Brute-force

Solving Ttsks with Brute-force

Solving Tasks with Brute Force

Brute force is a method where we try all possible options and choose the best valid one. The idea is straightforward: define the search space — all candidates that could be the answer — and apply linear search over it, checking each one.

It is simple to implement but can be slow, so we use it only when the search space is small enough to scan entirely within the time limit.

The Core Idea

Every brute force solution follows the same structure:

Define the search space — what are all possible answers?
Iterate over it — one or more loops
Check each candidate — does it satisfy the problem's conditions?
Track the best/first/count — depending on what the problem asks

Example 1: Maximum Sum Subarray of Length K

Given a list of $N$ integers and a number $K$ , find the maximum sum of any contiguous subarray of length exactly $K$ .

Search space: all starting indices from $0$ to $N - K$ .

Loops	Complexity	Max N
1 loop	O(n)	~10^7
2 loops	O(n^2)	~10^4
3 loops	O(n^3)	~500

Brute-force

Solving Tasks with Brute Force

The Core Idea

Example 1: Maximum Sum Subarray of Length K

Example 2: Two Sum — Does a Pair with Sum S Exist?

Example 3: Closest Pair of Values

Example 4: Count Pairs with Given Sum

Example 5: Maximum Product of Three Elements

Example 6: Smallest Divisor Greater Than 1

Example 7: Find the Largest Prime Up to N

Example 8: Maximum Subarray Sum (Any Length)

Example 9: Count Triplets with All Different Values

When is Brute Force Fast Enough?