LEVEL 5 OF 5

Advanced Problem Solving

Combine patterns to solve harder problems.

Dynamic Programming

Define a reusable answer for each state, then compute states from already solved smaller ones.

Keep the strongest reachable state when a local choice can be proven to preserve every future possibility.

Represent each range by its endpoints and sort by start so overlapping groups can be processed in one sweep.

Use bitwise identities to combine integer state. XOR has identity zero and cancels equal pairs.