Benefits of Decomposition

Decomposition breaks a problem into smaller sub-problems, and the benefits come from those parts: one huge problem is hard to hold in your head, while several small ones are manageable.

Each sub-problem is simpler to understand, write and test. You concentrate on one small job at a time: in a cinema booking program, getting the seat prices right is something you can finish and check before you touch anything else.

Different people can work on different sub-problems at the same time. One programmer could build the seat picker while another builds the card payment, so the project is finished sooner.

A finished sub-problem can be reused in another program. The payment section written for the cinema could go into a swimming pool booking system with little change, so nobody solves that problem a second time.

Decomposition also makes it clearer what the whole solution has to cover, because the sub-problems are a checklist of everything the finished program must do. And when something goes wrong, faults are easier to find: if a ticket prints the wrong price but the seat map looks right, you test the pricing part on its own instead of searching the whole program.