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Brute Force Algorithms

In short: A brute force algorithm solves a problem by trying every possible candidate answer and keeping the best (or first valid) one. It's usually simple but slow, often O(n^2) or exponential, so in interviews it's a starting point you then optimize.

A brute force algorithm finds a solution by trying all possible answers and picking the best one.

Say you're a cashier and need to give someone 67 cents (US) using as few coins as possible. How would you do it?

You could try running through all potential coin combinations and pick the one that adds to 67 cents using the fewest coins. That's a brute force algorithm, since you're trying all possible ways to make change.

Here are a few other brute force algorithms:

  • Trying to fit as many overlapping meetings as possible in a conference room? Run through all possible schedules, and pick the schedule that fits the most meetings in the room.
  • Trying to find the cheapest route through a set of cities? Try all possible routes and pick the cheapest one.
  • Looking for a minimum spanning tree in a graph? Try all possible sets of edges, and pick the cheapest set that's also a tree.

Brute force solutions are usually very slow since they involve testing a huge number of possible answers.

Brute force approaches are rarely the most efficient. Other approaches, like greedy algorithms or dynamic programming tend to be faster.

Even so, talking through a brute force solution can be a good first step in a coding interview. It's usually pretty easy to derive, so it allows you to quickly make progress and come up with something that works. From there, you have some helpful boundaries for refining your algorithm—you're only interested in solutions that are faster (and/or more space efficient) than the brute force solution you've already come up with.

See also:

Frequently Asked Questions

What is a brute force algorithm?

One that systematically tries all possible solutions (every combination, ordering, or pair) and checks each one, instead of using insight to narrow the search.

Is brute force ever a good approach?

Yes, for small inputs or as a first draft. In a coding interview, stating the brute force solution quickly gives you a correct baseline and a runtime to beat.

How do you improve on a brute force solution?

Look for repeated work you can cache (dynamic programming), a choice you can make greedily, a way to sort or use a hash table to skip comparisons, or a way to prune the search.

Last updated: October 21, 2026

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