Sprint 5.1 Recursion

Unit 5: Algorithm

Level 11 DigiPro

Learning Objectives

• Understand the concept of recursive functions.
• Identify the need for a base case in recursion.
• Learn about format and conversion functions.

Keywords

• Recursive
• Base case block
• str
• format()

Core Objectives

• Understanding the concept of recursive functions.
• Identifying the need for a base case in recursion.
• Learning about format and conversion functions.

Prior Knowledge Required

• Loops
• For loops
• While loops

Real Life Integration

• Utilize recursive functions in real-world programming scenarios.

Teaching Strategy: Rally Robin

• Teacher asks a question requiring multiple answers (e.g., a list) with a time limit.
• Partner A responds first.
• Partner B provides an alternative answer.
• Repeat the process until time runs out.

Recursive Functions

• Definition: A recursive function is one that calls itself repeatedly to solve a problem by breaking it down into smaller, similar problems.

Mathematical Example

• Sum of first n natural numbers:
  • sum(n) = 1 + 2 + 3 + ... + (n-1) + n
  • Can be rewritten as sum(n) = n + sum(n-1)
  • Recursive breakdown continues until reaching a base case.

Recursion in Python

• Example of finding the sum of first n natural numbers using recursion.
  • When calling sum(5), the function keeps calling itself with decrementing values.
  • Requires a base case to terminate when n reaches 1.

Structure of Recursive Function

1. Base Case Block: Specifies the termination condition to stop recursion.
2. Recursive Block: Calls itself with different parameters.

Common Errors

• RecursionError: Occurs if the base case is not implemented, leading to infinite recursion.

Formatting and Conversion Functions

• format() Method: Formats values and inserts them into string placeholders defined with {}.
• Conversion Functions:
  • str(): Converts values to a string.
  • int(): Converts a string to an integer.

Critical Thinking

• Discussion on the importance of GitHub for developers.

Master Challenges

Challenge 1

• Compute the sum of even numbers up to n using recursion.

Challenge 2

• Write a Python program to display multiples of 10 up to 100 using recursion.

Challenge 3

• Solution for Challenge 3 provided.

This sprint covers the fundamental concepts of recursion, highlighting the importance of a base case, and demonstrates practical applications and common errors in using recursive functions in Python. Additional formatting and conversion tools are also covered to enhance string handling in programming.