arrays lists stacks queues - encsusers.encs.concordia.ca/~sthiel/coen352/01b_arrays_lists...arrays...

Arrays Lists StacksQueues

S. Thiel

ImplementingSequences

Sequences

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Stacks

Queues

Dictionaries

Analysis

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Arrays Lists Stacks Queues

S. Thiel1

1Department of Computer Science & Software EngineeringConcordia University

June 26, 2019


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Outline

Implementing SequencesSequencesArraysListsStacksQueuesDictionariesAnalysis

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Implementing a Sequence Structure 1

I Recall the properties of a sequence

I Elements can be duplicated

I Different permutations constitute a different sequences

I How could we store this information structurally


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Implementing a Sequence Structure 2

I What is in the squence?

I How many items does it have?

I Where are we in the sequence?


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Implementing a Sequence Behaviour 1

I What behavior should it have?

I Is it empty?

I What is the first element?

I What is the last element?

I How many elements are there?


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Sequences and Order

I We say that sequences have an orderI We mean that a different permutation constitutes a

different sequence

I But there is also the idea that the elements can have anorder with respect to each other

I They can actually have many. . .I But we usually want to know if the sequence is sorted

before doing something with itI is this the permutation where each element is ordered

with respect to a given order (e.g. by size, cost,alphabetic. . . some ordinal measure)

I When we consider such orderings, we consider the valueof the element to be what we are comparing.

I Can an item have more than one value?


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Does Sorting Affect ADT?

I How we sort a data structure will be specific to the datastructure.

I Should the data structure care whether or not it issorted?

I Can we use data structures differently if we know theyare sorted?


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Implementing an Array

I A Sequence as adjacent values in memory

I This is called an Array

I P = 〈4, 12, 12, 18〉I If they are adjacent values, we can access by index

I What if we access an index bigger than the size?

I Is the size fixed? How can we “fix” this?

I How do we add and remove?

I How do we add in the middle?

I Does the idea of a current element make sense if wecan index?

I Maybe the idea of a current element is “external” to anArray’s implementation? Does it have to be?


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Implementing a List

I A Sequence as a value in memory and a pointer to thenext value.

I This is called a List

I P = 〈4, 12, 12, 18〉I Is there a concept of index?

I Is there a concept of current element?

I Is the size fixed?

I How do we add and remove?

I How do we add in the middle?


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Types of List

I We said value in memory, and a pointer to the nextvalue

I Could we have a list of these pointers? What do welose?

I Can we keep these pointers with the value?

I If we point to the next value, we need to know the first

I What if we want to go to the previous element? Can weadd another pointer?

I Singly and Doubly-Linked Lists.


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Stack Basics

I Like a list

I add and remove from one end

I no direct access, except from that end

I Simple

I Last-In, First-Out (LIFO)


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Where to Use a Stack

I Freelists from last lectureI Call stack in running code

I Sometimes replace recurions with iteration


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Stack Operations

I Peek

I Pop

I Push

I . . . some others, like size/clear


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Stack Implementations

I Array-Based

I List-Based

I What are the respective advantages?


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Double Stack Implementation

I If items will get passed between two stacks

I Stick them in the same array


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Stack Examples

I Call Stack (that’s what your Stacktrace is!)

I Dijkstra’s two-stack expression evaluation


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Queue Basics

I Like a list

I add from one end, remove from the other

I no direct access, except at the ends (usually just front)

I Simple

I First-In, First-Out (FIFO)


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Where to Use a Queue

I Playlists

I Waiting lists

I Generally when you know the max n

I or when dequeue will happen more


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Queue Operations

I frontvalue

I enqueue

I dequeue

I . . . some others, like size/clear


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Queue Implementations

I Array-BasedI circular implementation: yesI empty or full?I keep explicit sizeI or use an array of size n+1

I List-Based

I What are the respective advantages?


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Circular Queue Implementation

I Can use an array if we never have too many elements

I If two queues in one circular array?


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Dictionary Basics

I Slightly more complicated

I computers store and retrieve data

I Look something up using a key

I Know if two keys are different, generally have order

I Resulting data is not (or is more) than the key


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Dictionary Operations

I Clear

I Record

I Remove

I FindI RemoveAny?

I Seems unnatural, just to iterate...


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Dictionary Implementations 1

I We can call the underlying data the Database

I Array-Based?

I List-Based?

I Other?


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Dictionary Implementations 2

I Different Dictionaries for Different key types?

I Can different things have the same key?


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Array Operations

I add Θ (1)

I insert Θ (n)

I delete Θ (n)

I look up by index Θ (1)

I What about when Add is too big?


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LinkedList Operations

I add Θ (1)

I insert Θ (1) or Θ (n)?

I delete Θ (1) or Θ (n)?

I why qualify insert and delete?

I look up by index Θ (n)

I How do LinkedLists deal with the add problem fromarrays? Freelists?


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Stack Operations

I push Θ (1)

I pop Θ (1)

I how to do it wrong. . .


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Queue Operations

I enqueue Θ (1)

I dequeue Θ (1)

I how to do it wrong. . .


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Dictionary Operations

I clear Θ (1) ?I record

I unsorted Θ (1)I sorted Θ (n)

I remove Θ (n)I find

I unsorted Θ (n)I sorted

I Array Θ (log n)I LinkedList Θ (n)

I RemoveAny? Θ (1)


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Dictionary Operation Costs

I What is the cost of Binary Search in a LinkedList

I Can we fudge that?

I or move away from linear structures


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References I

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