Computational complexity theory

How fast can you solve a puzzle?

Imagine you're trying to find the quickest way to sort a deck of cards by color.

The time it takes to sort those cards depends on the sorting method you choose. Some methods are faster than others, even if the deck is the same size every time.

Example

If you use a simple method like picking cards one by one and placing them in the right color pile, it might take 100 seconds. But if you use a faster method like dividing the deck into smaller piles and sorting those first, it could take only 10 seconds.

Remember this

The sorting method's efficiency is what we call computational complexity, measuring time and space resources needed to solve a problem.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

Binary search

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Kolmogorov complexity

Kolmogorov complexity is uncomputable

P versus NP problem

P vs NP problem determines if problems verifiable in polynomial time are also solvable in polynomial time

Dijkstra's algorithm

Dijkstra's algorithm time complexity: O((V+E) log V)

Quantum computing

Quantum computers can solve certain problems exponentially faster than classical computers

Graph (abstract data type)

Time complexity of BFS and DFS: O(V + E)

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