Question

I’m looking for an intuitive, real-world example of a problem that takes (worst case) exponential time complexity to solve for a talk I am giving.

Here are examples for other time complexities I have come up with (many of them taken from this SO question):

• O(1) – determining if a number is odd or even
• O(log N) – finding a word in the dictionary (using binary search)
• O(N) – reading a book
• O(N log N) – sorting a deck of playing cards (using merge sort)
• O(N^2) – checking if you have everything on your shopping list in your trolley
• O(infinity) – tossing a coin until it lands on heads

Any ideas?

Answer 1

• O(10^N): trying to break a password by testing every possible combination (assuming numerical password of length N)

p.s. why is your last example is of complexity O(infinity) ? it’s linear search O(N) .. there are less than 7 billion people in the world.