10 Questions
What is the main application of a stack in the context of recursive functions?
Storing return addresses
What is the main advantage of using a stack machine for executing Polish notation expressions?
Faster execution speed
Which type of Polish notation is most commonly used in evaluating arithmetic expressions?
Postfix notation
In the context of stacks, what is the significance of the TOP pointer?
Tracking the next available position in the stack
What type of recursion involves a function calling itself directly?
Tail recursion
How do stack machines contribute to optimizing space utilization in memory?
Organizing data using the LIFO principle
In postfix notation, when an operator follows its operands, what type of notation is being used?
(Postfix) Reverse Polish notation
Which operation is NOT efficiently supported by a stack machine executing Polish notation expressions?
Logical reasoning
What does the TOP = 0 condition check for in the algorithm for POP operation on a stack?
(Under)flow condition
How does recursive function differ from standard function?
Recursive functions can call themselves
Study Notes
Polish Notation
- Infix, Prefix, and Postfix are three types of Polish Notation
- Polish Notation is a process of writing operators before or after operands in an expression
Recursive Functions
- Recursion is a problem-solving approach where a problem is solved by repeatedly applying the same solution to smaller instances
- Recursive function is a programming technique that allows expressing operations in terms of themselves
- Examples of recursive functions:
- Factorial of a number:
Factorial(n) = 1 if n = 0, n * factorial(n-1) if n > 0 - Fibonacci series:
fibo(n) = 0 if n = 0 or n = 1, fibo(n) = fibo(n-1) + fibo(n-2) if n > 1 - Greatest Common Divisor (GCD):
gcd(a, b) = gcd(a-b, b) if a > b, gcd(a, b-a) if a < b, a or b if a = b
- Factorial of a number:
Converting Infix to Postfix Expression
- Steps to convert infix expression to postfix expression using stack:
- Print operands as they arrive
- If stack is empty or contains a left parenthesis on top, push the incoming operator onto the stack
- If incoming symbol is ‘(‘, push it onto stack
- If incoming symbol is ‘)’, pop the stack and print operators until left parenthesis is found
- If incoming symbol has higher precedence than the top of the stack
- If incoming symbol has lower precedence than the top of the stack, pop and print the top
- If expression ends, pop and print all operators of stack
Queue Data Structure
- A queue is a linear list of elements with deletion at one end (front) and insertion at the other end (rear)
- Also called First-in-First-out (FIFO) lists
- Real-life examples of Queue: row of students at a registration center, movie ticket window, line of cars waiting at a traffic signal
- Two ways to implement a queue: circular queue using array, linked structures (pointers)
- Primary queue operations: Enqueue (insert an element at the rear), Dequeue (remove an element from the front)
Circular Queue
- A circular queue is a type of queue data structure
- Algorithm for POP operation:
- Check for stack underflow
- Delete an element from the top of the stack
- Decrement pointer
- Return deleted element
Applications of Stack
- Three main applications of stack: recursion, stack machines, Polish notation
- Stack machine provides faster execution of Polish notation
- Better used for stacking local machines
- Used for representation of arithmetic expression
Explore Polish Notation types - Infix, Prefix, Postfix, and understand recursive functions with examples. Learn about solving problems using recursion and how recursive functions work.
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