1 Joe Meehean

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 empty is the queue empty  size  enqueue (add) add item to end of queue  dequeue (remove) remove and return item at front of queue  peek return (do not remove) item at front of queue 3

 Similar to List ADT with restricted operations implemented using arrays or linked nodes 4

 Fields Node *phead_; int size_; 0 0 size_: phead_: 1 1 //Empty //After q.enqueue(A) A A 5 size_: phead_:

2 2 //After q.enqueue(B) A A B B 2 2 //After q.enqueue(B) B B A A OR  Enqueue to end or insert at the front? 6 size_: phead_: size_: phead_:

EnQ at Front Single TailPtr Double TailPtr enqueue???? dequeue???? peek???? EnQ at Back Single TailPtr Double TailPtr enqueue???? dequeue???? peek???? 7

EnQ at Front Single TailPtr Double TailPtr enqueueO(1) dequeueO(N) O(1) peekO(N)O(1)O(N)O(1) EnQ at Back SingleDouble TailPtr enqueueO(N) O(1) dequeueO(1) peekO(1) 8

 Fields T *items_; int size_; int capacity_; X X //Empty //After q.enqueue(X) capacity_: size_: items_: size_: items_:

2 2 X X Y Y //After q.enqueue(Y) 2 2 Y Y X X //After q.enqueue(Y) OR  Enqueue to end or insert at the front? capacity_: size_: items_: 4 4 capacity_: size_: items_:

Method enQ at front dQ at end enQ at end dQ at front enqueue ?? dequeue ?? peek ?? 11

Method enQ at front dQ at end enQ at end dQ at front enqueue avg: O(1) dequeue O(1) peek O(1) 12

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 Array implementation of queue 14 Method enQ at front dQ at end enQ at end dQ at front enqueue avg: O(1) dequeue O(1) peek O(1)

 O(1) for enqueue and dequeue  Don’t force 1 st item to index 0  New fields int first_ int last_ 3 3 X X Y Y Z Z A A q.enqueue(X) “”(Y) “”(Z) q.dequeue() q.enqueue(A) 15 size_: items_: first_ last_

void enqueue(const T& newItem){ if(size_ == capacity_) {...} last_++; items_[last_] = newItem; size++; } T dequeue(){ size--; first_++; return items_[first_ - 1]; }  O(1) if array not full (avg case) 16

 What if we call q.enqueue(C)? could expand array? wastes space X X Y Y Z Z A A B B size_: items_: first_ last_

Z A B X X Y Y Z Z A A B B size_: items_: first_ last_ XY first_ last_

Z A B C C Y Y Z Z A A B B size_: items_: first_ last_ CY first_ last_ q.enqueue(C) //enqueued at //pos 0

void enqueue(const T& newItem){ if( size_ == capacity_ ){ doubleCapacity(); } // increment the last index last_++; // wrapping if necessary if(last_ == capacity_){ last_ = 0; } items_[last] = newItem; size_++; } 20

 Expanding the array C C D D A A B B items_: C C D D A A B B 4 4 size_: 4 4 capacity_: items_: size_: capacity_: first_ last_ first_ last_

 Expanding the array C C D D A A B B items_: C C D D A A B B 4 4 size_: 4 4 capacity_: 0123 Big hole in the middle 22 items_: size_: capacity_: first_ last_ first_ last_

A A B B C C D D 5 67 C C D D A A B B first_ last_ first_ last_

 Allocate new array of twice the size: tmp  Copy items_[first] to items_[capacity_- 1] into tmp starting at position first  Copy items_[0] to items_[first - 1] into tmp starting at position capacity_  Fix member data set items_ to point at tmp delete old items last_ = first_ + capacity_ – 1 capacity_ *= 2 24

 Space linked list stores pointer and data array stores only data array can be mostly empty toss up  Time linked all O(1) circular array all O(1) in avg case  Ease of implementation linked by a mile 25

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