The Quest Begins (The "Why")
I still remember the first time I saw Jump Game II on a whiteboard during an interview. The problem statement is simple: given an array where each element tells you the maximum jump length from that position, find the minimum number of jumps needed to reach the last index. My brain immediately went to dynamic programming — fill a table, try every possible jump, O(n²) time, O(n) space. I coded it, ran the test cases, and felt like I was brute‑forcing a puzzle in Dark Souls: every move felt costly, and I kept dying on the same spot.
Honestly, I was frustrated. There had to be a smarter way, something that didn’t require me to explore every possible path like I was grinding for XP. That’s when I recalled a little nugget from my algorithms class: sometimes the best next step is obvious if you look ahead just far enough.
The Revelation (The Insight)
The greedy insight for Jump Game II is beautifully simple: at each jump, you only need to know the farthest index you can reach with the current number of jumps, and when you exhaust that range, you commit to another jump.
