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<!DOCTYPE html>
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<title>Hash Table</title>
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<div class="editor-contents">
<h1>Hash Table</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn what hash table is. Also, you will find working examples of hash table operations in C, C++, Java and Python.</p>
<div id="node-1506" class="node node-algorithm clearfix" about="/dsa/hash-table" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Hash Table" class="rdf-meta element-hidden"></span>
<div class="content">
<p id="introduction">The Hash table data structure stores elements in key-value pairs where</p>
<ul><li id="definition"><strong>Key</strong>- unique integer that is used for indexing the values</li>
<li id="definition"><strong>Value</strong> - data that are associated with keys.</li>
</ul><figure><img alt="Hash Table key and data" src="//cdn.programiz.com/sites/tutorial2program/files/Hash-0.png" title="hash table data" width="250" height="111"><figcaption>Key and Value in Hash table</figcaption></figure><hr><h2 id="hashing">Hashing (Hash Function)</h2>
<p>In a hash table, a new index is processed using the keys. And, the element corresponding to that key is stored in the index. This process is called <strong>hashing</strong>.</p>
<p>Let <var>k</var> be a key and <var>h(x)</var> be a hash function.</p>
<p>Here, <var>h(k)</var> will give us a new index to store the element linked with <var>k</var>.</p>
<figure><img alt="Hash Table representation" src="//cdn.programiz.com/sites/tutorial2program/files/Hash-2_0.png" title="Hash Table representation" width="600" height="479"><figcaption>Hash table Representation</figcaption></figure><p>To learn more, visit <a href="/dsa/hash-table.html" title="Hashing">Hashing</a>.</p>
<hr><h2 id="collision">Hash Collision</h2>
<p>When the hash function generates the same index for multiple keys, there will be a conflict (what value to be stored in that index). This is called a <strong>hash collision.</strong></p>
<p>We can resolve the hash collision using one of the following techniques.</p>
<ul><li>Collision resolution by chaining</li>
<li>Open Addressing: Linear/Quadratic Probing and Double Hashing</li>
</ul><hr><h2 id="chaining">1. Collision resolution by chaining</h2>
<p>In chaining, if a hash function produces the same index for multiple elements, these elements are stored in the same index by using a doubly-linked list.</p>
<p>If <code>j</code> is the slot for multiple elements, it contains a pointer to the head of the list of elements. If no element is present, <code>j</code> contains <code>NIL</code>.</p>
<figure><img alt="chaining method used to resolve collision in hash table" src="//cdn.programiz.com/sites/tutorial2program/files/Hash-3_1.png" title="Collision resolution by doubly linked list." width="800" height="425"><figcaption>Collision Resolution using chaining</figcaption></figure><p><strong>Pseudocode for operations</strong></p>
<pre style="max-height: 600px;"><code class="dsa hljs kotlin">chainedHashSearch(T, k)
<span class="hljs-keyword">return</span> T[h(k)]
chainedHashInsert(T, x)
T[h(x.key)] = x <span class="hljs-comment">//insert at the head</span>
chainedHashDelete(T, x)
T[h(x.key)] = NIL</code></pre>
<hr><h2 id="open-addressing">2. Open Addressing</h2>
<p>Unlike chaining, open addressing doesn't store multiple elements into the same slot. Here, each slot is either filled with a single key or left <code>NIL</code>.</p>
<p>Different techniques used in open addressing are:</p>
<h3>i. Linear Probing</h3>
<p>In linear probing, collision is resolved by checking the next slot.</p>
<p><code>h(k, i) = (h′(k) + i) mod m</code></p>
<p>where</p>
<ul><li><code>i = {0, 1, ….}</code></li>
<li><code>h'(k)</code> is a new hash function</li>
</ul><p>If a collision occurs at <code>h(k, 0)</code>, then <code>h(k, 1)</code> is checked. In this way, the value of <code>i</code> is incremented linearly.</p>
<p></p><div class="clearfix"></div><p>The problem with linear probing is that a cluster of adjacent slots is filled. When inserting a new element, the entire cluster must be traversed. This adds to the time required to perform operations on the hash table.</p>
<h3>ii. Quadratic Probing</h3>
<p>It works similar to linear probing but the spacing between the slots is increased (greater than one) by using the following relation.</p>
<p><code>h(k, i) = (h′(k) + c</code><code><sub>1</sub></code><code>i + c</code><code><sub>2</sub></code><code>i</code><code><sup>2</sup></code><code>) mod m</code></p>
<p>where,</p>
<ul><li><code>c</code><code><sub>1</sub></code> and <code>c</code><code><sub>2</sub></code> are positive auxiliary constants,</li>
<li><code>i = {0, 1, ….}</code></li>
</ul><h3>iii. Double hashing</h3>
<p>If a collision occurs after applying a hash function <code>h(k)</code>, then another hash function is calculated for finding the next slot.</p>
<p><code>h(k, i) = (h</code><code><sub>1</sub></code><code>(k) + ih</code><code><sub>2</sub></code><code>(k)) mod m</code></p>
<hr><h2 id="good-hashing">Good Hash Functions</h2>
<p>A good hash function may not prevent the collisions completely however it can reduce the number of collisions.</p>
<p>Here, we will look into different methods to find a good hash function</p>
<h3>1. Division Method</h3>
<p>If <code>k</code> is a key and <code>m</code> is the size of the hash table, the hash function <code>h()</code> is calculated as:</p>
<p><code>h(k) = k mod m</code></p>
<p>For example, If the size of a hash table is <code>10</code> and <code>k = 112</code> then <code>h(k) = 112</code> mod <code>10 = 2</code>. The value of <code>m</code> must not be the powers of <code>2</code>. This is because the powers of <code>2</code> in binary format are <code>10, 100, 1000, …</code>. When we find <code>k mod m</code>, we will always get the lower order p-bits.</p>
<pre>if m = 22, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 01
if m = 23, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 001
if m = 24, k = 17, then h(k) = 17 mod 22 = 10001 mod 100 = 0001
if m = 2p, then h(k) = p lower bits of m</pre>
<h3>2. Multiplication Method</h3>
<p><code>h(k) = ⌊m(kA mod 1)⌋</code></p>
<p>where,</p>
<ul><li><code>kA mod 1</code> gives the fractional part <code>kA</code>,</li>
<li><code>⌊ ⌋</code> gives the floor value</li>
<li><code>A</code> is any constant. The value of <code>A</code> lies between 0 and 1. But, an optimal choice will be <code>≈ (√5-1)/2</code> suggested by Knuth.</li>
</ul><h3>3. Universal Hashing</h3>
<p>In Universal hashing, the hash function is chosen at random independent of keys.</p>
<hr><h2 id="code">Python, Java and C/C++ Examples</h2>
<div class="tabbed-editor">
<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>
<div id="java1" onclick="changejava()" class="tabbed-editor__node"><a href="#java-code">Java</a></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Python program to demonstrate working of HashTable </span>
hashTable = [[],] * <span class="hljs-number">10</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">checkPrime</span><span class="hljs-params">(n)</span>:</span>
<span class="hljs-keyword">if</span> n == <span class="hljs-number">1</span> <span class="hljs-keyword">or</span> n == <span class="hljs-number">0</span>:
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">2</span>, n//<span class="hljs-number">2</span>):
<span class="hljs-keyword">if</span> n % i == <span class="hljs-number">0</span>:
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>
<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">getPrime</span><span class="hljs-params">(n)</span>:</span>
<span class="hljs-keyword">if</span> n % <span class="hljs-number">2</span> == <span class="hljs-number">0</span>:
n = n + <span class="hljs-number">1</span>
<span class="hljs-keyword">while</span> <span class="hljs-keyword">not</span> checkPrime(n):
n += <span class="hljs-number">2</span>
<span class="hljs-keyword">return</span> n
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">hashFunction</span><span class="hljs-params">(key)</span>:</span>
capacity = getPrime(<span class="hljs-number">10</span>)
<span class="hljs-keyword">return</span> key % capacity
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">insertData</span><span class="hljs-params">(key, data)</span>:</span>
index = hashFunction(key)
hashTable[index] = [key, data]
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">removeData</span><span class="hljs-params">(key)</span>:</span>
index = hashFunction(key)
hashTable[index] = <span class="hljs-number">0</span>
insertData(<span class="hljs-number">123</span>, <span class="hljs-string">"apple"</span>)
insertData(<span class="hljs-number">432</span>, <span class="hljs-string">"mango"</span>)
insertData(<span class="hljs-number">213</span>, <span class="hljs-string">"banana"</span>)
insertData(<span class="hljs-number">654</span>, <span class="hljs-string">"guava"</span>)
<span class="hljs-keyword">print</span>(hashTable)
removeData(<span class="hljs-number">123</span>)
<span class="hljs-keyword">print</span>(hashTable)</code></pre></div>
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<div class="code-editor__area" id="java-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Java program to demonstrate working of HashTable </span>
<span class="hljs-keyword">import</span> java.util.*;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">HashTable</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String args[])</span>
</span>{
Hashtable<Integer, Integer>
ht = <span class="hljs-keyword">new</span> Hashtable<Integer, Integer>();
ht.put(<span class="hljs-number">123</span>, <span class="hljs-number">432</span>);
ht.put(<span class="hljs-number">12</span>, <span class="hljs-number">2345</span>);
ht.put(<span class="hljs-number">15</span>, <span class="hljs-number">5643</span>);
ht.put(<span class="hljs-number">3</span>, <span class="hljs-number">321</span>);
ht.remove(<span class="hljs-number">12</span>);
System.out.println(ht);
}
} </code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Implementing hash table in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdlib.h></span></span>
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">set</span>
{</span>
<span class="hljs-keyword">int</span> key;
<span class="hljs-keyword">int</span> data;
};
<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">set</span> *<span class="hljs-title">array</span>;</span>
<span class="hljs-keyword">int</span> capacity = <span class="hljs-number">10</span>;
<span class="hljs-keyword">int</span> size = <span class="hljs-number">0</span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">hashFunction</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key)</span>
</span>{
<span class="hljs-keyword">return</span> (key % capacity);
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">checkPrime</span><span class="hljs-params">(<span class="hljs-keyword">int</span> n)</span>
</span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">if</span> (n == <span class="hljs-number">1</span> || n == <span class="hljs-number">0</span>)
{
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">2</span>; i < n / <span class="hljs-number">2</span>; i++)
{
<span class="hljs-keyword">if</span> (n % i == <span class="hljs-number">0</span>)
{
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
}
<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">getPrime</span><span class="hljs-params">(<span class="hljs-keyword">int</span> n)</span>
</span>{
<span class="hljs-keyword">if</span> (n % <span class="hljs-number">2</span> == <span class="hljs-number">0</span>)
{
n++;
}
<span class="hljs-keyword">while</span> (!checkPrime(n))
{
n += <span class="hljs-number">2</span>;
}
<span class="hljs-keyword">return</span> n;
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">init_array</span><span class="hljs-params">()</span>
</span>{
capacity = getPrime(capacity);
<span class="hljs-built_in">array</span> = (struct <span class="hljs-built_in">set</span> *)<span class="hljs-built_in">malloc</span>(capacity * <span class="hljs-keyword">sizeof</span>(struct <span class="hljs-built_in">set</span>));
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < capacity; i++)
{
<span class="hljs-built_in">array</span>[i].key = <span class="hljs-number">0</span>;
<span class="hljs-built_in">array</span>[i].data = <span class="hljs-number">0</span>;
}
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">insert</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key, <span class="hljs-keyword">int</span> data)</span>
</span>{
<span class="hljs-keyword">int</span> index = hashFunction(key);
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[index].data == <span class="hljs-number">0</span>)
{
<span class="hljs-built_in">array</span>[index].key = key;
<span class="hljs-built_in">array</span>[index].data = data;
size++;
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Key (%d) has been inserted \n"</span>, key);
}
<span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[index].key == key)
{
<span class="hljs-built_in">array</span>[index].data = data;
}
<span class="hljs-keyword">else</span>
{
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Collision occured \n"</span>);
}
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">remove_element</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key)</span>
</span>{
<span class="hljs-keyword">int</span> index = hashFunction(key);
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[index].data == <span class="hljs-number">0</span>)
{
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n This key does not exist \n"</span>);
}
<span class="hljs-keyword">else</span>
{
<span class="hljs-built_in">array</span>[index].key = <span class="hljs-number">0</span>;
<span class="hljs-built_in">array</span>[index].data = <span class="hljs-number">0</span>;
size--;
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Key (%d) has been removed \n"</span>, key);
}
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">()</span>
</span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">0</span>; i < capacity; i++)
{
<span class="hljs-keyword">if</span> (<span class="hljs-built_in">array</span>[i].data == <span class="hljs-number">0</span>)
{
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n array[%d]: / "</span>, i);
}
<span class="hljs-keyword">else</span>
{
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n key: %d array[%d]: %d \t"</span>, <span class="hljs-built_in">array</span>[i].key, i, <span class="hljs-built_in">array</span>[i].data);
}
}
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">size_of_hashtable</span><span class="hljs-params">()</span>
</span>{
<span class="hljs-keyword">return</span> size;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span>
</span>{
<span class="hljs-keyword">int</span> choice, key, data, n;
<span class="hljs-keyword">int</span> c = <span class="hljs-number">0</span>;
init_array();
<span class="hljs-keyword">do</span>
{
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"1.Insert item in the Hash Table"</span>
<span class="hljs-string">"\n2.Remove item from the Hash Table"</span>
<span class="hljs-string">"\n3.Check the size of Hash Table"</span>
<span class="hljs-string">"\n4.Display a Hash Table"</span>
<span class="hljs-string">"\n\n Please enter your choice: "</span>);
<span class="hljs-built_in">scanf</span>(<span class="hljs-string">"%d"</span>, &choice);
<span class="hljs-keyword">switch</span> (choice)
{
<span class="hljs-keyword">case</span> <span class="hljs-number">1</span>:
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Enter key -:\t"</span>);
<span class="hljs-built_in">scanf</span>(<span class="hljs-string">"%d"</span>, &key);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Enter data -:\t"</span>);
<span class="hljs-built_in">scanf</span>(<span class="hljs-string">"%d"</span>, &data);
insert(key, data);
<span class="hljs-keyword">break</span>;
<span class="hljs-keyword">case</span> <span class="hljs-number">2</span>:
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Enter the key to delete-:"</span>);
<span class="hljs-built_in">scanf</span>(<span class="hljs-string">"%d"</span>, &key);
remove_element(key);
<span class="hljs-keyword">break</span>;
<span class="hljs-keyword">case</span> <span class="hljs-number">3</span>:
n = size_of_hashtable();
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Size of Hash Table is-:%d\n"</span>, n);
<span class="hljs-keyword">break</span>;
<span class="hljs-keyword">case</span> <span class="hljs-number">4</span>:
display();
<span class="hljs-keyword">break</span>;
<span class="hljs-keyword">default</span>:
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Invalid Input\n"</span>);
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nDo you want to continue (press 1 for yes): "</span>);
<span class="hljs-built_in">scanf</span>(<span class="hljs-string">"%d"</span>, &c);
} <span class="hljs-keyword">while</span> (c == <span class="hljs-number">1</span>);
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Implementing hash table in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><list></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">HashTable</span>
{</span>
<span class="hljs-keyword">int</span> capacity;
<span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>> *table;
<span class="hljs-keyword">public</span>:
HashTable(<span class="hljs-keyword">int</span> V);
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">insertItem</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key, <span class="hljs-keyword">int</span> data)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deleteItem</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key)</span></span>;
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">checkPrime</span><span class="hljs-params">(<span class="hljs-keyword">int</span> n)</span>
</span>{
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">if</span> (n == <span class="hljs-number">1</span> || n == <span class="hljs-number">0</span>)
{
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">2</span>; i < n / <span class="hljs-number">2</span>; i++)
{
<span class="hljs-keyword">if</span> (n % i == <span class="hljs-number">0</span>)
{
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
}
<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">getPrime</span><span class="hljs-params">(<span class="hljs-keyword">int</span> n)</span>
</span>{
<span class="hljs-keyword">if</span> (n % <span class="hljs-number">2</span> == <span class="hljs-number">0</span>)
{
n++;
}
<span class="hljs-keyword">while</span> (!checkPrime(n))
{
n += <span class="hljs-number">2</span>;
}
<span class="hljs-keyword">return</span> n;
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">hashFunction</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key)</span>
</span>{
<span class="hljs-keyword">return</span> (key % capacity);
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">displayHash</span><span class="hljs-params">()</span></span>;
};
HashTable::HashTable(<span class="hljs-keyword">int</span> c)
{
<span class="hljs-keyword">int</span> size = getPrime(c);
<span class="hljs-keyword">this</span>->capacity = size;
table = <span class="hljs-keyword">new</span> <span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>>[capacity];
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">HashTable::insertItem</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key, <span class="hljs-keyword">int</span> data)</span>
</span>{
<span class="hljs-keyword">int</span> index = hashFunction(key);
table[index].push_back(data);
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">HashTable::deleteItem</span><span class="hljs-params">(<span class="hljs-keyword">int</span> key)</span>
</span>{
<span class="hljs-keyword">int</span> index = hashFunction(key);
<span class="hljs-built_in">list</span><<span class="hljs-keyword">int</span>>::iterator i;
<span class="hljs-keyword">for</span> (i = table[index].begin();
i != table[index].end(); i++)
{
<span class="hljs-keyword">if</span> (*i == key)
<span class="hljs-keyword">break</span>;
}
<span class="hljs-keyword">if</span> (i != table[index].end())
table[index].erase(i);
}
<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">HashTable::displayHash</span><span class="hljs-params">()</span>
</span>{
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < capacity; i++)
{
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"table["</span> << i << <span class="hljs-string">"]"</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">auto</span> x : table[i])
<span class="hljs-built_in">cout</span> << <span class="hljs-string">" --> "</span> << x;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
}
}
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span>
</span>{
<span class="hljs-keyword">int</span> key[] = {<span class="hljs-number">231</span>, <span class="hljs-number">321</span>, <span class="hljs-number">212</span>, <span class="hljs-number">321</span>, <span class="hljs-number">433</span>, <span class="hljs-number">262</span>};
<span class="hljs-keyword">int</span> data[] = {<span class="hljs-number">123</span>, <span class="hljs-number">432</span>, <span class="hljs-number">523</span>, <span class="hljs-number">43</span>, <span class="hljs-number">423</span>, <span class="hljs-number">111</span>};
<span class="hljs-keyword">int</span> size = <span class="hljs-keyword">sizeof</span>(key) / <span class="hljs-keyword">sizeof</span>(key[<span class="hljs-number">0</span>]);
<span class="hljs-function">HashTable <span class="hljs-title">h</span><span class="hljs-params">(size)</span></span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++)
h.insertItem(key[i], data[i]);
h.deleteItem(<span class="hljs-number">12</span>);
h.displayHash();
}</code></pre></div>
</div>
</div>
<hr><h2 id="application">Applications of Hash Table</h2>
<p>Hash tables are implemented where</p>
<ul><li>constant time lookup and insertion is required</li>
<li>cryptographic applications</li>
<li>indexing data is required</li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#introduction">Hash Table</a></li>
<li><a href="#hashing">Hashing</a></li>
<li><a href="#collision">Hash Collision</a></li>
<li><a href="#chaining">Chaining</a></li>
<li><a href="#open-addressing">Open Addressing</a></li>
<li><a href="#good-hashing">Good Hash Function</a></li>
<li><a href="#implementation">Hash Table Implementation</a></li>
<li><a href="#application">Applications</a></li>
</ul></div></div></div> </div>
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Quick Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/counting-sort.html">
Counting Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
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Radix Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
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Bucket Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/heap-sort.html">
Heap Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/shell-sort.html">
Shell Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
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Linear Search</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
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Binary Search</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/greedy-algorithm.html">
Greedy Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/ford-fulkerson-algorithm.html">
Ford-Fulkerson Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dijkstra-algorithm.html">
Dijkstra's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/kruskal-algorithm.html">
Kruskal's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/prim-algorithm.html">
Prim's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/huffman-coding.html">
Huffman Code</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dynamic-programming.html">
Dynamic Programming</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/floyd-warshall-algorithm.html">
Floyd Warshall Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/longest-common-subsequence.html">
Longest Common Subsequence</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/backtracking-algorithm.html">
Backtracking Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/rabin-karp-algorithm.html">
Rabin-Karp Algorithm</a></button>
<br>
<br/>
<h2>Free Courses on YouTube</h2>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="
https://www.youtube.com/watch?v=IbSXF7eT-AU&list=PLR_5PTwg_uAQw40OhdvAwN4NvzWv0xOZ2">
Python Full Course Playlist</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://www.youtube.com/watch?v=UEl6wB90Gs8">
105 STL Algorithms in Less Than an Hour</a></button>