📜 WAYPOINT LESSON
Checkpoint — Fuse the Window
⭐⭐⭐ advanced⏳ 25 min read📍 Lesson 224 of 281
Bounded-jump collection: the recurrence is easy, surviving n = 200000 with k = 2000 requires the monotonic-deque fusion. The W re-scans its window and dies on budget.
Checkpoint — Fuse the Window. dp[i] = g_i + max over the last k dp values is correct on paper; the naive loop is O(n·k) ≈ 4·10^8 and fails the budget. The fused monotonic deque answers every window-max in amortized O(1): O(n) total. The W is algorithmically correct — it fails because its complexity family is wrong. That is the mastery point: correctness and survivability are separate theorems.