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@@ -3609,16 +3609,16 @@
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<!-- Page content -->
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<h1 id="61-hash-table">6.1 Hash table<a class="headerlink" href="#61-hash-table" title="Permanent link">¶</a></h1>
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<p>A <u>hash table</u>, also known as a <u>hash map</u>, is a data structure that establishes a mapping between keys and values, enabling efficient element retrieval. Specifically, when we input a <code>key</code> into the hash table, we can retrive the corresponding <code>value</code> in <span class="arithmatex">\(O(1)\)</span> time complexity.</p>
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<p>A <u>hash table</u>, also known as a <u>hash map</u>, is a data structure that establishes a mapping between keys and values, enabling efficient element retrieval. 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 complexity.</p>
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<p>As shown in Figure 6-1, given <span class="arithmatex">\(n\)</span> students, each student has two data fields: "Name" and "Student ID". If we want to implement a query function that takes a student ID as input and returns the corresponding name, we can use the hash table shown in Figure 6-1.</p>
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<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>
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<p align="center"> Figure 6-1 Abstract representation of a hash table </p>
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<p>In addition to hash tables, arrays and linked lists can also be used to implement query functionality, but the time complexity is different. Their efficiency is compared in Table 6-1:</p>
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<ul>
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<li><strong>Inserting elements</strong>: Simply append the element to the tail of the array (or linked list). The time complexity of this operation is <span class="arithmatex">\(O(1)\)</span>.</li>
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<li><strong>Searching for elements</strong>: As the array (or linked list) is unsorted, searching for an element requires traversing through all of the elements. The time complexity of this operation is <span class="arithmatex">\(O(n)\)</span>.</li>
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<li><strong>Deleting elements</strong>: To remove an element, we first need to locate it. Then, we delete it from the array (or linked list). The time complexity of this operation is <span class="arithmatex">\(O(n)\)</span>.</li>
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<li><strong>Inserting an element</strong>: Simply append the element to the tail of the array (or linked list). The time complexity of this operation is <span class="arithmatex">\(O(1)\)</span>.</li>
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<li><strong>Searching for an element</strong>: As the array (or linked list) is unsorted, searching for an element requires traversing through all of the elements. The time complexity of this operation is <span class="arithmatex">\(O(n)\)</span>.</li>
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<li><strong>Deleting an element</strong>: To remove an element, we first need to locate it. Then, we delete it from the array (or linked list). The time complexity of this operation is <span class="arithmatex">\(O(n)\)</span>.</li>
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</ul>
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<p align="center"> Table 6-1 Comparison of time efficiency for common operations </p>
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@@ -3654,7 +3654,7 @@
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</tbody>
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</table>
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</div>
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<p>It can be seen that <strong>the time complexity for operations (insertion, deletion, searching, and modification) in a hash table is <span class="arithmatex">\(O(1)\)</span></strong>, which is highly efficient.</p>
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<p>As observed, <strong>the time complexity for operations (insertion, deletion, searching, and modification) in a hash table is <span class="arithmatex">\(O(1)\)</span></strong>, which is highly efficient.</p>
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<h2 id="611-common-operations-of-hash-table">6.1.1 Common operations of hash table<a class="headerlink" href="#611-common-operations-of-hash-table" title="Permanent link">¶</a></h2>
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<p>Common operations of a hash table include: initialization, querying, adding key-value pairs, and deleting key-value pairs. Here is an example code:</p>
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<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>
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@@ -3685,7 +3685,7 @@
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">unordered_map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">></span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
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<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* Add operation */</span>
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<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>
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<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// Add key-value pair (key, value) to hash table</span>
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<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">"Xiao Ha"</span><span class="p">;</span>
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<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">"Xiao Luo"</span><span class="p">;</span>
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<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">"Xiao Suan"</span><span class="p">;</span>
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@@ -3706,7 +3706,7 @@
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Map</span><span class="o"><</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">></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"><></span><span class="p">();</span>
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<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
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<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* Add operation */</span>
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<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>
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<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// Add key-value pair (key, value) to hash table</span>
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<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">"Xiao Ha"</span><span class="p">);</span><span class="w"> </span>
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<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">"Xiao Luo"</span><span class="p">);</span><span class="w"> </span>
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<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">"Xiao Suan"</span><span class="p">);</span><span class="w"> </span>
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@@ -3726,7 +3726,7 @@
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<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>
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Dictionary</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">></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>
|
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<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-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// Add key-value pair (key, value) to hash table</span>
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<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">"Xiao Ha"</span><span class="w"> </span><span class="p">},</span>
|
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<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">"Xiao Luo"</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">"Xiao Suan"</span><span class="w"> </span><span class="p">},</span>
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@@ -3748,7 +3748,7 @@
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<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>
|
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<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-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Add key-value pair (key, value) to 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">"Xiao Ha"</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">"Xiao Luo"</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">"Xiao Suan"</span>
|
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@@ -3769,7 +3769,7 @@
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<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-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// Add key-value pair (key, value) to 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">"Xiao Ha"</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">"Xiao Luo"</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">"Xiao Suan"</span>
|
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@@ -3809,7 +3809,7 @@
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<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>
|
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<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"><</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">></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-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// Add key-value pair (key, value) to 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">'Xiao Ha'</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">'Xiao Luo'</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">'Xiao Suan'</span><span class="p">);</span>
|
||||
@@ -3835,7 +3835,7 @@
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">Map</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">></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-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="c1">// Add key-value pair (key, value) to 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">"Xiao Ha"</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">"Xiao Luo"</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">"Xiao Suan"</span><span class="p">;</span>
|
||||
@@ -3858,7 +3858,7 @@
|
||||
<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"><</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">String</span><span class="o">></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-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// Add key-value pair (key, value) to 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">"Xiao Ha"</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">"Xiao Luo"</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">"Xiao Suan"</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
|
||||
@@ -4075,10 +4075,10 @@
|
||||
<h2 id="612-simple-implementation-of-a-hash-table">6.1.2 Simple implementation of a hash table<a class="headerlink" href="#612-simple-implementation-of-a-hash-table" title="Permanent link">¶</a></h2>
|
||||
<p>First, let's consider the simplest case: <strong>implementing a hash table using only one array</strong>. In the hash table, each empty slot in the array is called a <u>bucket</u>, and each bucket can store a 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 corresponding 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 consists of all the keys, and the output space consists of all the buckets (array indices). In other words, given a <code>key</code>, <strong>we can use the hash function to determine the storage location of the corresponding key-value pair in the array</strong>.</p>
|
||||
<p>When given a <code>key</code>, the calculation process of the hash function consists of the following two steps:</p>
|
||||
<p>With a given <code>key</code>, the calculation of the hash function consists of two steps:</p>
|
||||
<ol>
|
||||
<li>Calculate the hash value by using a certain hash algorithm <code>hash()</code>.</li>
|
||||
<li>Take the modulus of the hash value with the bucket count (array length) <code>capacity</code> to obtain the array <code>index</code> corresponding to that key.</li>
|
||||
<li>Take the modulus of the hash value with the bucket count (array length) <code>capacity</code> to obtain the array <code>index</code> corresponding to the key.</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>
|
||||
|
||||
Reference in New Issue
Block a user