Problem of the Day

Problem of the Day

You are trapped alone in a dark room with: Candle; Wood stove; and Gas lamp (with full tank).

You only have one match; what do you light 1st?

Problem of the Day

You are trapped alone in a dark room with: Candle; Wood stove; and Gas lamp (with full tank).

You only have one match; what do you light 1st?

The match!

LECTURE 40:IMPLEMENTING HEAPS

CSC 212 – Data Structures

Priority Queue ADT

Prioritizes Entrys using their keys For Entrys with equal priorities, order not

specified Priority given to each value when added

to PQ Normally, the priority not changeable while

in PQ Access single Entry: one with the lowest

priority Returns Entry using min() or removeMin()

Heaps

Binary-tree based PQ implementation Still structured using parent-child

relationship At most 2 children & 1 parent for each node

in tree Heaps must also satisfy 2 additional

properties Parent at least as important as its children Can not use any tree; must form complete

binary tree

2

95

67

Implement CompleteBinaryTree Already know basics, this extends BinaryTree Use existing tree implementation to make

easier 2 implementations of BinaryTree: which to

use? Sequence-based possible should be 1st

question? Continue relying on trick of mapping children

to indices FullPQException not helpful, so can this

work? Even if so, how much extra space would this

require?

Sequence-based BinaryTree

Node at index specified for location in TREE Root node stored at index 0 Root’s left child at index 1 Right child of root at index 2 Left child’s right child at index 4 Right child’s left child at index 5 Node at index n’s left child is at index 2n + 1 Node at index n’s right child is at index 2n +

2

Sequence-based BinaryTree

Node at index specified for location in TREE Root node stored at index 0 Root’s left child at index 1 Right child of root at index 2 Left child’s right child at index 4 Right child’s left child at index 5 Node at index n’s left child is at index 2n + 1 Node at index n’s right child is at index 2n +

2

But how much space will this need for to hold a heap?

Sequence to Implement Heap

2

0

2

0


2

9

0 1

2

0

1

9


2

9 3

0 1 2

2

0

1

9

2

3

`


2

9 3

99

0 1 2 3

2

0

1

9

2

3

3

99

`


2

9 3

99

0 1 2 3

2

0

1

9

2

3

3

99

`

Add nodes to end of the SequenceSimilarly, remove node at end

NO space is wasted for this!

Swapping Data in a Heap

Two ways to swap Entrys in a heap Preserve the nodes, but exchange their

elements Move nodes within tree & leave the elements




Preserving nodes & swapping Entrys means




Preserving nodes & swapping Entrys means Setting two references (one in each node)

If decide you want to move nodes around instead





If decide you want to move nodes around instead Set two references for parents (one in each

node)






node) Set another two references for left children

(1 in each)







(1 in each) Swap right children in each node (2 more

references)


Two ways to swap Entrys in a heap Preserving nodes & swapping Entrys

means Setting two references (one in each node)




references)

Either way CAN work; Which do you choose?


Two ways to swap Entrys in a heap Preserving nodes & swapping Entrys

means Setting two references (one in each node)




references)

Either way CAN work; Which do you (NOT Alec)

choose?

Keys In a PriorityQueue

Must order keys used within PriorityQueue What types could be used to achieve this

ordering?

What Type For This Priority?

For Everything Else There Are…

Final Exam Schedule

Lab Mastery Exam is:Tues., Dec. 14th from 2:45PM – 3:45PM in OM 119

Final Exam is: Fri., Dec. 17th from 8AM – 10AM in OM 200

Problem of the Day

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