Tables and Priority Queues Tables Previously: each node stored one - - PowerPoint PPT Presentation

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Tables and Priority Queues Tables Previously: each node stored one - - PowerPoint PPT Presentation

Feb 03, 2024 124 likes •476 views

Tables and Priority Queues Tables Previously: each node stored one item Now: Groups of related information in records Records indexed by key Key is just one of the pieces of information the one you want to be able to search on

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SLIDE 1

Tables and Priority Queues

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Binary searching & introduction to trees

2 CMPS 12B, UC Santa Cruz

Tables

Previously: each node stored one item Now: Groups of related information in records

Records indexed by key Key is just one of the pieces of information – the one you

want to be able to search on

Support fast searching by key – O(logn) Also support scanning for other information in

records

But not as fast – O(n) instead of O(logn)

Examples

Student records List of pirated MP3s

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Binary searching & introduction to trees

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Table ADT – Operations

  • 1. Create an empty table
  • 2. Determine whether a table is empty
  • 3. Determine the number of items in a table
  • 4. Insert a new item into the table
  • 5. Delete the item with a given search key from the

table

  • 6. Retrieve the item with a given search key from the

table

  • 7. Traverse the items in a table in sorted search-key
  • rder
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Binary searching & introduction to trees

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SearchKeys

public abstract class KeyedItem { private Comparable searchKey; public KeyedItem(Comparable key) { searchKey = key; } public Comparable getKey() { return searchKey; } }

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City extends KeyedItem

public class City extends KeyedItem { private String country; private int population; public City(String theCity, String theCountry, int pop) { super(theCity); country = theCountry; population = pop; } public String toString() { return getKey() + ", " + country + " " + population; } public void setPopulation(int pop) { population = pop; } public int getPopulation() { return population; } public String getCountry() { return Country; } }

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TableInterface

import searchkeys.*; public interface TableInterface { public boolean tableIsEmpty(); public int tableLength(); public void tableInsert(KeyedItem newItem) throws TableException; public boolean tableDelete(Comparable searchKey); public KeyedItem tableRetrieve( Comparable searchKey); }

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Implementing the Table

Linear implementations

Unsorted array Unsorted linked list Sorted (by key) array Sorted (by key) linked list

Non-linear implementations

Binary search tree

Criteria

What operations are needed? How often will different operations be used? How important are the different operations?

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Examples

Small, unsorted data, fixed size

Array

Small, unsorted data, variable size

Linked list

Small, sorted data, variable size

Linked list

Large, unsorted data, variable size

Linked list

Large, sorted data, variable size

Binary search tree

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Comparison of Implementation Alternatives

O(n) O(n) O(n) O(1) Unsorted array Traversal Retrieval Deletion Insertion O(n) O(logn) O(logn) O(logn) Binary search tree O(n) O(n) O(n) O(n) Sorted linked list O(n) O(logn) O(n) O(n) Sorted array O(n) O(n) O(n) O(1) Unsorted linked list

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See Table Code

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Priority Queue

It is often useful to assign a priority to different data

items

so that urgent items can be processed first

Examples

Time in a todo list Importance in a list of phone calls to make …

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Priority Queue ADT

  • 1. Create an empty priority queue
  • 2. Determine whether a priority queue is empty
  • 3. Insert a new item into a priority queue
  • 4. Retrieve and then delete the item in a priority queue

with the highest priority

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Binary searching & introduction to trees

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Implementing Priority Queues: Heaps

A complete binary tree that is

Empty, or Whose root has heaps as its subtrees, and whose root contains a key greater than or equal to the key

  • f each of its children

Heaps are always balanced There is no order on the values of the keys of the two

children of a node

Unlike binary search trees

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Array-based Implementation of a Heap

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Breadth-first order in the array Complete tree ⇒ no gaps in array

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Inserting into the Heap

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Breadth-first order in the array Complete tree ⇒ no gaps in array

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Deleting from the Heap (1)

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Always delete the root

It has the highest priority

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Deleting from the Heap (2)

9 6 5 2 3

Oops, now we have two heaps

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Deleting from the Heap (3)

9 6 5 2 3

Repairing the heap: Move the last element to the top

1 2 5 3 6 9 1

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Deleting from the Heap (4)

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Repairing the heap: Now “trickle down” by comparing

and swapping until heap is restored

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Deleting from the Heap (5)

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Repairing the heap: Now “trickle down” by comparing

and swapping until heap is restored

2 5 3 6 1 9 9

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Deleting from the Heap (6)

3 6 5 2 1

Calculating indices:

leftchild = 2*parent+1 Rightchild = 2*parent+2

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Deleting from the Heap (7)

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Now it’s a heap again Total time O(logn)

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Inserting to a heap

The opposite of deleting Insert at the bottom, then “trickle up”

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Heapsort

  • One way
  • Insert everything into the heap, then
  • Take everything back out
  • Faster way
  • 1. Make it a heap

for(int index = n/2; n >= 0; n--) { heapRebuild(array, index, n); }

  • 2. Swap the first item (largest) with the last (last--)
  • 3. heapRebuild(array, index, last);
  • 4. Repeat until all items are in the right place
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Heapsort

Make it a heap by doing

heapRebuild to each node

Starting with leaf nodes

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Heapsort

Swap first and “last”

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LAST

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Heapsort

last = last – 1 heapRebuild()

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LAST

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Heapsort

Swap first and “last”

6 9 1 3 5 2

LAST

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Heapsort

last = last - 1 heapRebuild()

6 9 1 3 2 5

LAST

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Binary searching & introduction to trees

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Heapsort

Swap first and “last”

6 9 5 3 2 1

LAST

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Binary searching & introduction to trees

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Heapsort

last = last - 1 heapRebuild()

6 9 5 1 2 3

LAST

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Binary searching & introduction to trees

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Heapsort

Swap first and “last”

6 9 5 3 2 1

LAST

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Heapsort

last = last – 1 heapRebuild()

6 9 5 3 1 2

LAST

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Heapsort

Swap first and “last” Done!

6 9 5 3 2 1

LAST