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# Stack in Data Structure

The Last-In-First-Out (LIFO) principle governs the operation of a stack, which is a linear data structure. Although the Stack only has one end, the Queue has two (front and rear). It only has one pointer, top, which points to the topmost element of the stack. When a new element is added to the stack, it is placed at the top and can only be withdrawn. To put it another way, a stack can be thought of as a container into which data can be inserted and deleted from the top. In the actual world, there are several examples of stacks.

Consider the canteen, where platters are piled high with food. The top plate is the first to be removed, but the bottom plate is the one that stays in the stack the longest. As a result, the LIFO (Last In First Out)/FILO (First In Last Out) order is easily discernible.

## Stack in Data Structure

### ⌚ Introduction

A stack is a linear data structure that performs operations in a predetermined order. LIFO (Last In First Out) or FILO (First In Last Out) could be used (First In Last Out). In the actual world, there are several examples of stacks.
Consider the canteen, where platters are piled high with food. The top plate is the first to be removed, but the bottom plate is the one that stays in the stack the longest. As a result, the LIFO (Last In First Out)/FILO (First In Last Out) order is easily discernible.

Some Key Points :

π Because it behaves like a real-life stack, such as a stack of books, it's called a stack.
π A Stack is an abstract data type with a fixed capacity, which means it can only store components of a specific size.
π It's a data structure that inserts and deletes elements in a predetermined order, either LIFO or FILO.

### ⌚Working of Stack

Stack follows the LIFO pattern. The stack consists of five memory blocks, as illustrated in the diagram below; consequently, the stack's size is five.
Assume we want to put the items in a stack that is now empty. We've taken a size 5 stack and are pushing the components one by one until the stack is full, as shown below.
The size of our stack is 5 because it is full. We can see that when we added a new element to the stack in the scenarios above, it travelled from top to bottom. The stack is completely packed from bottom to top.
Because the opposite end of the stack is closed, there is only one path in and out when we delete something from it. The LIFO pattern is used, which means that the item that was placed first is the last to be removed. Because the number 5 was placed first in the previous example, it will only be deleted once the rest of the elements have been removed.

### ⌚Operations on Stack

Some of the most popular operations on the stack are as follows:

π push() :Pushing an element into a stack is done with the push() method. When the stack is full, the overflow condition occurs.
π pop(): A pop is an operation that removes an element from the stack. When the stack is empty, which means there are no elements on the stack, it enters an underflow state.
π isEmpty() Return true if stack is empty
π isFull() determines whether the stack is full or not.
π peek(): This function returns the element at the given coordinates.
π count() : A function that returns the total number of elements in a stack is count().
π alter() makes a change to the element at the given place.
π display() returns a list of all available elements in the stack.

Push Operation :

The PUSH operation is broken down into the following steps:

π Before adding an element to a stack, we make sure it's not already full.
π When we try to insert the element into a stack that is already full, we get an overflow problem.
π When we create a stack, we set the value of top to -1 to ensure that it is empty.
π When a new element is added to a stack, the top value is first incremented (top=top+1), and the element is then relocated to the new top position.
π The items will be added to the stack until it reaches its maximum capacity.

Pop Operation :

The steps involved in the POP procedure are as follows:

π Before eliminating an element from the stack, we make sure it's empty.
π We get an underflow problem when we try to remove an element from an empty stack.
π We start with the element pointed to by the top if the stack isn't empty.
π After the pop operation, the top is decremented by one, i.e. top=top-1.

### ⌚Stack in C++ STL

Stacks are a type of container adapter that works on the LIFO (Last In First Out) principle, in which a new element is added to one end (top) and an element is removed from the other end (bottom) (bottom). A stack's underlying container is an encapsulated object of type vector or deque (by default) or list (sequential container class), with a defined set of member functions for accessing its elements. To create a stack, we must include the stack> header file in our code. This syntax is then used to define the std:: keyword. stack:

```    template <class Type, class Container = deque<<ype> > class stack;
```

Type : Type is the type of the element in the std::stack.
Container : It's possible to utilise any valid C++ type or even a user-defined type.
Member types : The Type of the underlying container object.
Members' Characteristics:
Value type is the first template argument, T. It distinguishes between the many types of elements. The second template argument is the container type. It denotes the sort of container behind it. The size type is an unsigned and integral type.
The functions associated with stack are as follows:

empty() β Determines whether the stack is empty β Time Complexity: O(1)
size() β Determines the stack's size -Time Complexity: O(1)
top() β Returns a reference to the top most element of the stack β Time Complexity: O(1)
push(g) β Pushes the element 'g' to the top of the stack β Time Complexity: O(1)
pop() β Deletes the stack's topmost element.- Time Complexity: O(1)

```#include <iostream>
#include <stack>
using namespace std;
int main() {
stack<int> stack;
stack.push(10);
stack.push(20);
stack.push(30);
stack.push(40);

stack.pop();
stack.pop();

while (!stack.empty()) {
cout << ' ' << stack.top();
stack.pop();
}
}

Try it Yourself

```
```Ouput :
20 10
```

### ⌚Stack Class in Java

The Java Collection framework's Stack class depicts and implements a Stack data structure. The class is structured according to the last-in-first-out principle. In addition to the basic push and pop operations, the class offers three extra functions: empty, search, and peek. With the five functions provided, the class is said to extend Vector and is handled as a stack. The default Object() [native code] function for the class is Stack(), which creates an empty stack.

Declaration:

```    public class Stack extends Vector
```

Implemented Interfaces :

Serializable:Classes must implement the Serializable interface in order to be serialised and deserialized.
Cloneable: In Java, a class must implement this interface in order for its objects to be cloned.
Iterable<E> :This interface describes a set of iterable items, or elements that can be iterated.
Collection<E> : A collection consists of elements that represent a group of objects. The Collection interface is used to move collections of items around when maximum generality is desired.
List<E> : You can retain an ordered collection of items using the List interface. It is the child interface of a Collection.

We must import the java.util.stack package and utilise the Stack() function Object() { [native code] } of this class to create a stack. The example below builds a new Stack. Syntax :

```    Stack<=&;t;E> stack = new Stack<E>();
```

Here, E is the type of Object.

Example :

```import java.io.*;
import java.util.*;

class Test
{
static void stack_push(Stack<Integer> st)
{
for(int i = 0; i < 5; i++)
{
st.push(i);
}
}

static void stack_pop(Stack<Integer> st)
{
for(int i = 0; i < 5; i++)
{
Integer y = (Integer) st.pop();
System.out.println(y);
}
}

static void stack_peek(Stack<Integer> stack)
{
Integer element = (Integer) stack.peek();
System.out.println("Element on stack top: " + element);
}

public static void main (String[] args)
{
Stack<Integer> stack = new Stack<Integer>();

stack_push(stack);
stack_pop(stack);
stack_push(stack);
stack_peek(stack);
}
}

Try it Yourself

```
```Output :
Element on stack top: 4
```

### ⌚ Stack in Python

A stack in Python can be implemented in a variety of ways. This article describes how to build a stack using data structures and modules from the Python library.

In Python, stack can be implemented in the following ways:

πlist
π Collections.deque
π queue.LifoQueue

Append() adds elements to the bottom of the stack instead of pushing them to the top, whereas pop() removes them in LIFO order. Unfortunately, the list contains a few flaws. The biggest issue is that it may face speed issues as it increases. The list's contents are stored in memory adjacent to each other; if the stack grows larger than the current block of memory, Python must allocate more memory. As a result, certain add() calls may take a lengthy time compared to others.

```
stack = []

stack.append('x')
stack.append('y')
stack.append('z')

print('Initial stack')
print(stack)

print('\nElements popped from stack:')
print(stack.pop())
print(stack.pop())
print(stack.pop())

print('\nStack after elements are popped:')
print(stack)

Try it Yourself

```
```Output :
Initial stack
['x', 'y', 'z']

Elements popped from stack:
z
y
x

Stack after elements are popped:
[]

```

### ⌚ Stack in C#

A Stack in Data Structure is a collection of things that is ordered by last-in, first-out. When you need last-in, first-out access to items, this is the method to utilise. It's a compilation that's both generic and non-generic. System is where the generic stack is defined. Collections. The generic namespace is defined under System, whereas the non-generic stack is defined under Generic. We'll talk about non-generic type stack in the Collections namespace. A stack is used to construct a dynamic collection that expands in response to your program's requirements. You can store components of the same type or various types in a stack.

Points to Remember:

π The interfaces IEnumerable, ICollection, and ICloneable are all implemented by the Stack class.
πPushing the element refers to the act of adding a new item to a list.
πIt's known as popping the element when it's removed.
πThe number of elements that a Stack can hold is its capacity.
πThe capacity of a Stack is automatically raised as needed as elements are added to it through reallocation. A Duplicate elements are allowed to be stored in Stack.
π For reference types, a Stack accepts null as a valid value.

The following are the three constructors for the Stack class that are used to generate a stack:

Stack(): This function Object() { [native code] } is used to make an empty instance of the Stack class with the default initial capacity.
Stack(ICollection): This function Object() { [native code] } creates a Stack object with the same starting capacity as the number of elements copied from the provided collection.
Stack(Int32): This function Object() { [native code] } is used to make an empty Stack instance with the supplied initial capacity or the default initial capacity, whichever is greater. Let's look at how to make a stack with the Stack() function Object() { [native code] }:

```using System;
using System.Collections;

class Main {

// Main Method
static public void Main()
{

Stack st = new Stack();

st.Push("A");
st.Push("B");
st.Push('G');
st.Push(null);
st.Push(1234);
st.Push(490.98);

foreach(var x in st)
{
Console.WriteLine(x);
}
}
}
```
```Output :
490.98
1234

G
B
A
```

### ⌚Application of Stack

The following are some of the stack's applications:

πSymbol balancing: To balance a symbol, utilise stack.
πString reversal: Stack can also be used to reverse a string. For instance, if we want to invert a "logicmojo" string, we can do it with a stack. To begin, we stack the string's characters until we reach the null character. After we've put all of the characters to the bottom of the stack, we'll start eliminating them one by one.
πUNDO/REDO: It can also be used for UNDO/REDO-related activities. For instance, we have an editor in which we type 'a,' then 'b,' and finally 'c,' resulting in abc as the editor's text. As a result, the states a, ab, and abc are stored in a stack. There would be two stacks: one for UNDO status and the other for REDO status. If we wish to do UNDO and go to the 'ab' state, we use the pop operation.
πRecursion: A function is considered to be recursive when it calls itself. The compiler creates a system stack that keeps all of the function's previous records to keep track of previous states. DFS (Depth First Search): This search is conducted using a Graph that use the stack data structure. Let's pretend we're trying to solve a maze problem and need to find a way out. If we are driving along a road and realise that we have made a wrong turn. To get back to the beginning of the path and start over, we'll need to use the stack data structure.
πConversion of expressions: Stack can convert expressions. This is one of the most important applications in the stack. A list of expression conversions is shown below:

Infix to prefix
Infix to postfix
Prefix to infix
Prefix to postfix
Postfix to infix
πMemory Management : The stack is in charge of memory management. To assign memory, contiguous memory blocks are employed. The memory is called stack memory because all of the variables are assigned in a function called stack memory. The memory size given to the program is known to the compiler. When the function is built, all of the variables are assigned to the stack memory. Once the function has completed its execution, all variables assigned to the stack are released.

### πConclusion

Stack in Data Structure, After completely overviewed the page now, you are able to know what is stack, operations on stack, Stack in C++, Java, Python and C#.

In computer science, a stack is a basic data structure that adheres to the Last In First Out (LIFO) rule. It functions by storing and retrieving elements in a specific order.

Element addition and removal in a stack always start from the same end, often known as the "top" of the stack. The LIFO principle states that the last piece added to the stack gets deleted first. This behavior is comparable to a stack of items where the top object is the first one to be accessed or removed and new objects are always added on top.

The essential actions carried out on a stack are:

1. Push: Pushing an element up the stack is what it means to do. Any previously existing elements below the new element keep their relative order, and the new element rises to the top of the stack.

2. Pop: The term "pop" refers to the removal of the topmost stacking piece. The element that is "popped" becomes the bottom of the stack and is permanently removed from it.

3. Peek: The topmost element's value is retrieved without removing it, and this operation is known as "peek." With the peek operation, you can look at the top-most stack element without changing the stack itself.

4. IsEmpty: Determines whether or not the stack is empty. A boolean value indicating if there are any elements in the stack is returned by this operation.

Typically, the stack is pictured as a vertical structure with pieces stacked on top of one another. An element "sits" on top of the earlier components when it is pushed onto the stack.

The top element is also deleted when an element is popped, exposing the element below.

Stacks come in handy for a number of situations, including but not restricted to:

1. Function calls: To manage function calls and keep track of the execution flow, computer languages and compilers employ stacks. When a function has finished running, it is removed off the stack, which enables the program to resume where it left off when the function was called.

2. Expression evaluation: Arithmetic expressions infix, postfix, and prefix notations are evaluated using stacks. They aid in upholding the precedence of operations and evaluating expressions in accordance with certain rules.

3. Undo/Redo operations: Stacks are used in programs that need the ability to undo and redo actions. Each action taken by the user is added to a stack, which they may then remove pieces from to undo or redo their actions.

4. Backtracking algorithms: Many algorithms use stacks to record the current state of their search or exploration, including depth-first search and backtracking. This makes traversing a list of potential outcomes and going back in time efficient.

Stack operations are straightforward and effective, making them a useful data structure in many branches of computer science. Because of its LIFO nature and capacity for managing nested actions or states, it excels in situations where efficiency and access to the most recent element are crucial.

There are primarily two sorts of stacks in the context of the stack data structure: fixed-size stacks and dynamic stacks. How each of these types manages the stack's size and capacity varies. Let's examine each kind in greater detail:

1. Fixed-Size Stacks: Fixed-size stacks have a fixed capacity that stays the same during the course of their existence.

- The stack's size is fixed during construction and cannot be changed later.

- An overflow condition occurs when the stack is full and more elements are attempted to be pushed onto it.

- Fixed-size stacks are implemented using arrays, and their maximum number of elements is determined by their fixed length.

- Push and pop operations on fixed-size stacks take a constant amount of time and are reasonably easy to implement.

- However, if the number of pieces exceeds the stack's capacity, the restriction of a fixed size may result in inefficiencies.

2. Dynamic Stacks: These stacks, sometimes referred to as resizable stacks, can change in size according to the number of elements they include.

- They can expand or contract as necessary and dynamically allocate memory.

- Typically, dynamic stacks have a lower initial capacity and dynamically rise when new pieces are added.

- The stack is resized by allocating a larger memory block and copying the old pieces to the new block when it reaches its maximum capacity.

- In comparison to fixed-size stacks, dynamic stacks are more adaptable because they can hold any number of items.

- The items must be copied to the new memory block, which adds time and memory overhead to enlarging the stack.

- Dynamic stacks frequently use tactics like incremental resizing or doubling the capacity to reduce the resizing overhead.

Both static and dynamic stacks provide the same basic operations: push, pop, peek, and isEmpty, and both follow the Last In First Out (LIFO) concept. The distinction is in how they manage the stack's capacity:

- Fixed-size stacks have a consistent capacity that, once set, cannot be changed. They are appropriate when there is no requirement for dynamic memory allocation or resizing and the quantity of elements to be stored is known in advance.

- On the other hand, dynamic stacks provide flexibility by dynamically resizing the stack as necessary. They are helpful when handling a varied number of items is necessary and the number of elements to be stored can fluctuate.

It's important to keep in mind that depending on the programming language and particular needs of an application, the implementation details of stacks, whether fixed-size or dynamic, can change. The nature of the issue and the expected size variability of the stack determine which of the two types should be used.

Elements can be added, removed, and accessed using a number of core operations that the stack data structure provides. Here are thorough explanations of a stack's fundamental functions:

1. Push: Pushing an element causes it to be added to the top of the stack.

- It accepts the parameter for the element to be added and moves it to the top of the stack.

- The newly added element rises to the top of the stack following the push action, and any existing components below it keep their relative positions.

- Depending on the implementation, pushing an element onto a full stack could cause an overflow problem.

2. Pop: The element is taken out of the stack's top position using the pop operation.

- It brings back the stack element that was dumped.

- The element below the top element becomes the new top of the stack following the pop action.

- Depending on the implementation, popping an element from an empty stack could lead to an underflow problem.

3. Peek: The peek operator just returns the stack's top member without erasing it.

- Without altering the stack itself, you can check the value of the topmost piece.

- The stack's state and its components are unaffected by the peek operation.

4. IsEmpty: This operation determines whether the stack is empty.

- If there are any elements in the stack or not, a boolean value is returned.

- The isEmpty operator returns true if the stack is empty and false otherwise.

5. IsFull: This operation determines whether the stack is full.

- If the stack has reached its capacity, a boolean value that indicates whether it has or not is returned.

- The definition of "full" depends on the particular implementation and the stack's capacity.

- Since some stacks may be dynamically resizable and able to expand as necessary, not all stack implementations have an isFull action.

The basis for modifying and accessing elements in a stack is provided by these fundamental operations taken as a whole. They enable Last In First Out (LIFO) ordering for both the addition and removal of items. While the peek operation gives read-only access to the top element, the push and pop actions change the state of the stack. Before carrying out any operations, the stack's status is checked using the isEmpty and isFull procedures to make sure it is in the desired state.

While these activities are basic to a stack, it's crucial to remember that other operations can be defined based on the needs of the application. These extra processes could involve cleaning the stack, determining its size, or looking for a particular piece inside the stack. Depending on the implementation and requirements of the problem being solved, a stack's supported operations may change.

The stack data structure's Last In First Out (LIFO) characteristic and effective operations make it useful in a variety of fields. Here are a few typical uses for a stack:

1. Expression Parsing: Stacks are frequently employed to evaluate the outcomes of parsing arithmetic expressions.

- Stacks aid in ensuring the proper order of operations in infix notation, where operators are positioned between operands (for example, 3 + 5).

- Operators are placed on the stack during parsing, and when operands are encountered, the required operations are carried out using the operands and operators at the top of the stack.

2. Backtracking Algorithms: Backtracking algorithms, like depth-first search (DFS), frequently use stacks to keep track of states or decisions.

- The decisions that were made in order during the search process are kept in the stack.

- The program re-examines alternate paths after analyzing probable solutions by popping pieces from the stack.

3. Undo/Redo capability:

- Applications that offer undo and redo capability use stacks.

- Each action taken by the user is added to the stack, giving them the option to undo or redo it.

- The stack keeps track of the user's actions in order to allow the application to browse through their past.

4. Function Calls: In programming languages, stacks are essential for controlling function calls.

- Each function call has a stack frame maintained by the stack during program execution that includes local variables, parameters, return addresses, and other pertinent data.

- A new stack frame is added to the stack each time a function is called, and when the function is finished, its stack frame is removed from the stack, giving control back to the calling function.

5. Implementations of Compilers and Interpreters: Stacks are essential to the functioning of compiler and interpreter implementations.

- They are used to manage control flow, track variables, and maintain execution contexts in addition to storing interim results.

- Stacks help with resource management by keeping track of hierarchical constructions like loops, conditionals, and subroutines.

6. Parenthesis Matching: Stacks are used to address problems with the matching or balancing of parentheses.

- They aid in determining whether parentheses, brackets, or braces are properly nested and closed in an expression.

- Opening symbols are added to the stack, and the top symbol in the stack is used as a match when a closing symbol is encountered.

These are only a few applications that show how stacks are used in different branches of computer science and software development. Stacks are flexible tools for organizing data and regulating program flow in a variety of circumstances because to their LIFO nature, simplicity, and efficiency.

Last In First Out (LIFO) is the fundamental tenet of stacks. The last piece added into the stack is the first one to be withdrawn, which describes how a stack behaves.

A stack data structure's operations and ordering are governed by the LIFO concept.

Let's examine the fundamental idea behind a stack in more detail:

1. Last In First Out (LIFO): According to the LIFO concept, the oldest element should be at the bottom of the stack and the newest element should be at the top.

- The top of the stack is where items are added or removed, and until the top elements are removed, no element above the top of the stack is accessible.

- Any existing items below a newly added element keep their relative order when a new element is added, making it the new top of the stack.

- The element directly behind the one that is removed from the stack becomes the new top.

2. Operations on Stacks:

- Push: The push operation involves moving an element to the top of the stack. The new element rises to the top of the stack, keeping any earlier elements in its place. The size of the stack is increased by this action.

- Pop: The pop operation is the act of removing the topmost element from the stack. The element that is "popped" becomes the bottom of the stack and is permanently removed from it. The size of the stack is reduced by this action.

- Peek: The peek action involves looking at the element at the top of the stack without deleting it. Without altering the stack, it enables access to the value of the topmost element.

- IsEmpty: Determines whether or not the stack is empty. If there are no elements on the stack, this operation returns true; otherwise, it returns false.

3. Visualizing the Stack: You can think of a stack as a vertical structure that looks like a pile of stuff.

- Elements are layered on top of one another, with the newest addition being at the top and the oldest being at the bottom.

- The only entry point for adding or removing items is at the top of the stack.

- Until the elements above them are deleted, the elements below the top are unavailable.

4. Stack Activity: - A stack's LIFO behavior simulates real-world situations. Imagine a stack of books or plates where the last item added to the top is the first to be removed. When the sequence of access or processing is crucial, such as when evaluating expressions or controlling function calls, the LIFO approach is appropriate.

Certainly! Two popular methods for implementing a stack data structure are by using an array and by using a linked list. Let's examine each technique of implementation in greater detail:

1. Array Implementation: In the array implementation, the stack's components are kept in a fixed-size array.

- An index variable that links to the most recent piece added to the stack serves as the top of the stack.

- The stack is initially empty, and its top index is set to 1.

- The top index is increased and the element is put in the array at the relevant index when an element is pushed onto the stack.

- The element at the top index is retrieved when an element is popped from the stack, and the top index is decreased.

- The top index being -1, which denotes an empty stack, is checked by the isEmpty procedure.

- The isFull operation determines whether the top index equals the array's size minus one, which denotes a full stack.

Simple and memory-efficient array implementation. Its finite size, nevertheless, means that if the stack expands too much, it can run into problems. It can be expensive to resize the array and copy elements.

2. Implementing Linked Lists: - The components of the stack are stored in a dynamic linked list in the linked list implementation.

- The data and a reference to the following node are contained in each node of the linked list, which each represents a component of the stack.

- The head of the linked list serves as a representation of the top of the stack.

- A new node is generated and its data is set to the new element when an element is put onto the stack. The linked list's current top (head) is the new node's next reference. The new node takes over as the top.

- The top node (head) is dropped when an element is removed from the stack, and the following node takes its place as the new top.

- By examining whether the head is null, the isEmpty operation determines whether the stack is empty.

- The linked list approach enables the stack to expand and contract as necessary because a linked list is capable of dynamic memory allocation.

Implementing a linked list offers versatility in handling a varied number of components. Unlike an array implementation, it doesn't have a fixed size restriction. To store the data and keep track of the following references, each node in the linked list requires extra memory.

It's important to keep in mind that these are simply two typical methods for building a stack. Stack implementations can also make use of other types of data structures, such as dynamic arrays or other linked data structures. The needs of the application, the anticipated size of the stack, memory efficiency, and the requirement for dynamic resizing all play a role in the implementation choice.

The first element in a stack data structure is frequently referred to as the "bottom" or "initial" element. It's crucial to remember that the terminology used to describe the first piece can change based on the situation and the angle from which the stack is seen. Let's examine the many features of the top member in a stack:

1. Bottom Element: The first element to be added to a stack is at the bottom of the stack.

- Subsequent components are stacked on top of it; it is the oldest element in the stack.

- Up until all the elements above it have been taken out, the lowest element stays in place.

- Unless all the items on top of it have been deleted, the bottom element is unreachable and cannot be accessed or removed.

2. Initial Element: The first element to be added to an empty stack is referred to as the initial element.

- A stack is empty and devoid of any elements when it is first built or reset.

- When an element is added using the push operation, the initial element becomes the stack's top element.

- As new components are pushed onto the stack, older elements are stacked on top of the newer ones.

3. Top Element: The element at the top of the stack is the most recent addition.

- It was the final item pushed into the stack.

- The element that will be accessed or removed next using the pop or peek operation is the one at the top.

It's crucial to realize that the idea of a stack's first element is relative and dependent on the sequence in which operations are carried out on the stack. The most recent piece is placed on top, with the oldest element serving as the bottom element in the stack. The top element is removed first when executing pop operations, while following components are accessed or removed in reverse order.

There are essentially two types of stack data structures: static stack and dynamic stack. These types vary in terms of their fundamental implementation and how they manage the stack's size and capacity. Let's examine each kind in greater detail:

1. Static Stack - Also referred to as a fixed-size stack, a static stack has a specified fixed capacity.

- The stack's initial size, which is fixed for the duration of the stack, never changes.

- Arrays are commonly used to implement static stacks, and the size of the array specifies how many elements the stack may retain in total.

- If space is available within the defined capacity, an element that is pushed onto a static stack is added to the top of the stack.

- When an element is added to a static stack that is already full, the predetermined limit is exceeded, causing an overflow problem.

- Since the memory for the stack is pre-allocated, static stacks are memory-efficient and simple to create.

- However, if the number of pieces is greater than the stack's capacity, their fixed size may be a drawback.

- The stack must be enlarged or a new stack with a bigger capacity must be built in order to handle more elements than the fixed limit.

2. Dynamic Stack: A dynamic stack, sometimes referred to as a resizable stack, can change in size depending on how many components it contains.

- Linked lists or dynamic arrays are frequently used to implement dynamic stacks.

- A dynamic stack might begin with a minimal initial size and change in size when pieces are added or removed.

- If there is room on a dynamic stack when an element is pushed onto it, it is added to the top like it would be on a static stack.

- A dynamic stack is, however, resized by allotting a larger memory block when it reaches its maximum size.

- Resizing entails making a new memory block, copying the current pieces into it, and updating the references or pointers on the stack.

- This technique of scaling enables a dynamic stack to support any number of pieces.

- Dynamic stacks are adaptable and can accommodate various element counts without experiencing overflow circumstances.

- Resizing the stack, however, requires memory allocation and element copying, which adds time and memory overhead.

- Dynamic stacks may employ tactics like tripling the capacity or using incremental resizing to reduce the resizing overhead.

Both static and dynamic stacks offer the same essential operations: push, pop, peek, and isEmpty, and both follow the Last In First Out (LIFO) principle. They manage the size and capacity of the stack differently, which makes a difference:

Static stacks are generated with a defined capacity, and unless specifically downsized or recreated, their size remains constant.

Dynamic stacks are able to adapt to changing element counts by dynamically adjusting their size when new items are added or removed.

Certainly! Let's go over a stack data structure's benefits and drawbacks in more detail:

The advantages of a stack data structure include:

1. Simple to Use: Stacks are reasonably easy to use and comprehend. A stack's fundamental operations, including as push, pop, peek, and isEmpty, are simple to implement, making it approachable for beginners and ensuring usability.

2. Last In First Out (LIFO) Order: Stacks follow the LIFO principle, which makes them effective for tasks requiring order maintenance or processing components in reverse order. In situations like retracing, undo/redo capabilities, and function call management, LIFO order is useful.

3. Memory Efficiency: Because stacks only need space for the elements they are storing, they offer efficient memory consumption. Because there is less dynamic memory allocation related to the stack, memory resources can be used effectively.

Disadvantages of the Stack Data Structure:

1. Lack of Random Access: Elements cannot be accessed randomly through stacks. It can be time-consuming and wasteful to access or edit elements in the middle of a stack without first removing all the elements on top. Stacks are not appropriate for situations requiring frequent random access because they are primarily intended for sequential processing.

2. Limited Functionality for Some activities: Searching and sorting activities do not work well with stacks. Stacks do not offer direct access to elements at any point, unlike other data structures like arrays or linked lists. It could be necessary to use additional data structures or algorithms to carry out these actions effectively.

3. Problems with Recursion: Using stacks directly to implement Recursion, a technique where a function calls itself, can be difficult. Since the runtime system of the programming language controls the stack utilized in function calls, attempting to manually simulate recursion using stacks can be difficult and error-prone.

It's crucial to remember that the benefits and drawbacks of a stack data structure depend on the particular specifications of the issue at hand. While stacks thrive in some situations, such as keeping the order or handling function calls, they might not be the best option in all circumstances. Selecting the best data structure for a given problem and ensuring efficient and effective solution design are made easier by knowing a stack's advantages and disadvantages.

Certainly! Let's talk about the various ways an array and a linked list may be used to accomplish the push operation on a stack:

1. Array Implementation: In the array implementation, the stack's components are kept in a fixed-size array.

- In order to use the push operation:

- To begin with, determine whether the stack is already full by comparing the top index to the array's size minus one.

- If there is space on the stack, raise the top index and insert the new element at the new top index location.

- When the stack is full, an overflow condition is present and the push operation cannot be carried out.

Since accessing an array element by index is a constant time operation, the push operation in an array implementation has a temporal complexity of O(1).

2. Linked List Implementation: In the linked list implementation, the elements of the stack are stored in a dynamic linked list.

- In order to use the push operation:

- Make a new node to reflect the newly inserted element.

- Change the new node's data to reflect the value of the new element.

- Change the new node's next reference to the linked list's current top node (head).

- Update the head to point to the new node to make it the new stack's top node.

Since adding a new node to the list's beginning is a constant-time operation, the push operation in a linked list implementation likewise has an O(1) time complexity.

Implementations using linked lists and arrays both enable effective pushing of elements into the stack. The decision between the two methods is influenced by things like the anticipated stack size, memory needs, and the requirement for dynamic resizing. While linked list implementations can accommodate a variable number of elements and offer dynamic resizing possibilities, array implementations offer direct access to elements using indices and have fixed capacities.

It's important to note that there are more ways to implement the push operation on a stack in addition to these. Depending on the needs and trade-offs, different data structures or methods may also be utilized, such as dynamic arrays or even a combination of arrays and linked lists. Performance, memory utilization, and adaptability should all be taken into account when choosing an implementation strategy.

Certainly! Let's talk about the various approaches to use an array and a linked list to accomplish the pop operation on a stack:

1. Array Implementation: In the array implementation, the stack's components are kept in a fixed-size array.

- In order to use the pop operation:

- Start by comparing the top index with -1 to see if the stack is not empty.

- Retrieve the element at the top index and temporarily store it if the stack is not empty.

- To remove the top element from the stack, decrement the top index.

- As a result of the pop action, return the element that was temporarily saved.

- It signals an underflow condition and the pop operation cannot be carried out if the stack is already empty.

Since accessing an array element by index and decrementing the index are constant time operations, the pop operation in an array implementation likewise has an O(1) time complexity.

2. Linked List Implementation: In the linked list implementation, the elements of the stack are stored in a dynamic linked list.

- In order to use the pop operation:

- Check to see if the linked list's head (top) is not null to see whether the stack is not empty.

- Retrieve the data from the head node, which stands for the top element, if the stack is not empty.

- Remove the top node by updating the head to point to the subsequent node in the linked list.

- As a consequence of the pop action, return the data that was retrieved.

- It signals an underflow condition and the pop operation cannot be carried out if the stack is already empty.

Since removing the first node from a linked list is a constant-time operation, the pop operation in a linked list implementation likewise has an O(1) time complexity.

Implementations using arrays and linked lists both enable effective popping of elements from the stack. The decision between the two methods is influenced by things like the anticipated stack size, memory needs, and the requirement for dynamic resizing. While linked list implementations can support a variable number of elements and offer dynamic resizing capabilities, array implementations offer direct access to elements via indices.

It's important to remember that there are other ways to implement the pop operation on a stack than these. Depending on the needs and trade-offs, different data structures or methods may also be utilized, such as dynamic arrays or even a combination of arrays and linked lists. Performance, memory utilization, and adaptability should all be taken into account when choosing an implementation strategy.

Fundamental data structures for managing and arranging collections of components include stacks and queues. Despite certain similarities, they are unique from one another and have separate functions. The following are the main variations between queues and stacks:

1. Sequence of Events:

- Stack: The Last In First Out (LIFO) concept is used in stacks. The first item to be removed from the stack is the last one to be added. The same end, frequently referred to as the top of the stack, is where elements are added and deleted.

- Queue: The First In First Out (FIFO) principle governs queues. The first item to be removed is the first one that is placed to the queue. The front or head of the queue is where items are removed after being added at one end, which is frequently referred to as the back or rear of the queue.

2. Insertion and Extraction:

- Stack: The top of the stack is where elements are added to and taken out of. The top element gets popped off the stack as further items are pushed onto it.

- Queue: Items are added to the back of the line and taken away from the front. The front element is dequeued, and new elements are added.

3. Efficiency of Operation:

- Stack: Because they directly reach the top of the stack, the push, pop, and peek operations on a stack have an O(1) time complexity. Adding and removing pieces at one end is effectively done with stacks.

- Queue: On a queue, the enqueue, dequeue, and peek operations all have an O(1) time complexity, making them effective for adding and removing elements at opposite ends.

4. Utilization and Uses:

- Stack: When managing a last-in, first-out order is necessary, stacks are frequently employed. Examples include function calls, expression evaluation, undo/redo actions, and backtracking algorithms.

- Queue: Queues are utilized in scenarios involving a first-in, first-out order, such as simulations, task scheduling, message queuing, and breadth-first search.

5. Organization and Representation: - Stack: Stacks may be constructed using dynamic arrays, linked lists, or arrays in arrays. The top is the only accessible point in a linear arrangement of components that makes up the underlying structure.

- Queue: Arrays, linked lists, or dynamic arrays can also be used to build queues. The access locations are indicated by front and back pointers, while the underlying structure is a linear arrangement of components.

6. Elements Access:

- Stack: Only the top element can be accessed directly through stacks. Elements on top must be removed in order to access elements in the centre of the stack.

- Line: Lines offer easy access to both the front and back elements. Dequeuing elements until you reach the desired element is necessary when accessing elements that are in the middle.

In conclusion, the main difference between queues and stacks is the order of operations (FIFO for queues and LIFO for stacks) and the accompanying insertion and removal behaviors. While queues work well for first-in, first-out situations, stacks are best for managing last-in, first-out situations. Programmers can select the best data structure depending on their unique requirements and problem-solving needs by being aware of these variances.

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