Lecture on Recursion by The Simple Engineer

Introduction

• Focus on understanding recursion using animations and examples.
• Goal: Strengthen algorithmic mental model around recursion.
• Recursion involves calling the same function within itself.

Understanding Recursion

• Analogy: ATM line to illustrate recursion.
  • Iterative approach vs. recursive approach.
  • Recursive process involves asking the same question up the line until a stopping condition.
  • Base case reached when the first person is identified.
• Recursive code is often simple and elegant.

Blueprint for Recursion

1. Break down the problem into subproblems.
2. Identify stopping condition or base case.

Examples of Recursion

• Line Queue Example: Counting position in line.
• Essay Revision Example: Revisit and revise until a satisfactory draft is achieved.

Key Components of Recursion

• Base Case: Condition to stop recursion.
• Recursive Call: Call the function with progress towards the base case.

Pros and Cons of Recursion

• Pros:
  • Simplifies code for recursive data structures like trees and graphs.
  • Reduces need for complex loops.
  • Elegant solutions for complex problems.
• Cons:
  • Higher memory usage due to call stack growth.
  • Potential for stack overflow.
  • May lead to complex code if overused.

Recursive Data Structures

• Well-Suited For:
  • Trees, graphs, JSON objects.

Call Stack and Recursion

• Analogy: Task management with interruptions.
• Call Stack: Stores method invocations and local variables.
• Stack Overflow: Occurs when exceeding memory buffer for recursive calls.

Technical Examples

Recursion with Strings

• Reversing Strings: Base case with empty string, recursive processing by shrinking the string.
• Palindrome Check: Compare characters from both ends.

Recursion with Numbers

• Decimal to Binary Conversion: Dividing by 2 and logging remainders.
• Sum of Natural Numbers: Recursive summing with a base case of 1.

Divide and Conquer Algorithms

• Binary Search: Divide search space using recursive calls.
• Fibonacci Sequence: Recursive calculation with memoization for optimization.
• Merge Sort: Divide, sort, and merge recursively.

Linked Lists

• Reversal of Linked List: Recursive node reversal.
• Merging Sorted Lists: Combine two sorted lists using recursion.

Trees

• Binary Search Tree Insertion: Recursive comparison and placement.
• Printing Leaf Nodes: Depth-first traversal to print leaves.

Graphs

• Depth First Search (DFS): Explore nodes deeply before backtracking.

Optimization Techniques

• Memoization: Store results of expensive calls to avoid redundant work.
• Tail Call Optimization: Make recursive calls the last instruction to improve efficiency.

Conclusion

• Recursion can solve complex problems elegantly but must be used judiciously.
• Next steps include learning about backtracking in recursion.

Resources

• The Simple Engineer YouTube and social media for more content.