Computer Science › Algorithms

Brute Force

Trying every possibility; the baseline before optimizing.

Also known as: exhaustive search, naive solution

A brute-force solution tries every possibility until it finds the answer. It’s the simplest approach, often the obvious one, and a good starting point.

def two_sum(nums, target):
    for i in range(len(nums)):
        for j in range(i + 1, len(nums)):
            if nums[i] + nums[j] == target:
                return i, j

It checks every pair, so the cost is O(n²). For ten items that’s fine. For a million, it’s a trillion comparisons.

A smarter version uses a dictionary to remember what it has seen:

def two_sum(nums, target):
    seen = {}
    for i, n in enumerate(nums):
        if target - n in seen:
            return seen[target - n], i
        seen[n] = i

One pass, O(n).

Why start with it

• It’s usually correct and easy to write. Correctness comes first.
• It’s a baseline. You can compare the clever version’s results against it in tests.
• It might be good enough. If the input is small, don’t over-engineer (premature optimization).
• It reveals the structure of the problem, which points to the optimization.

When it stops working

Brute force grows fast with input size, and some problems explode: trying every ordering of 20 items is more than 2 × 10¹⁸ possibilities. Then you need pruning (backtracking), better data structures, or smarter algorithms such as dynamic programming and greedy methods (dynamic programming).

Practical tip

When you get stuck on a problem (or in an interview), say the brute-force answer out loud first. Then find what’s wasted: repeated work, or a search that could use a sorted order or a hash table.