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CSE 326: Data Structures Lecture #5 Heaps More

CSE 326: Data Structures Lecture #5 Heaps More. Steve Wolfman Winter Quarter 2000. We get slide printouts every class. 4 pages of notes per day  50 students  3 lectures per week  10 weeks per quarter  engineer’s fudge factor  10,000 pages one 60 foot pine tree  80,000 pages

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CSE 326: Data Structures Lecture #5 Heaps More

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  1. CSE 326: Data StructuresLecture #5Heaps More Steve Wolfman Winter Quarter 2000

  2. We get slide printouts every class • 4 pages of notes per day  50 students  3 lectures per week  10 weeks per quarter  engineer’s fudge factor  10,000 pages • one 60 foot pine tree  80,000 pages • Frankye Jones’s frantic effort = one paycheck for Steve • paycheck + www.americanforests.org = 1 tree / $1 • How about two trees per person?

  3. Today’s Outline • Things Steve Didn’t Finish on Wednesday (Heaps) • Extra heap operations • d-Heaps • Return Quizzes

  4. Other Priority Queue Operations • decreaseKey • given a pointer to an object in the queue, reduce its priority value • increaseKey • given a pointer to an object in the queue, increase its priority value • remove • given a pointer to an object in the queue, remove it • buildHeap • given a set of items, build a heap

  5. DecreaseKey, IncreaseKey, and Remove void decreaseKey(int obj) { assert(size >= obj); temp = Heap[obj]; newPos = percolateUp(obj, temp); Heap[newPos] = temp; } void increaseKey(int obj) { assert(size >= obj); temp = Heap[obj]; newPos = percolateDown(obj, temp); Heap[newPos] = temp; } void remove(int obj) { assert(size >= obj); percolateUp(obj, NEG_INF_VAL); deleteMin(); }

  6. BuildHeapFloyd’s Method. Thank you, Floyd. 12 5 11 3 10 6 9 4 8 1 7 2 pretend it’s a heap and fix the heap-order property! 12 5 11 3 10 6 9 4 8 1 7 2

  7. Build(this)Heap 12 12 5 11 5 11 3 10 2 9 3 1 2 9 4 8 1 7 6 4 8 10 7 6 12 12 5 2 1 2 3 1 6 9 3 5 6 9 4 8 10 7 11 4 8 10 7 11

  8. Finally… 1 3 2 4 5 6 9 12 8 10 7 11 runtime:

  9. Thinking about Heaps • Observations • finding a child/parent index is a multiply/divide by two • operations jump widely through the heap • each operation looks at only two new nodes • inserts are at least as common as deleteMins • Realities • division and multiplication by powers of two are fast • looking at one new piece of data sucks in a cache line • with huge data sets, disk accesses dominate

  10. Solution: d-Heaps 1 • Each node has d children • Still representable by array • Good choices for d: • optimize performance based on # of inserts/removes • choose a power of two for efficiency • fit one set of children in a cache line • fit one set of children on a memory page/disk block 3 7 2 4 8 5 12 11 10 6 9 12 1 3 7 2 4 8 5 12 11 10 6 9

  11. One More Operation • Merge two heaps. Ideas?

  12. To Do • Turn in Project I (due today) • Start on Homework II (due Jan 20th) • Read chapter 6 in the book

  13. Coming Up • Mergeable heaps • Dictionary ADT and Self-Balancing Trees • First project due (January 14th) • A day off (January 17th)! • Second homework assignment due (January 20th)

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