Stacks are a fundamental data structure in computer science, characterized by their Last In, First Out (LIFO) behavior. This means that the last element added to the stack is the first one to be removed. Stacks are used in a variety of applications due to their simplicity and efficiency in managing data. In this section, we will explore some common applications of stacks.

When a function is called in a program, the current state (including local variables and the return address) is pushed onto the call stack. This allows the program to return to the correct state once the function execution is complete.

Consider the following Python code:

1. function_c is called.
2. function_b is called within function_c.
3. function_a is called within function_b.

The call stack will look like this at each step:

• Initial call to function_c: [function_c]
• Call to function_b within function_c: [function_c, function_b]
• Call to function_a within function_b: [function_c, function_b, function_a]

When function_a completes, it is popped from the stack, and control returns to function_b, and so on.

Stacks are used to evaluate expressions and parse syntax in compilers and interpreters. They help in converting infix expressions to postfix (Reverse Polish Notation) and evaluating them.

Consider the infix expression: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3

Conversion to Postfix

Using the Shunting Yard algorithm, the expression is converted to postfix: 3 4 2 * 1 5 - 2 3 ^ ^ / +

Evaluation

Using a stack to evaluate the postfix expression:

1. Push operands onto the stack.
2. When an operator is encountered, pop the required number of operands, apply the operator, and push the result back onto the stack.

Text editors use stacks to implement the undo feature. Each change made to the document is pushed onto a stack. When the user performs an undo operation, the last change is popped from the stack and reverted.

Consider a text editor where the following operations are performed:

1. Type "Hello"
2. Type " World"
3. Delete " World"

The stack will look like this:

• After typing "Hello": ["Hello"]
• After typing " World": ["Hello", "Hello World"]
• After deleting " World": ["Hello", "Hello World", "Hello"]

When the undo operation is performed, the last state ("Hello") is popped from the stack and restored.

Stacks are used in backtracking algorithms to explore all possible solutions to a problem by trying out different paths and backtracking when a path does not lead to a solution.

Consider solving a maze where you need to find a path from the start to the end. The stack is used to keep track of the current path. If a dead end is reached, the algorithm backtracks by popping the stack until a new path can be explored.

Depth-First Search (DFS) is a graph traversal algorithm that uses a stack to explore as far as possible along each branch before backtracking.

Consider the following graph:

Starting from node A, the DFS traversal using a stack would be:

1. Push A onto the stack.
2. Pop A and push its adjacent nodes B and C.
3. Pop C (last pushed) and push its adjacent nodes (none in this case).
4. Pop B and push its adjacent nodes D and E.
5. Continue this process until all nodes are visited.

Stacks are a versatile data structure with numerous applications in computer science and programming. They are essential for managing function calls, evaluating expressions, implementing undo mechanisms, solving problems using backtracking, and traversing graphs using DFS. Understanding these applications helps in leveraging stacks effectively in various programming scenarios.