Problem of the Day  At low tide, a ship docks in the harbor  Ship is 9’ above the water line when it docks  Over the side hangs a rope ladder w/ rungs 1’ apart  Tide rises at a rate of 9” per hour After 6 hours what length of ladder will still be above water?

Problem of the Day  At low tide, a ship docks in the harbor  Ship is 9’ above the water line when it docks  Over the side hangs a rope ladder w/ rungs 1’ apart  Tide rises at a rate of 9” per hour After 6 hours what length of ladder will still be above water? 9’ – the ladder will rise with the boat!

CSC 212 – Data Structures

Queue ADT  Creates fair & equal system to handle data in order added  Structure for element processing in order added

Queue ADT  Creates fair & equal system to handle data in order added  Structure for element processing in order added From each according to his ability, to each according to his needs Karl Marx

Deque ADT  Limited inequality when processing elements process either end of structure  Add and remove to process either end of structure  Can’t use middle elements, however

Deque ADT  Limited inequality when processing elements process either end of structure  Add and remove to process either end of structure  Can’t use middle elements, however Four legs good, two legs better From Animal Farm George Orwell

Priority Queue ADT  Priority queue uses strict ordering of data  Values assigned priority when added to the queue completely biased order  Priorities used to process in completely biased order

Priority Queue ADT  Priority queue uses strict ordering of data  Values assigned priority when added to the queue completely biased order  Priorities used to process in completely biased order First you get the sugar, then you get the power, then you get the women

Priority Queue ADT  PriorityQueue yet another Collection  Prioritize each datum contained in the collection  PQ is organized from lowest to highest priority  Access smallest priority only sort of like Queue  min() & removeMin() return priority & value  Implementation not defined: this is still an ADT  Remember that organization & order is theoretical only

 PriorityQueue yet another Collection  Prioritize each datum contained in the collection  PQ is organized from lowest to highest priority  Access smallest priority only sort of like Queue  min() & removeMin() return priority & value  Implementation not defined: this is still an ADT  Remember that organization & order is theoretical only Priority Queue ADT

Entry s in a PriorityQueue  PriorityQueues use Entry to hold data  As with Position, implementations may differ  Entry has 2 items that define how it gets used  PQ will only use key – the priority given to the Entry  Value is important data to be processed by program

P RIORITY Q UEUE Operations D EQUE Q UEUE P RIORITY Q UEUE addFront() addLast() enqueue()insert() getFront() getLast() front()min() removeFront() removeLast() dequeue()removeMin()

Sequence -based Priority Queue

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 5 Sequence

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 5

Sequence Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 1 5

Sequence 1 Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 5

Sequence 1 Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 3 5

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space Sequence 1 35

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 9 Sequence 135

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space Sequence 1 359

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space 0 Sequence 1359

Using Sorted Sequence  Entry s stored in increasing order of priority  insert() checks each index to find where to add  Once found, Position s may shift to make space

Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift

Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift

1 Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift 359

Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift 59 3

5 Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift 9

Using Sorted Sequence  Entry s stored in increasing order of priority  min() returns 0 th element in the Sequence  Planned well, removeMin() does not need to shift Sequence 9

Using Sorted Sequence  Entry s stored in increasing order of priority  No shifting ever required if planned well. How?  What is big-Oh complexity of this approach? insert(): removeMin(): min():

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed 5 Sequence

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 5

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 1 5

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 5 1

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 5 3 1

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 5 13

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence

Unsorted Sequence s ♥ Clutter  Entry s can be stored in any order  Add Entry to Sequence end during insert()  Guarantees that this is fast with no shifting needed Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 139

Unsorted Does It… Later  Put off work until min() & removeMin()  Scan Sequence to find Entry with smallest priority  Still should not shift when removing from Sequence Sequence 5 39

Unsorted Sequence Complexity  What is big-Oh complexity of this approach? insert(): removeMin(): min():

Why Use Sorted Sequence ?  Cheap to check & remove data with this approach  But it is relatively expensive to add data  When insert() rare relative to calling min()  Good trade-off here, so sorted Sequence worth it

Why Use Sorted Sequence ?  Cheap to check & remove data with this approach  But it is relatively expensive to add data  When insert() rare relative to calling min()  Good trade-off here, so sorted Sequence worth it

Why Use Unsorted Sequence ?  Cheap to add data with this approach  But it is relatively expensive to remove or check it  When would this trade-off work?

Why Use Unsorted Sequence ?  Cheap to add data with this approach  But it is relatively expensive to remove or check it  When would this trade-off work? Examples?

For Next Lecture  Complete your (last) weekly assignment  Read GT 8.3 before next Monday's lecture  Why did we discuss binary trees before this?  Does order really matter?  Reasons using this over Sequence-based approaches?  Programming project #3 due soon