overlapping subproblems

Overlapping subproblems occur when a problem can be broken down into smaller parts, some of which are repeated multiple times during the solution process. Think of solving a complex puzzle where many pieces are reused in different sections; working on these common pieces repeatedly saves time if approached efficiently. In computational terms, it means the same calculations are performed multiple times for different parts of a problem. Recognizing and storing these results—called memoization—helps solve the overall problem more efficiently by avoiding unnecessary repeated work.