1. Tables and Priority Queues
Chapter 11

2. Chapter 11 -- Tables and Priority Queues
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3. Chapter 11 -- Tables and Priority Queues
The ADT Table
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4. Chapter 11 -- Tables and Priority Queues
Selecting an Implementation
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5. Chapter 11 -- Tables and Priority Queues
A Sorted Array-Based Implementation of the ADT Table
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6. Chapter 11 -- Tables and Priority Queues
A Binary Search Tree Implementation of the ADT Table
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7. The ADT Priority Queue: A Variation of the ADT Table
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8. Chapter 11 -- Tables and Priority Queues
Heaps
A heap is an ADT that is similar to a binary search tree, although it differs from a binary search tree in two significant ways
A heap is ordered in a much weaker sense
Heaps are always complete binary trees.
So,
A heap is a complete binary tree
1) that is empty or
2) Root contains a search key that is greater than or equal to the search key of each of its children, and Whose root has heaps as its subtrees
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9. Chapter 11 -- Tables and Priority Queues
Here is the UML diagram for a heap class.
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10. Chapter 11 -- Tables and Priority Queues
Because a heap is a complete binary tree, you can use an array-based implementation of a binary tree, as you saw in Chapter 10.
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11. Chapter 11 -- Tables and Priority Queues
A Heap Implementation of the ADT Priority Queue
We need the following members:
items: an array of heap items
size: an integer equal to the number of items in the heap.
Now lets talk about the following functions:
heapDelete
heapInsert
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12. Chapter 11 -- Tables and Priority Queues
heapDelete
where is the largest element?
rootItem = items[0];
Now we are left with two disjoint heaps
So we have to fix it.
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13. Chapter 11 -- Tables and Priority Queues
Copy the last element up
Items[0] = items[size-1];
size--;
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14. Chapter 11 -- Tables and Priority Queues
Now fix it (trickle down)
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15. Chapter 11 -- Tables and Priority Queues
heapInsert
add new item to the end
items[size] = newItem;
size++;
Now fix the heap (float the new item up to the correct location)
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16. Chapter 11 -- Tables and Priority Queues
Heapsort
Strategy
Transforms the array into a heap
Removes the heap's root (the largest element) by exchanging it with the heap’s last element
Transforms the resulting semiheap back into a heap
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17. Chapter 11 -- Tables and Priority Queues
Heapsort
Compared to mergesort
Both heapsort and mergesort are O(n * log n) in both the worst and average cases
However, heapsort does not require a second array
Compared to quicksort
Quicksort is O(n * log n) in the average case
It is generally the preferred sorting method, even though it has poor worst-case efficiency : O(n2)
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18. Chapter 11 -- Tables and Priority Queues
Heapsort
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19. Chapter 11 -- Tables and Priority Queues
Summary
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20. Chapter 11 -- Tables and Priority Queues
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