Priority Queue
Anton Apostolatos
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Binary Heaps: Data Structures and Operations, Slides of Data Structures and Algorithms
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Priority Queue
Anton Apostolatos
Queue: order items by when they were placed - first in, first
out ( FIFO )
Function
s
enqueue
dequeue
first
size
isEmpty
Unsorted List
PQueue
Sorted Singly-Linked
List
Unsorted Doubly-Linked
List
Binary
Heap
Binary
Heap
Slides by Chris Gregg!
Binary Heaps
There are two types of heaps:
Min Heap
(root is the smallest element)
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5
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14 13
2
17
7
50
3
36
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25 1
Max Heap
(root is the largest element)
Binary Heaps (Min Heap)
K
All K All K
Binary Heaps
Circle the min-heap(s):
22
12
11
5
85
8
10
14 13
25
24
26
13
99
36
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Binary Heaps
Circle the min-heap(s):
22
12
11
5
85
8
10
14 13
25
24
26
13
99
36
19
46 42
Binary Heaps
What is the best way to store a
heap?
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We could use a node-based solution, but…
Binary Heaps
It turns out that an array works great
for storing a binary heap!
We will put the root at index 1 instead of
index 0 (this makes the math work out just
a bit nicer).
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[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Heap Operations
- min() : return an element of h with the
smallest key.
- insert(e) : insert element e into the
heap.
- removeMin() : removes the smallest
element from h.
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Heap Operations: min()
min()
Just return the root!
return heap[1] 12
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[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Heap Operations: insert(k)
Insert item at element array[heap.size()+1]
(this probably destroys the heap property)
Perform a “ bubble up ” or “ up-heap ”
operation:
Compare the added element with its parent
if in correct order, stop
If not, swap and repeat
Heap Operations: insert(k)
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22 43
5
11
8
10
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14
5 10 8 12 11 14 13 22 43
[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Start by inserting the key at the first empty
position. This is always at index
heap.size()+.
Heap Operations: insert(9)