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Factorial definition

n! = n * (n-1) * ... * 1 and 0! = 1.

Factorial definition

Factorial is the product of all integers from 1 to n, denoted n!. For example, 5! = 120.

0! is defined as 1. It is computed as n! = n * (n-1) * ... * 1. Factorial is used in permutation and combination calculations.

Recursive definition

Factorial's recursive definition: 0! = 1, n! = n * (n-1)!. This naturally solves factorial with recursion.

The base case is 0! = 1. The recursive step is n * (n-1)!. Each call decreases n and eventually reaches 0.

Practice Recursive factorial

Write factorial(n). If n=0 return 1, else n * factorial(n-1). Print 120 with print(factorial(5)).

Starter code

solution.py
def factorial(n):
    # Compute factorial

Sample solution

solution.py
def factorial(n):
    # Compute factorial
    if n == 0:
        return 1
    return n * factorial(n - 1)
print(factorial(5))

Expected output

120

Questions and answers

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

1 What is 5!?

  • 20
  • 100
  • 120
  • 25 Correct answer

Explanation: 5! = 120.

2 Base value

Question 
0! = ____
Answer 
0! = 1

Explanation: 1 is right.

3 Factorial definition: match the terms

Term Meaning
n! n*(n-1)!
0! 1
5! 120
3! 6

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