Introduction to Stacks

A stack is a fundamental data structure in computer science that follows the Last-In, First-Out (LIFO) principle. It is an ordered collection of elements where the addition of new elements and the removal of existing elements occur at the same end. This end is commonly referred to as the top of the stack.

Stacks are heavily used in programming for various purposes, including function calls, expression evaluation, history tracking, and more. They provide an efficient way to manage data in certain scenarios.

Basic Properties of Stacks

Here are some key properties of stacks:

• LIFO Ordering: Stacks follow the LIFO ordering, which means that the last element added to the stack will be the first one to be removed.

• Two Fundamental Operations: Stacks support two fundamental operations:

  • Push: Adds an element to the top of the stack.
  • Pop: Removes and returns the top element from the stack. If the stack is empty, an error may occur.

• Peek/Top: Retrieves the top element of the stack without removing it.

Implementation of Stacks

There are several ways to implement a stack, including using arrays, linked lists, or dynamic arrays. Each implementation has its own advantages and disadvantages depending on the specific use case.

Array-Based Stack

An array-based stack uses a fixed-size array to store the elements. The top of the stack is tracked using an index variable that points to the last inserted element. When the stack is full, it cannot accommodate additional elements. This implementation provides constant-time complexity for the push and pop operations.

Linked List-Based Stack

A linked list-based stack uses a linked list to store the elements. Each node in the linked list represents an element, and the top of the stack is represented by the head of the linked list. This implementation allows for dynamic resizing and can accommodate an arbitrary number of elements. However, it requires additional memory to store the references of the nodes.

Example

Let's take a look at an example Java code that demonstrates the basic operations of a stack:

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}

class Main {

  public static void main(String[] args) {

    // Create an empty stack

    Stack<Integer> stack = new Stack<>();

​

    // Push elements into the stack

    stack.push(5);

    stack.push(10);

    stack.push(15);

​

    // Check if the stack is empty

    boolean isEmpty = stack.isEmpty();

​

    // Get the size of the stack

    int size = stack.size();

​

    // Peek at the top element of the stack

    int topElement = stack.peek();

​

    // Pop an element from the stack

    int poppedElement = stack.pop();

​

    // Print the elements

    System.out.println("Stack: " + stack);

    System.out.println("Is Empty: " + isEmpty);

    System.out.println("Size: " + size);

    System.out.println("Top Element: " + topElement);

    System.out.println("Popped Element: " + poppedElement);

  }

Implementing a Stack

When implementing a stack, there are several ways to represent the underlying data structure. The choice of implementation depends on various factors, such as the programming language used, the application requirements, and the desired performance characteristics.

Array-Based Stack

One common way to implement a stack is by using an array. In this implementation, the stack elements are stored in a fixed-size array, and an index variable is used to keep track of the top element.

Here's an example of how an array-based stack can be implemented in Java:

1public class ArrayStack {
2  private int maxSize;
3  private int[] stackArray;
4  private int top;
5
6  public ArrayStack(int size) {
7    maxSize = size;
8    stackArray = new int[maxSize];
9    top = -1;
10  }
11
12  public void push(int value) {
13    if (isFull()) {
14      System.out.println("Stack is full. Cannot push element.");
15      return;
16    }
17
18    stackArray[++top] = value;
19  }
20
21  public int pop() {
22    if (isEmpty()) {
23      System.out.println("Stack is empty. Cannot pop element.");
24      return -1;
25    }
26
27    return stackArray[top--];
28  }
29
30  public int peek() {
31    if (isEmpty()) {
32      System.out.println("Stack is empty. No top element.");
33      return -1;
34    }
35
36    return stackArray[top];
37  }
38
39  public boolean isEmpty() {
40    return top == -1;
41  }
42
43  public boolean isFull() {
44    return top == maxSize - 1;
45  }
46}

In the above implementation, the ArrayStack class has a stackArray variable to hold the elements, a top variable to keep track of the top element's index, and methods to perform stack operations such as push, pop, and peek. The isFull and isEmpty methods check if the stack is full or empty, respectively.

The advantage of using an array-based stack is that it provides constant-time complexity for the push and pop operations. However, it requires a fixed-size array, which may limit the number of elements the stack can hold. Additionally, if the stack becomes full, further push operations will result in an error.

Linked List-Based Stack

Another way to implement a stack is by using a linked list. In this implementation, each element of the stack is represented by a node in the linked list, and the top of the stack is represented by the head of the linked list.

Here's an example of how a linked list-based stack can be implemented in Java:

1public class LinkedListStack {
2  private Node top;
3
4  public void push(int value) {
5    Node newNode = new Node(value);
6    newNode.next = top;
7    top = newNode;
8  }
9
10  public int pop() {
11    if (isEmpty()) {
12      System.out.println("Stack is empty. Cannot pop element.");
13      return -1;
14    }
15
16    int value = top.data;
17    top = top.next;
18    return value;
19  }
20
21  public int peek() {
22    if (isEmpty()) {
23      System.out.println("Stack is empty. No top element.");
24      return -1;
25    }
26
27    return top.data;
28  }
29
30  public boolean isEmpty() {
31    return top == null;
32  }
33
34  private class Node {
35    private int data;
36    private Node next;
37
38    public Node(int value) {
39      data = value;
40    }
41  }
42}

In the above implementation, the LinkedListStack class uses a nested Node class to represent the elements of the stack. The push, pop, peek, and isEmpty methods are similar to the array-based implementation but operate on the linked list structure.

The advantage of using a linked list-based stack is that it allows for dynamic resizing and can accommodate an arbitrary number of elements. However, it requires additional memory to store references to the next nodes in the list, which may result in a higher memory overhead compared to the array-based implementation.

Conclusion

When implementing a stack, consider the specific requirements of your application and the trade-offs between the array-based and linked list-based implementations. Both options have their advantages and disadvantages, and the choice depends on factors such as memory efficiency, performance, and flexibility.

Now that you understand different ways to implement a stack and their pros and cons, let's move on to exploring the common operations performed on a stack in the next section.

Stack Operations

In this section, we will explore the common operations performed on a stack. A stack supports three primary operations:

• Push: Adds an element to the top of the stack
• Pop: Removes and returns the top element from the stack
• Peek: Returns the top element from the stack without removing it

These operations are essential for manipulating the stack and implementing various algorithms and data structures.

Let's start by understanding the push operation.

1// Push operation
2void push(int value) {
3  // Add implementation here
4}

The push operation adds an element to the top of the stack. It takes the element to be added as a parameter and inserts it into the stack. The push operation may fail if the stack is already full, in which case an error can be returned or an exception can be thrown.

Next, let's move on to the pop operation.

1// Pop operation
2int pop() {
3  // Add implementation here
4  return 0; // return the popped element
5}

The pop operation removes and returns the top element from the stack. It takes no parameters and modifies the stack by removing the top element. The pop operation may fail if the stack is empty, in which case an error can be returned or an exception can be thrown.

Finally, let's discuss the peek operation.

1// Peek operation
2int peek() {
3  // Add implementation here
4  return 0; // return the top element
5}

The peek operation returns the top element from the stack without removing it. It takes no parameters and simply returns the value of the top element. The peek operation does not modify the stack.

Understanding these basic stack operations is crucial for utilizing stacks effectively in various scenarios. In the next section, we will explore real-world applications of stacks and see how they are used in practice.

Applications of Stacks

Stacks are widely used in computer science due to their ability to efficiently manage data in a Last-In-First-Out (LIFO) manner. Let's explore some common real-world applications of stacks:

• Function Call Stack: Stacks are essential in programming languages for managing function calls. Whenever a function is called, a new frame is pushed onto the stack, which contains information about the function's local variables and return address. This allows functions to execute and return in the correct order.
• Expression Evaluation: Stacks are often used to evaluate arithmetic expressions. For example, the expression 5 10 + 3 * can be evaluated using a stack-based calculator algorithm. Here's an example in Java:

1<<code>>

• Browser History: Many web browsers use a stack to implement the Back and Forward buttons. Each time you visit a new page, it is pushed onto the stack. When you click the Back button, the previous page is popped from the stack and displayed.

• Undo/Redo: Stacks are commonly used to implement undo/redo functionality. Each action performed by the user is stored as a command object and pushed onto the stack. When the user performs the undo operation, the top command is popped from the stack and reversed. The redo operation can then reapply the command by pushing it back onto the stack.

• Balanced Parentheses: Stacks are essential for checking the validity of parentheses in programming languages. A stack can be used to keep track of opening and closing parentheses. When an opening parenthesis is encountered, it is pushed onto the stack. When a closing parenthesis is encountered, the stack's top element is checked to ensure it matches the closing parenthesis.

• Backtracking Algorithms: Backtracking algorithms, such as depth-first search, heavily rely on stacks to store state information during the search process. Each time a decision is made, the current state is pushed onto the stack. If the search reaches a dead end, the top state is popped from the stack to backtrack and explore alternative paths.

These are just a few examples of how stacks are used in computer science. Their simplicity and efficiency make them a powerful tool for solving a wide range of problems.

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}

class Main {

  public static void main(String[] args) {

    // replace with your Java logic here

    System.out.println("Implementing a stack-based calculator:");

​

    String expression = "5 10 + 3 *";

    double result = evaluate(expression);

​

    System.out.println("Result: " + result);

  }

​

  static double evaluate(String expression) {

    Stack<Double> stack = new Stack<>();

    String[] tokens = expression.split(" ");

​

    for (String token : tokens) {

      if (isNumber(token)) {

        stack.push(Double.parseDouble(token));

      } else {

        double operand2 = stack.pop();

        double operand1 = stack.pop();

        double result = 0;

​

        switch(token) {

          case "+":

            result = operand1 + operand2;

            break;

          case "-":

            result = operand1 - operand2;

Stack Exercises

To reinforce your understanding of stacks, let's practice some stack-related problems. These exercises will help you solidify your knowledge of stack operations and their applications. Solve each problem and compare your solution with the provided solution code.

1. Valid Parentheses: Write a function isValid that takes a string as input and determines if the string's parentheses are properly balanced.

2. Next Greater Element: Given an array of integers, find the next greater element for each element in the array. The next greater element is the first element to the right that is greater than the current element. If there is no such element, the output should be -1.

3. Evaluate Reverse Polish Notation: Write a function evalRPN that evaluates a given arithmetic expression in Reverse Polish Notation (RPN).

Remember to review the concepts covered in the previous screens and apply them to these exercises. Good luck!

Stack Complexity Analysis

When working with stacks, it's important to understand the time and space complexity of the fundamental operations: push, pop, and peek. Analyzing the complexity of stack operations helps in determining the efficiency and performance characteristics of a stack-based solution.

Let's break down the complexity of each operation:

• Push: The push operation adds an element to the top of the stack. This operation runs in constant time, O(1), as it only requires updating the top pointer and placing the new element at the top.

• Pop: The pop operation removes the top element from the stack. Similar to push, the pop operation also runs in constant time, O(1), as it only involves updating the top pointer and removing the element from the top.

• Peek: The peek operation retrieves the top element from the stack without modifying the stack. Like push and pop, the peek operation has a time complexity of O(1) since it only involves accessing the top element.

The space complexity of a stack depends on the number of elements stored in it. If a stack holds n elements, the space complexity would be O(n) as it requires memory to store each element.

Understanding the complexity of stack operations helps in selecting the appropriate data structure for a given problem and optimizing its performance. By leveraging the constant time complexity of stack operations, you can design efficient solutions for a wide range of problems.

Now that we've analyzed the complexity of stack operations, let's put our knowledge into practice with some exercises in the next screen.

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}

class Stack {

    private int maxSize;

    private int[] stackArray;

    private int top;

​

    public Stack(int size) {

        maxSize = size;

        stackArray = new int[maxSize];

        top = -1;

    }

​

    public void push(int value) {

        if (top == maxSize - 1) {

            System.out.println("Stack is full. Unable to push.");

            return;

        }

        stackArray[++top] = value;

    }

​

    public int pop() {

        if (top == -1) {

            System.out.println("Stack is empty. Unable to pop.");

            return -1;

        }

        return stackArray[top--];

    }

​

    public int peek() {

        if (top == -1) {

Putting It All Together

Congratulations! You've learned about stacks in-depth, including their properties, implementation, common operations, applications, and complexity analysis. Let's summarize the key concepts you've learned:

• Stack Definition: A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle. Elements are added or removed from the top of the stack.

• Stack Implementation: Stacks can be implemented using arrays or linked lists. Array-based implementation provides constant time access to the top element, while linked list-based implementation allows for dynamic sizing.

• Stack Operations: The fundamental operations on a stack are push (adding an element to the top), pop (removing the top element), and peek (retrieving the top element without modifying the stack).

• Applications of Stacks: Stacks find applications in various real-world scenarios, such as web browsers' navigation history, undo/redo functionality in applications, syntax parsing, depth-first search (DFS) algorithm, and more.

• Stack Complexity Analysis: Stack operations, including push, pop, and peek, have a time complexity of O(1) as they take constant time. The space complexity of a stack is O(n) as it depends on the number of elements stored.

Let's see a practical example of using a stack in Java:

1<<code>>

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class Main {

  public static void main(String[] args) {

    // replace with your Java logic here

    Stack<String> stack = new Stack<String>();

​

    stack.push("Hello");

    stack.push("World");

​

    System.out.println(stack.peek());

    System.out.println(stack.pop());

    System.out.println(stack.peek());

  }

}