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 Many Rivers.
A stale priority frontier increases wait time for everyone.
How you win
- 1Recognize when K-way heap merge matches the clues
- 2Keep this true after every move: the heap contains the smallest unmerged value from every nonempty list
- 3Reach the result within O(N log k)
Rules and pressure
- Target cost: O(N log k)
- State rule: the heap contains the smallest unmerged value from every nonempty list
Lesson 1 of 3
Live algorithm trace
K-way heap merge
Complete execution1 of 6
1
root
4
5
1
3
4
2
6
Push one front from each of the three sorted lists.
1
push the first value of every list2
pop the smallest front3
append it to output4
push the next value from its list5
repeat until heap is empty6
return outputheap = 1A,1B,2Coutput = []lists = [1,4,5] [1,3,4] [2,6]
Truth to preserve / Cost target
Truth to preserve
the heap contains the smallest unmerged value from every nonempty list
Cost target
O(N log k)
Each sorted list exposes one next candidate. A min-heap compares those k fronts, emits the smallest, then advances only the list that supplied it.
Your call · What should guide every step of this algorithm?