CSE 373: Data Structures & Algorithms Pseudocode; ADTs, Slides of Data Structures and Algorithms

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CSE 373: Data Structures & Algorithms

Pseudocode; ADTs; Priority Queues;

Heaps

Riley Porter

Winter 2017

Winter 2017 CSE373: Data Structures & Algorithms 1

Course LogisGcs

Winter 2017 CSE373: Data Structures and Algorithms 2

• HW 1 released Monday. Due a week from Tuesday.

• Java Review Session early next week, room and Gme

TBA and posted on the course website

• Slides posted and updated from last Gme with links

correctly working in PDF version

More Pseudocode

Winter 2017 CSE373: Data Structures and Algorithms 4

Algorithm: Given a list of names in the format "firstName

lastName", make a Map of all first names as keys with sets of last

names as their values

Pseudocode:

create the empty result map while list has more names to process { firstName is name split up until space lastName is name split from space to the end if firstName not in the map yet { put firstName in map as a key with an empty set as the value } add lastName to the set for the first name move to the next name in the list }

Pseudocode PracGce

Winter 2017 CSE373: Data Structures and Algorithms 5

Come up with pseudocode for the following algorithm:

Algorithm: Given a list of integers, find the index of the

maximum integer in the list.

Terminology Review

• Abstract Data Type (ADT)

• MathemaGcal descripGon of a "thing" with set of

operaGons

• Algorithm

• A high level, language-­‐independent descripGon of a step-­‐

by-­‐step process

• Data structure

• A specific organizaGon of data and family of algorithms for

implemenGng an ADT

• ImplementaGon of a data structure

• A specific implementaGon in a specific language Winter 2017 CSE373: Data Structures and Algorithms 7

Another ADT: Priority Queue

A priority queue holds comparable data

– Given x and y , is x less than, equal to, or greater

than y

– Meaning of the ordering can depend on your data

– Many data structures require this: dicGonaries,

sorGng

– Typically elements are comparable types, or have

two fields: the priority and the data

Winter 2017 8 CSE373: Data Structures & Algorithms

PrioriGes

• Each item has a "priority"
  • The lesser item is the one with the greater priority
  • So "priority 1" is more important than "priority 4"
  • Can resolve Ges arbitrarily
• OperaGons:
  • insert
  • deleteMin
  • is_empty
• deleteMin returns and deletes the item with greatest

priority (lowest priority value)

• insert is like enqueue , deleteMin is like dequeue
  • But the whole point is to use prioriGes instead of FIFO Winter 2017 10 CSE373: Data Structures & Algorithms insert deleteMin

Priority Queue Example

Given the following, what values are a , b , c and d?

insert element1 with priority 5 insert element2 with priority 3 insert element3 with priority 4 a = deleteMin // a =? b = deleteMin // b =? insert element4 with priority 2 insert element5 with priority 6 c = deleteMin // c =? d = deleteMin // d =? Winter 2017 11 CSE373: Data Structures & Algorithms

Some ApplicaGons

• Run mulGple programs in the operaGng system

• "criGcal" before "interacGve" before "compute-­‐ intensive", or let users set priority level

• Select print jobs in order of decreasing length

• "Greedy" algorithms (we’ll revisit this idea)

• Forward network packets in order of urgency

• Select most frequent symbols for data

compression (Huffman CSE 143)

• SorGng (first insert all, then repeatedly

deleteMin )

Winter 2017 13 CSE373: Data Structures & Algorithms

Possible ImplementaGons

• Unsorted Array

– insert by inserGng at the end

– deleteMin by linear search

• Sorted Circular Array

– insert by binary search, shij elements over

– deleteMin by moving “front”

Winter 2017 14 CSE373: Data Structures & Algorithms

One ImplementaGon: Heap

Heaps are implemented with Trees

A binary min-­‐heap (or just binary heap or

heap ) is a data structure with the properGes:

• Structure property: A complet e binary tree

• Heap property: The priority of every (non-­‐

root) node is greater than the priority of its

parent

– Not a binary search tree

Winter 2017 16 CSE373: Data Structures & Algorithms

Tree Review

• root of tree:

• leaves of tree:

• children of B:

• parent of C:

• subtree C:

• height of tree:

• height of E:

• depth of E:

• degree of B:

Winter 2017 17 CSE373: Data Structures & Algorithms

D F G

B^ C

A

H

E

• perfect tree:

• complete tree:

Structure Property: Completeness

• A Binary Heap is a complete binary tree:

– A binary tree with all levels full, with a possible

excepGon being the bomom level, which is filled

lej to right

Examples:

Winter 2017 19 CSE373: Data Structures & Algorithms

are these trees complete****?

Structure Property: Completeness

• A Binary Heap is a complete binary tree:

– A binary tree with all levels full, with a possible

excepGon being the bomom level, which is filled

lej to right

Examples:

Winter 2017 20 CSE373: Data Structures & Algorithms

incomplete 40

complete