Meet in the Middle
Meet in the Middle
Introduction to Meet in the Middle
Meet in the Middle is a problem-solving technique used when a direct brute-force solution is too slow.
The idea is to split the problem into two parts, solve each part separately, and then combine the partial results.
It is especially useful when brute force is around and is too large (for example, ).
Concept
The main idea is to find a constraint that can be split into two halves.
After that, we solve both halves independently and use their partial results to build the final answer.
This is often a good balance between full brute force and more advanced algorithms.
Subset Sum Problem
A classic example of Meet in the Middle is Subset Sum.
Problem Statement
Given a set of integers where and a target sum , determine whether there exists a subset whose sum is exactly .