class="w"> </span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Fa&quot;</span><span class="p">);</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ya&quot;</span><span class="p">);</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="n">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">15937</span><span class="p">);</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="n">map</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="cm">/* Add operation */</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ha&quot;</span><span class="w"> </span><span class="p">},</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Luo&quot;</span><span class="w"> </span><span class="p">},</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Suan&quot;</span><span class="w"> </span><span class="p">},</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Fa&quot;</span><span class="w"> </span><span class="p">},</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="m">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ya&quot;</span><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">};</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">map</span><span class="p">.</span><span class="n">Remove</span><span class="p">(</span><span class="m">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="nx">hmap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">string</span><span class="p">)</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Xiao Ha&quot;</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Xiao Luo&quot;</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Xiao Suan&quot;</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Xiao Fa&quot;</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Xiao Ya&quot;</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">name</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nb">delete</span><span class="p">(</span><span class="nx">hmap</span><span class="p">,</span><span class="w"> </span><span class="mi">10583</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">var</span> <span class="nv">map</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">:</span> <span class="nb">String</span><span class="p">]</span> <span class="p">=</span> <span class="p">[:]</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="bp">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;Xiao Ha&quot;</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;Xiao Luo&quot;</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="bp">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;Xiao Suan&quot;</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="bp">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;Xiao Fa&quot;</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="bp">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="p">=</span> <span class="s">&quot;Xiao Ya&quot;</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span> <span class="nv">name</span> <span class="p">=</span> <span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="o">!</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="bp">map</span><span class="p">.</span><span class="n">removeValue</span><span class="p">(</span><span class="n">forKey</span><span class="p">:</span> <span class="mi">10583</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Ha&#39;</span><span class="p">);</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Luo&#39;</span><span class="p">);</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Suan&#39;</span><span class="p">);</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Fa&#39;</span><span class="p">);</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Ya&#39;</span><span class="p">);</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="p">();</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Ha&#39;</span><span class="p">);</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Luo&#39;</span><span class="p">);</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Suan&#39;</span><span class="p">);</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Fa&#39;</span><span class="p">);</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;Xiao Ya&#39;</span><span class="p">);</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nAfter adding, the hash table is\nKey -&gt; Value&#39;</span><span class="p">);</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nInput student number 15937, query name &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">name</span><span class="p">);</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nAfter deleting 10583, the hash table is\nKey -&gt; Value&#39;</span><span class="p">);</span>
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">map</span><span class="p">[</span><span class="m">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Xiao Ha&quot;</span><span class="p">;</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Xiao Luo&quot;</span><span class="p">;</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">map</span><span class="p">[</span><span class="m">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Xiao Suan&quot;</span><span class="p">;</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">map</span><span class="p">[</span><span class="m">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Xiao Fa&quot;</span><span class="p">;</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">map</span><span class="p">[</span><span class="m">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Xiao Ya&quot;</span><span class="p">;</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="m">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">collections</span>::<span class="n">HashMap</span><span class="p">;</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* Initialize hash table */</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">map</span>: <span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="cm">/* Add operation */</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// Add key-value pair (key, value) to the hash table</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ha&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Luo&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Suan&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">13279</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Fa&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Xiao Ya&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="cm">/* Query operation */</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="c1">// Input key into hash table, get value</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">_name</span>: <span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">15937</span><span class="p">);</span>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="cm">/* Delete operation */</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="c1">// Delete key-value pair (key, value) from hash table</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="kd">let</span><span class="w"> </span><span class="n">_removed_value</span>: <span class="nb">Option</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">10583</span><span class="p">);</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C does not provide a built-in hash table</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Code Visualization</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=2&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=2&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen &gt;</a></div></p>
</details>
<p>There are three common ways to traverse a hash table: traversing key-value pairs, keys, and values. Example code is as follows:</p>
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<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># Traverse hash table</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># Traverse key-value pairs key-&gt;value</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a> <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1"># Traverse keys only</span>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a> <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># Traverse values only</span>
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a> <span class="nb">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// Traverse key-value pairs key-&gt;value</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">kv</span><span class="o">:</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">}</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="c1">// Traverse using iterator key-&gt;value</span>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">begin</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">end</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// Traverse key-value pairs key-&gt;value</span>
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">kv</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">getKey</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">getValue</span><span class="p">());</span>
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="c1">// Traverse keys only</span>
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="c1">// Traverse values only</span>
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// Traverse key-value pairs Key-&gt;Value</span>
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">var</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="n">Key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="c1">// Traverse keys only</span>
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Keys</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="c1">// Traverse values only</span>
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// Traverse key-value pairs key-&gt;value</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// Traverse keys only</span>
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="c1">// Traverse values only</span>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// Traverse key-value pairs Key-&gt;Value</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="k">for</span> <span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span> <span class="k">in</span> <span class="bp">map</span> <span class="p">{</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a> <span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">value</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">}</span>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// Traverse keys only</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="k">for</span> <span class="n">key</span> <span class="k">in</span> <span class="bp">map</span><span class="p">.</span><span class="n">keys</span> <span class="p">{</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a> <span class="bp">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="c1">// Traverse values only</span>
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="k">for</span> <span class="n">value</span> <span class="k">in</span> <span class="bp">map</span><span class="p">.</span><span class="n">values</span> <span class="p">{</span>
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a> <span class="bp">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse key-value pairs Key-&gt;Value&#39;</span><span class="p">);</span>
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse keys only Key&#39;</span><span class="p">);</span>
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse values only Value&#39;</span><span class="p">);</span>
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse key-value pairs Key-&gt;Value&#39;</span><span class="p">);</span>
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse keys only Key&#39;</span><span class="p">);</span>
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nTraverse values only Value&#39;</span><span class="p">);</span>
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// Traverse key-value pairs Key-&gt;Value</span>
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">map</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">print</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">$</span><span class="n">key</span><span class="s1"> -&gt; </span><span class="si">$</span><span class="n">value</span><span class="s1">&#39;</span><span class="p">);</span>
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">});</span>
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="c1">// Traverse keys only Key</span>
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="n">print</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">});</span>
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a>
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="c1">// Traverse values only Value</span>
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="n">print</span><span class="p">(</span><span class="n">value</span><span class="p">);</span>
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="p">});</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* Traverse hash table */</span>
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// Traverse key-value pairs Key-&gt;Value</span>
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">map</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key} -&gt; {value}&quot;</span><span class="p">);</span>
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">}</span>
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a>
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// Traverse keys only Key</span>
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key}&quot;</span><span class="p">);</span><span class="w"> </span>
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a>
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="c1">// Traverse values only Value</span>
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{value}&quot;</span><span class="p">);</span>
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// C does not provide a built-in hash table</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">hash_map.zig</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// Zig example is not provided</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>Code Visualization</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20%23%20%E9%81%8D%E5%8E%86%E9%94%AE%E5%80%BC%E5%AF%B9%20key-%3Evalue%0A%20%20%20%20for%20key,%20value%20in%20hmap.items%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key,%20%22-%3E%22,%20value%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E9%94%AE%20key%0A%20%20%20%20for%20key%20in%20hmap.keys%28%29%3A%0A%20%20%20%20%20%20%20%20print%28key%29%0A%20%20%20%20%23%20%E5%8D%95%E7%8B%AC%E9%81%8D%E5%8E%86%E5%80%BC%20value%0A%20%20%20%20for%20value%20in%20hmap.values%28%29%3A%0A%20%20%20%20%20%20%20%20print%28value%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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</details>
<h2 id="612-simple-implementation-of-hash-table">6.1.2 &nbsp; Simple implementation of hash table<a class="headerlink" href="#612-simple-implementation-of-hash-table" title="Permanent link">&para;</a></h2>
<p>First, let's consider the simplest case: <strong>implementing a hash table using just an array</strong>. In the hash table, each empty slot in the array is called a <u>bucket</u>, and each bucket can store one key-value pair. Therefore, the query operation involves finding the bucket corresponding to the <code>key</code> and retrieving the <code>value</code> from it.</p>
<p>So, how do we locate the appropriate bucket based on the <code>key</code>? This is achieved through a <u>hash function</u>. The role of the hash function is to map a larger input space to a smaller output space. In a hash table, the input space is all possible keys, and the output space is all buckets (array indices). In other words, input a <code>key</code>, <strong>and we can use the hash function to determine the storage location of the corresponding key-value pair in the array</strong>.</p>
<p>The calculation process of the hash function for a given <code>key</code> is divided into the following two steps:</p>
<ol>
<li>Calculate the hash value using a certain hash algorithm <code>hash()</code>.</li>
<li>Take the modulus of the hash value with the number of buckets (array length) <code>capacity</code> to obtain the array index <code>index</code>.</li>
</ol>
<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
</code></pre></div>
<p>Afterward, we can use <code>index</code> to access the corresponding bucket in the hash table and thereby retrieve the <code>value</code>.</p>
<p>Assuming array length <code>capacity = 100</code> and hash algorithm <code>hash(key) = key</code>, the hash function is <code>key % 100</code>. Figure 6-2 uses <code>key</code> as the student number and <code>value</code> as the name to demonstrate the working principle of the hash function.</p>
<p><a class="glightbox" href="../hash_map.assets/hash_function.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Working principle of hash function" class="animation-figure" src="../hash_map.assets/hash_function.png" /></a></p>
<p align="center"> Figure 6-2 &nbsp; Working principle of hash function </p>
<p>The following code implements a simple hash table. Here, we encapsulate <code>key</code> and <code>value</code> into a class <code>Pair</code> to represent the key-value pair.</p>
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<div class="highlight"><span class="filename">array_hash_map.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span> <span class="nc">Pair</span><span class="p">:</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Key-value pair&quot;&quot;&quot;</span>
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">key</span>
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="k">class</span> <span class="nc">ArrayHashMap</span><span class="p">:</span>
<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Hash table based on array implementation&quot;&quot;&quot;</span>
<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Constructor&quot;&quot;&quot;</span>
<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a> <span class="c1"># Initialize an array, containing 100 buckets</span>
<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span>
<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a> <span class="k">def</span> <span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Hash function&quot;&quot;&quot;</span>
<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a> <span class="n">index</span> <span class="o">=</span> <span class="n">key</span> <span class="o">%</span> <span class="mi">100</span>
<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a> <span class="k">return</span> <span class="n">index</span>
<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>
<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a> <span class="k">def</span> <span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Query operation&quot;&quot;&quot;</span>
<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a> <span class="n">pair</span><span class="p">:</span> <span class="n">Pair</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a> <span class="k">return</span> <span class="kc">None</span>
<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a> <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>
<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a> <span class="k">def</span> <span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Add operation&quot;&quot;&quot;</span>
<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a> <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">pair</span>
<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a>
<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a> <span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Remove operation&quot;&quot;&quot;</span>
<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a> <span class="c1"># Set to None, representing removal</span>
<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a> <span class="k">def</span> <span class="nf">entry_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]:</span>
<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Get all key-value pairs&quot;&quot;&quot;</span>
<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a> <span class="n">result</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a> <span class="k">return</span> <span class="n">result</span>
<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a>
<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a> <span class="k">def</span> <span class="nf">key_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Get all keys&quot;&quot;&quot;</span>
<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">)</span>
<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a> <span class="k">return</span> <span class="n">result</span>
<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a>
<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a> <span class="k">def</span> <span class="nf">value_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Get all values&quot;&quot;&quot;</span>
<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a> <span class="k">return</span> <span class="n">result</span>
<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a>
<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a> <span class="k">def</span> <span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Print hash table&quot;&quot;&quot;</span>
<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a> <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a>
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="p">[</span><span class="k">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* Key-value pair */</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a>
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>
<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="cm">/* Hash table based on array implementation */</span>
<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="kd">class</span> <span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>
<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w"> </span><span class="c1">// Initialize an array, containing 100 buckets</span>
<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a>
<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w"> </span><span class="cm">/* Hash function */</span>
<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a>
<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w"> </span><span class="cm">/* Query operation */</span>
<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a>
<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w"> </span><span class="cm">/* Add operation */</span>
<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">);</span>
<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a>
<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w"> </span><span class="cm">/* Remove operation */</span>
<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w"> </span><span class="c1">// Set to null, indicating removal</span>
<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a>
<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w"> </span><span class="cm">/* Get all key-value pairs */</span>
<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w"> </span><span class="n">pairSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a>
<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w"> </span><span class="cm">/* Get all keys */</span>
<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-67" name="__codelineno-29-67" href="#__codelineno-29-67"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-29-68" name="__codelineno-29-68" href="#__codelineno-29-68"></a><span class="w"> </span><span class="n">keySet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">);</span>
<a id="__codelineno-29-69" name="__codelineno-29-69" href="#__codelineno-29-69"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-70" name="__codelineno-29-70" href="#__codelineno-29-70"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
<a id="__codelineno-29-71" name="__codelineno-29-71" href="#__codelineno-29-71"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-72" name="__codelineno-29-72" href="#__codelineno-29-72"></a>
<a id="__codelineno-29-73" name="__codelineno-29-73" href="#__codelineno-29-73"></a><span class="w"> </span><span class="cm">/* Get all values */</span>
<a id="__codelineno-29-74" name="__codelineno-29-74" href="#__codelineno-29-74"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-75" name="__codelineno-29-75" href="#__codelineno-29-75"></a><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-29-76" name="__codelineno-29-76" href="#__codelineno-29-76"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-77" name="__codelineno-29-77" href="#__codelineno-29-77"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-29-78" name="__codelineno-29-78" href="#__codelineno-29-78"></a><span class="w"> </span><span class="n">valueSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
<a id="__codelineno-29-79" name="__codelineno-29-79" href="#__codelineno-29-79"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-80" name="__codelineno-29-80" href="#__codelineno-29-80"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
<a id="__codelineno-29-81" name="__codelineno-29-81" href="#__codelineno-29-81"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-82" name="__codelineno-29-82" href="#__codelineno-29-82"></a>
<a id="__codelineno-29-83" name="__codelineno-29-83" href="#__codelineno-29-83"></a><span class="w"> </span><span class="cm">/* Print hash table */</span>
<a id="__codelineno-29-84" name="__codelineno-29-84" href="#__codelineno-29-84"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-85" name="__codelineno-29-85" href="#__codelineno-29-85"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-86" name="__codelineno-29-86" href="#__codelineno-29-86"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
<a id="__codelineno-29-87" name="__codelineno-29-87" href="#__codelineno-29-87"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-88" name="__codelineno-29-88" href="#__codelineno-29-88"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-89" name="__codelineno-29-89" href="#__codelineno-29-89"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="n">file</span><span class="p">]{</span><span class="n">utils</span><span class="o">/</span><span class="n">pair</span><span class="p">.</span><span class="n">swift</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_hash_map.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
</code></pre></div>
</div>
</div>
</div>
<h2 id="613-hash-collision-and-resizing">6.1.3 &nbsp; Hash collision and resizing<a class="headerlink" href="#613-hash-collision-and-resizing" title="Permanent link">&para;</a></h2>
<p>Fundamentally, the role of the hash function is to map the entire input space of all keys to the output space of all array indices. However, the input space is often much larger than the output space. Therefore, <strong>theoretically, there must be situations where "multiple inputs correspond to the same output"</strong>.</p>
<p>For the hash function in the above example, if the last two digits of the input <code>key</code> are the same, the output of the hash function will also be the same. For example, when querying for students with student numbers 12836 and 20336, we find:</p>
<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="m">12836</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="m">20336</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
</code></pre></div>
<p>As shown in Figure 6-3, both student numbers point to the same name, which is obviously incorrect. This situation where multiple inputs correspond to the same output is known as <u>hash collision</u>.</p>
<p><a class="glightbox" href="../hash_map.assets/hash_collision.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Example of hash collision" class="animation-figure" src="../hash_map.assets/hash_collision.png" /></a></p>
<p align="center"> Figure 6-3 &nbsp; Example of hash collision </p>
<p>It is easy to understand that the larger the capacity <span class="arithmatex">\(n\)</span> of the hash table, the lower the probability of multiple keys being allocated to the same bucket, and the fewer the collisions. Therefore, <strong>expanding the capacity of the hash table can reduce hash collisions</strong>.</p>
<p>As shown in Figure 6-4, before expansion, key-value pairs <code>(136, A)</code> and <code>(236, D)</code> collided; after expansion, the collision is resolved.</p>
<p><a class="glightbox" href="../hash_map.assets/hash_table_reshash.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Hash table expansion" class="animation-figure" src="../hash_map.assets/hash_table_reshash.png" /></a></p>
<p align="center"> Figure 6-4 &nbsp; Hash table expansion </p>
<p>Similar to array expansion, resizing a hash table requires migrating all key-value pairs from the original hash table to the new one, which is time-consuming. Furthermore, since the capacity <code>capacity</code> of the hash table changes, we need to recalculate the storage positions of all key-value pairs using the hash function, which adds to the computational overhead of the resizing process. Therefore, programming languages often reserve a sufficiently large capacity for the hash table to prevent frequent resizing.</p>
<p>The <u>load factor</u> is an important concept for hash tables. It is defined as the ratio of the number of elements in the hash table to the number of buckets. It is used to measure the severity of hash collisions and <strong>is often used as a trigger for resizing the hash table</strong>. For example, in Java, when the load factor exceeds <span class="arithmatex">\(0.75\)</span>, the system will resize the hash table to twice its original size.</p>
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