Greedy Layered Jumps: When to Use It

Start with the idea

A problem is a good match for Greedy Layered Jumps when it asks for minimum jumps in forward-reach arrays. Here the concrete task is: Return the minimum jumps to the final index. The visible input [2,3,1,1,4] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. When the method sorts intervals or events, use the coordinate and tie break required by its proof. Other greedy walks keep an invariant without sorting. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Treat the current reach as a BFS layer and commit a jump when the scan reaches its boundary. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? A greedy step commits to a local choice. Give the exchange or dominance reason that an optimal solution can still include that choice. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(n) time · O(1) space; identify the operation responsible for it and the extra memory it needs.