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<!DOCTYPE html>

<head>

<title>Stack Data Structure</title>

window.dataLayer = window.dataLayer || [];

function gtag() { dataLayer.push(arguments); }

gtag('js', new Date());

gtag('config', 'G-HCERBDV76D');

</script>

</head>

<body>

<nav>

Python Tutorial

</a>

</div>

<span>

</span>

<span>

</span>

<span>

</span>

</div>

</div>

<li>

Home

</a>

</li>

<li>

Projects

</a>

</li>

<li>

Free Course

</a>

</li>

<li>

DSA

</a>

</li>

</ul>

</div>

</nav>

</div>

<h3>Page Index</h3>

<ul>

<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures

(I)</a></li>

<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures

(II)</a></li>

<li><a href="/dsa.html#tree-1" title="Tree based DSA (I)">Tree based DSA (I)</a></li>

<li><a href="/dsa.html#tree-2" title="Tree based DSA (II)">Tree based DSA (II)</a></li>

<li><a href="/dsa.html#graph" title="Graph Data Structures and Algorithm">Graph based

DSA</a></li>

<li><a href="/dsa.html#sorting-searching" title="Sorting and Searching">Sorting and

Searching</a></li>

<li><a href="/dsa.html#greedy-algorithm" title="Greedy Algorithms">Greedy Algorithms</a>

</li>

<li><a href="/dsa.html#dynamic-programming" title="Dynamic Programming">Dynamic

Programming</a></li>

<li><a href="/dsa.html#other-algorithms" title="Other Algorithms">Other Algorithms</a>

</li>

</ul>

</div>

<h1>Stack Data Structure</h1>

<p class="editor-contents__short-description">In this tutorial, you will learn about the stack data structure and its implementation in Python, Java and C/C++.</p>

<p id="definition">A stack is a linear data structure that follows the principle of <strong>Last In First Out (LIFO)</strong>. This means the last element inserted inside the stack is removed first.</p>

<p>You can think of the stack data structure as the pile of plates on top of another.</p>

<figure><img alt="elements on stack are added on top and removed from top just like a pile of plate" src="//cdn.programiz.com/sites/tutorial2program/files/stack-of-plates_0.png" title="Pile of plates act as a stack" width="456" height="380"><figcaption>Stack representation similar to a pile of plate</figcaption></figure><p>Here, you can:</p>

<ul><li>Put a new plate on top</li>

<li>Remove the top plate</li>

</ul><p>And, if you want the plate at the bottom, you must first remove all the plates on top. This is exactly how the stack data structure works.</p>

<hr><h2 id="stack-terms">LIFO Principle of Stack</h2>

<p>In programming terms, putting an item on top of the stack is called <strong>push</strong> and removing an item is called <strong>pop</strong>.</p>

<figure><img alt="represent the LIFO principle by using push and pop operation" src="//cdn.programiz.com/sites/tutorial2program/files/stack.png" title="Stack operations" width="814" height="482"><figcaption>Stack Push and Pop Operations</figcaption></figure><p>In the above image, although item <strong>3</strong> was kept last, it was removed first. This is exactly how the <strong>LIFO (Last In First Out) Principle</strong> works.</p>

<p>We can implement a stack in any programming language like C, C++, Java, Python or C#, but the specification is pretty much the same.</p>

<hr><h2 id="spec">Basic Operations of Stack</h2>

<p></p><div class="clearfix"></div><p>There are some basic operations that allow us to perform different actions on a stack.</p>

<ul><li><strong>Push</strong>: Add an element to the top of a stack</li>

<li><strong>Pop</strong>: Remove an element from the top of a stack</li>

<li><strong>IsEmpty</strong>: Check if the stack is empty</li>

<li><strong>IsFull</strong>: Check if the stack is full</li>

<li><strong>Peek</strong>: Get the value of the top element without removing it</li>

</ul><hr><h2 id="working">Working of Stack Data Structure</h2>

<p>The operations work as follows:</p>

<ol><li>A pointer called <var>TOP</var> is used to keep track of the top element in the stack.</li>

<li>When initializing the stack, we set its value to -1 so that we can check if the stack is empty by comparing <code>TOP == -1</code>.</li>

<li>On pushing an element, we increase the value of <var>TOP</var> and place the new element in the position pointed to by <var>TOP</var>.</li>

<li>On popping an element, we return the element pointed to by <var>TOP</var> and reduce its value.</li>

<li>Before pushing, we check if the stack is already full</li>

<li>Before popping, we check if the stack is already empty</li>

</ol><figure><img alt="Adding elements to the top of stack and removing elements from the top of stack" src="//cdn.programiz.com/sites/tutorial2program/files/stack-operations.png" title="" width="1152" height="582"><figcaption>Working of Stack Data Structure</figcaption></figure><hr><h2 id="code">Stack Implementations in Python, Java, C, and C++</h2>

<p>The most common stack implementation is using arrays, but it can also be implemented using lists.</p>

<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>

</div>

<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"># Stack implementation in python</span>

<span class="hljs-comment"># Creating a stack</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">create_stack</span><span class="hljs-params">()</span>:</span>

stack = []

<span class="hljs-keyword">return</span> stack

<span class="hljs-comment"># Creating an empty stack</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">check_empty</span><span class="hljs-params">(stack)</span>:</span>

<span class="hljs-keyword">return</span> len(stack) == <span class="hljs-number">0</span>

<span class="hljs-comment"># Adding items into the stack</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">push</span><span class="hljs-params">(stack, item)</span>:</span>

stack.append(item)

<span class="hljs-keyword">print</span>(<span class="hljs-string">"pushed item: "</span> + item)

<span class="hljs-comment"># Removing an element from the stack</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">pop</span><span class="hljs-params">(stack)</span>:</span>

<span class="hljs-keyword">if</span> (check_empty(stack)):

<span class="hljs-keyword">return</span> <span class="hljs-string">"stack is empty"</span>

<span class="hljs-keyword">return</span> stack.pop()

stack = create_stack()

push(stack, str(<span class="hljs-number">1</span>))

push(stack, str(<span class="hljs-number">2</span>))

push(stack, str(<span class="hljs-number">3</span>))

push(stack, str(<span class="hljs-number">4</span>))

<span class="hljs-keyword">print</span>(<span class="hljs-string">"popped item: "</span> + pop(stack))

<span class="hljs-keyword">print</span>(<span class="hljs-string">"stack after popping an element: "</span> + str(stack))

</code></pre></div>

</div>

<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">// Stack implementation in Java</span>

<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Stack</span> </span>{

<span class="hljs-keyword">private</span> <span class="hljs-keyword">int</span> arr[];

<span class="hljs-keyword">private</span> <span class="hljs-keyword">int</span> top;

<span class="hljs-keyword">private</span> <span class="hljs-keyword">int</span> capacity;

<span class="hljs-comment">// Creating a stack</span>

Stack(<span class="hljs-keyword">int</span> size) {

arr = <span class="hljs-keyword">new</span> <span class="hljs-keyword">int</span>[size];

capacity = size;

top = -<span class="hljs-number">1</span>;

}

<span class="hljs-comment">// Add elements into stack</span>

<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">void</span> <span class="hljs-title">push</span><span class="hljs-params">(<span class="hljs-keyword">int</span> x)</span> </span>{

<span class="hljs-keyword">if</span> (isFull()) {

System.out.println(<span class="hljs-string">"OverFlow\nProgram Terminated\n"</span>);

System.exit(<span class="hljs-number">1</span>);

}

System.out.println(<span class="hljs-string">"Inserting "</span> + x);

arr[++top] = x;

}

<span class="hljs-comment">// Remove element from stack</span>

<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">int</span> <span class="hljs-title">pop</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (isEmpty()) {

System.out.println(<span class="hljs-string">"STACK EMPTY"</span>);

System.exit(<span class="hljs-number">1</span>);

}

<span class="hljs-keyword">return</span> arr[top--];

}

<span class="hljs-comment">// Utility function to return the size of the stack</span>

<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">int</span> <span class="hljs-title">size</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">return</span> top + <span class="hljs-number">1</span>;

}

<span class="hljs-comment">// Check if the stack is empty</span>

<span class="hljs-function"><span class="hljs-keyword">public</span> Boolean <span class="hljs-title">isEmpty</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">return</span> top == -<span class="hljs-number">1</span>;

}

<span class="hljs-comment">// Check if the stack is full</span>

<span class="hljs-function"><span class="hljs-keyword">public</span> Boolean <span class="hljs-title">isFull</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">return</span> top == capacity - <span class="hljs-number">1</span>;

}

<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">void</span> <span class="hljs-title">printStack</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 <= top; i++) {

System.out.println(arr[i]);

}

<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>{

Stack stack = <span class="hljs-keyword">new</span> Stack(<span class="hljs-number">5</span>);

stack.push(<span class="hljs-number">1</span>);

stack.push(<span class="hljs-number">2</span>);

stack.push(<span class="hljs-number">3</span>);

stack.push(<span class="hljs-number">4</span>);

stack.pop();

System.out.println(<span class="hljs-string">"\nAfter popping out"</span>);

stack.printStack();

}

}</code></pre></div>

</div>

<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">// Stack implementation 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-meta">#<span class="hljs-meta-keyword">define</span> MAX 10</span>

<span class="hljs-keyword">int</span> count = <span class="hljs-number">0</span>;

<span class="hljs-comment">// Creating a stack</span>

<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">stack</span> {</span>

<span class="hljs-keyword">int</span> items[MAX];

<span class="hljs-keyword">int</span> top;

};

<span class="hljs-keyword">typedef</span> <span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">stack</span> <span class="hljs-title">st</span>;</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">createEmptyStack</span><span class="hljs-params">(st *s)</span> </span>{

s->top = <span class="hljs-number">-1</span>;

}

<span class="hljs-comment">// Check if the stack is full</span>

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isfull</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (s->top == MAX - <span class="hljs-number">1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}

<span class="hljs-comment">// Check if the stack is empty</span>

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isempty</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (s->top == <span class="hljs-number">-1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}

<span class="hljs-comment">// Add elements into stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">push</span><span class="hljs-params">(st *s, <span class="hljs-keyword">int</span> newitem)</span> </span>{

<span class="hljs-keyword">if</span> (isfull(s)) {

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"STACK FULL"</span>);

} <span class="hljs-keyword">else</span> {

s->top++;

s->items[s->top] = newitem;

}

count++;

}

<span class="hljs-comment">// Remove element from stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">pop</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (isempty(s)) {

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n STACK EMPTY \n"</span>);

} <span class="hljs-keyword">else</span> {

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Item popped= %d"</span>, s->items[s->top]);

s->top--;

}

count--;

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);

}

<span class="hljs-comment">// Print elements of stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printStack</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Stack: "</span>);

<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < count; i++) {

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, s->items[i]);

}

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);

}

<span class="hljs-comment">// Driver code</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> ch;

st *s = (st *)<span class="hljs-built_in">malloc</span>(<span class="hljs-keyword">sizeof</span>(st));

createEmptyStack(s);

push(s, <span class="hljs-number">1</span>);

push(s, <span class="hljs-number">2</span>);

push(s, <span class="hljs-number">3</span>);

push(s, <span class="hljs-number">4</span>);

printStack(s);

pop(s);

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nAfter popping out\n"</span>);

printStack(s);

}</code></pre></div>

</div>

<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">// Stack implementation in C++</span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdlib.h></span></span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>

<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;

<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> MAX 10</span>

<span class="hljs-keyword">int</span> size = <span class="hljs-number">0</span>;

<span class="hljs-comment">// Creating a stack</span>

<span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">stack</span> {</span>

<span class="hljs-keyword">int</span> items[MAX];

<span class="hljs-keyword">int</span> top;

};

<span class="hljs-keyword">typedef</span> <span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">stack</span> <span class="hljs-title">st</span>;</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">createEmptyStack</span><span class="hljs-params">(st *s)</span> </span>{

s->top = <span class="hljs-number">-1</span>;

}

<span class="hljs-comment">// Check if the stack is full</span>

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isfull</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (s->top == MAX - <span class="hljs-number">1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}

<span class="hljs-comment">// Check if the stack is empty</span>

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isempty</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (s->top == <span class="hljs-number">-1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}

<span class="hljs-comment">// Add elements into stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">push</span><span class="hljs-params">(st *s, <span class="hljs-keyword">int</span> newitem)</span> </span>{

<span class="hljs-keyword">if</span> (isfull(s)) {

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"STACK FULL"</span>;

} <span class="hljs-keyword">else</span> {

s->top++;

s->items[s->top] = newitem;

}

size++;

}

<span class="hljs-comment">// Remove element from stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">pop</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-keyword">if</span> (isempty(s)) {

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"\n STACK EMPTY \n"</span>;

} <span class="hljs-keyword">else</span> {

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Item popped= "</span> << s->items[s->top];

s->top--;

}

size--;

<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;

}

<span class="hljs-comment">// Print elements of stack</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">printStack</span><span class="hljs-params">(st *s)</span> </span>{

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Stack: "</span>);

<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < size; i++) {

<span class="hljs-built_in">cout</span> << s->items[i] << <span class="hljs-string">" "</span>;

}

<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;

}

<span class="hljs-comment">// Driver code</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> ch;

st *s = (st *)<span class="hljs-built_in">malloc</span>(<span class="hljs-keyword">sizeof</span>(st));

createEmptyStack(s);

push(s, <span class="hljs-number">1</span>);

push(s, <span class="hljs-number">2</span>);

push(s, <span class="hljs-number">3</span>);

push(s, <span class="hljs-number">4</span>);

printStack(s);

pop(s);

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"\nAfter popping out\n"</span>;

printStack(s);

}</code></pre></div>

</div>

<hr><h2 id="complexity">Stack Time Complexity</h2>

<p>For the array-based implementation of a stack, the push and pop operations take constant time, i.e. <code>O(1)</code>.</p>

<hr><h2 id="applications">Applications of Stack Data Structure</h2>

<p>Although stack is a simple data structure to implement, it is very powerful. The most common uses of a stack are:</p>

<ul><li><strong>To reverse a word</strong> - Put all the letters in a stack and pop them out. Because of the LIFO order of stack, you will get the letters in reverse order.</li>

<li><strong>In compilers</strong> - Compilers use the stack to calculate the value of expressions like <code>2 + 4 / 5 * (7 - 9)</code> by converting the expression to prefix or postfix form.</li>

<li><strong>In browsers</strong> - The back button in a browser saves all the URLs you have visited previously in a stack. Each time you visit a new page, it is added on top of the stack. When you press the back button, the current URL is removed from the stack, and the previous URL is accessed.</li>

</ul></div>

</div>

<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents

<li><a href="#stack-terms">Stack in Programming Terms</a></li>

<li><a href="#spec">Stack Specification</a></li>

<li><a href="#working">How a Stack Works</a></li>

<li><a href="#code">Python, Java and C/C++ Examples</a></li>

<li><a href="#complexity">Stack Complexity</a></li>

<li><a href="#applications">Stack Applications</a></li>

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