O(n!)
—Factorial Time
DangerEvery possible arrangement. Practical only for n ≤ 10.
Mental model
How many ways can you seat n people at a table? n choices for seat 1, n−1 for seat 2, n−2 for seat 3… multiply them: n! For n=20, that's more arrangements than atoms in the observable universe.
Interactive Visualisation
🪑 How many ways can you seat n people at a table? n choices for seat 1, (n−1) for seat 2, (n−2) for seat 3… Multiply them together: n! It grows so fast that n=20 produces more arrangements than atoms in the observable universe.
n:→ 3! = 6 orders
A
B
C
→ 3! = 6 orderingsn! is terrifyingly steep
n=11
n=22
n=36
n=424
n=5120
n=6720
n=75.0k
n=840k
How it scales
n = 5
120 ops
n = 8
40,320 ops
n = 10
3,628,800 ops
n = 12
479,001,600 ops