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Base case

The base case stops the recursion.

Choosing the base case

The base case directly solves the smallest version of the problem. Choosing the right base case ensures recursion works correctly.

For example, in computing n! the base case is 0! = 1. In summing, the base case is returning 0 for an empty array.

Recursive step

The recursive step reduces the problem to a smaller version and calls the function with it. Each call gets closer to the base case.

For example, sum(n) = n + sum(n-1). Each call decreases n and eventually reaches the base case (n=0).

Practice Sum (recursive)

Write sum_recursive(n). If n=0 return 0, else n + sum_recursive(n-1). Print 15 with print(sum_recursive(5)).

Starter code

solution.py
def sum_recursive(n):
    # Compute sum

Sample solution

solution.py
def sum_recursive(n):
    # Compute sum
    if n == 0:
        return 0
    return n + sum_recursive(n - 1)
print(sum_recursive(5))

Expected output

15

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Base value

Question 
0! is defined as ____.
Answer 
0! is defined as 1.

Explanation: 1 is right.

2 Base case: match the terms

Term Meaning
Base case Stops
Recursive step Reduces
0! = 1 Base
n! = n*(n-1)! Recursive

3 What happens without a base case?

  • Ends immediately
  • Infinite calls and stack overflow Correct answer
  • Runs fast
  • Becomes a loop

Explanation: Infinite calls and stack overflow.

All lessons in Beginner

1 What is an algorithm?

  1. Algorithm definition
  2. Algorithm properties
  3. Pseudocode
  4. Summary - Algorithm concept

2 Big-O notation

  1. Time complexity
  2. Big-O definition
  3. Comparing complexities
  4. Summary - Big-O

3 Array

  1. What is an array?
  2. Array access
  3. Looping over an array
  4. Summary - Arrays

4 Linear search

  1. Linear search idea
  2. Implementing search
  3. Best and worst case
  4. Summary - Linear search

5 Search project

  1. Project: Overview
  2. Grades array setup
  3. Search function
  4. Print the result

6 Bubble sort

  1. Bubble sort idea
  2. One pass
  3. Full sort
  4. Summary - Bubble sort

7 Selection sort

  1. Selection sort idea
  2. Finding the minimum
  3. Swapping
  4. Summary - Selection sort

8 Insertion sort

  1. Insertion sort idea
  2. Shifting
  3. Placement
  4. Summary - Insertion sort

9 Sorting project

  1. Project: Overview
  2. Price array
  3. Apply sorting
  4. Print the result

10 Recursion basics

  1. What is recursion?
  2. Base case
  3. Recursive step
  4. Summary - Recursion

11 Fibonacci

  1. Fibonacci sequence
  2. Recursive Fibonacci
  3. Call tree
  4. Summary - Fibonacci

12 Factorial

  1. Factorial definition
  2. Recursive factorial
  3. Choosing the base case
  4. Summary - Factorial

13 Recursion project

  1. Project: Overview
  2. Recursive power
  3. Combination
  4. Print the results

14 Binary search

  1. Binary search idea
  2. Left right pointers
  3. Base case
  4. Summary - Binary search

15 Linked list

  1. What is a linked list?
  2. Node definition
  3. Traversing the list
  4. Summary - Linked list

16 Stack

  1. What is a stack?
  2. Push and pop
  3. Peek and is_empty
  4. Summary - Stack

17 Queue

  1. What is a queue?
  2. Enqueue and dequeue
  3. Front and back
  4. Summary - Queue

18 Hash table

  1. What is a hash table?
  2. Hash function
  3. Collision
  4. Summary - Hash table

19 Set

  1. What is a set?
  2. Add and lookup
  3. Intersection and union
  4. Summary - Set

20 Beginner final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4