Problem context and objectives
Mission briefing
Matchmaking coordinator · Urgent players and jobs compete for limited slots
Keep the best next candidate available without sorting everything again: The Cooldown Forge.
A stale priority frontier increases wait time for everyone.
How you win
- 1Recognize when Max-heap cooldown scheduling matches the clues
- 2Keep this true after every move: the heap contains every currently eligible task and the queue contains exactly cooling tasks
- 3Reach the result within O(total intervals log distinct tasks)
Rules and pressure
- Target cost: O(total intervals log distinct tasks)
- State rule: the heap contains every currently eligible task and the queue contains exactly cooling tasks
New words in this mission
Open a term for a plain-language explanation.durable queue+
A waiting line that keeps work until a consumer finishes it. It absorbs bursts and lets failed work be retried.
Lesson 1 of 3
Live algorithm trace
Max-heap cooldown scheduling
Complete execution1 of 6
A
task
B
idle
A
B
idle
A
B
Build a max-heap from the two task frequencies; the displayed slots preview the schedule being constructed.
1
count tasks and build max heap2
release cooled tasks at current time3
pop the most frequent eligible task4
run it and decrement count5
queue it until time + n + 16
advance time even when idle7
return elapsed timecounts = A:3,B:3cooldown = 2time = 0
Truth to preserve / Cost target
Truth to preserve
the heap contains every currently eligible task and the queue contains exactly cooling tasks
Cost target
O(total intervals log distinct tasks)
A max-heap prioritizes the task with the most copies left. Completed tasks wait in a cooldown queue until eligible again; each time unit either runs one task or records an unavoidable idle slot.
Your call · What should guide every step of this algorithm?