Jump Game II

Problem

Same setup as Jump Game: integer array nums, start at index 0, nums[i] is the maximum jump length from i. This time you're guaranteed the last index is reachable, and you must return the minimum number of jumps to get there.

Examples

First case: jump 0 → 1 → 4 (two jumps). 0 → 2 → ? also works but never fewer. Second case: jump 0 → 1 → 4.

Constraints

1 ≤ n ≤ 10⁴ · 0 ≤ nums[i] ≤ 1000 · last index always reachable.

Attempt it first

You already know from Jump Game that tracking max_reach captures reachability. The new question is counting jumps — so the natural first instinct is a shortest-path / BFS framing. Try to write it that way before revealing the hint, then look for how to get the same answer without an explicit queue.