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Heaps and Priority Queues: Data Structures and Algorithms: Uncharted

Courses Data Structures and AlgorithmsHeaps and Priority Queues

Heaps and Priority QueuesPro

Keep the next priority at the root, restore the heap locally, and solve top-k work.

Data Structures and Algorithms
Unit 10 of 16
20 lessons
130 min
420 XP

This unit is part of Pro. Upgrade to open every lesson in it.

Lessons

20 total

1The Triage DeskDistinguish urgency order from arrival order and define a deterministic priority-queue tie rule.ProInteractiveConcept6 min20 XPOpen
2The Heap PropertyVerify a min-heap with the parent-less-than-or-equal-to-child invariant without imposing sibling order.ProInteractiveConcept6 min20 XPOpen
3A Tree in an ArrayApply heap parent-and-child index arithmetic to mapping one heap index to its parent and children.ProCodeConcept6 min20 XPOpen
4Sift UpApply append then sift-up heap insertion to pushing a new priority and swapping upward until its parent is safe.ProCodeConcept6 min20 XPOpen
5Sift DownApply root replacement then sift-down to removing the minimum and swapping the replacement toward its smaller child.ProCodeConcept6 min20 XPOpen
6A Working HeapApply complete min-heap push and pop state machine to assembling push and pop into one reusable minimum heap.ProCodeConcept6 min20 XPOpen
7Predict the HeapTrace array-backed heap state through one push and one pop, including every sift swap.ProInteractiveConcept6 min20 XPOpen
8Draw the HeapTranslate the specified heap insertion trace into array-index parent-child edges with no extra connection.ProDiagramConcept6 min20 XPOpen
9Build a Heap FastApply bottom-up linear heap construction to sifting internal nodes down from the bottom instead of replaying every push.ProCodeConcept6 min20 XPOpen
10Heapsort, LiteApply heapify then repeated minimum removal to removing every heap minimum to produce sorted output.ProCodeConcept6 min20 XPOpen
11Top-k HeadlinesApply size-k min-heap ranking to keeping only the k strongest trending scores in a bounded heap.ProCodeConcept6 min20 XPOpen
12kth SmallestApply k bounded heap removals to removing exactly k priorities to identify one rank.ProCodePractice8 min20 XPOpen
13The Running MedianApply balanced max-heap and min-heap stream to balancing a max-heap below and a min-heap above each streaming median.ProCodeConcept6 min20 XPOpen
14Priority InboxApply priority plus arrival-order heap to ordering messages by urgency and breaking ties by arrival counter.ProCodePractice8 min20 XPOpen
15The Max-Heap FlipApply maximum-heap comparator or negated priority to using a JavaScript comparator and Python negated priorities for maximum-first order.ProCodeConcept6 min20 XPOpen
16Library HeapsApply language-idiomatic heap removal to using Python heapq while keeping the hand-built JavaScript heap as the production tool.ProCodeConcept6 min20 XPOpen
17Merge k SortedApply one-frontier-entry-per-list heap merge to keeping one frontier value from each sorted list in a heap.ProCodePractice8 min20 XPOpen
18Heap or Sort?Choose a bounded heap for repeated extremes or top-k results and a full sort for complete global order.ProInteractiveConcept6 min20 XPOpen
19Where Heaps HideRecognize scheduling, timers, pathfinding, streaming medians, and top-k as repeated priority-removal problems.ProInteractiveConcept6 min20 XPOpen
20Heaps Mastery CheckApply heap construction priority removal and top-k synthesis to building a heap and removing its first k priorities in order.ProCodeMastery check10 min40 XPOpen