Heapsort example
Andrej Ivaskovic
University of Cambridge
February 1, 2015
Andrej Ivaskovic (University of Cambridge)
Heapsort example
February 1, 2015
1 / 25
Input
Initial state of the heap
We are given an array that needs to be sorted:
QWERTYUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
2 / 25
Making the array satisfy the max-heap property
heapify(6)
QWERTY[U]IOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
3 / 25
Making the array satisfy the max-heap property
heapify(6)
QWERTY[U]IOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
3 / 25
Making the array satisfy the max-heap property
heapify(5)
QWERT[Y]UIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
4 / 25
Making the array satisfy the max-heap property
heapify(5)
QWERT[Y]UIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
4 / 25
Making the array satisfy the max-heap property
heapify(4)
QWER[T]YUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
5 / 25
Making the array satisfy the max-heap property
heapify(4)
QWER[T]YUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
5 / 25
Making the array satisfy the max-heap property
heapify(3)
QWE[R]TYUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
6 / 25
Making the array satisfy the max-heap property
heapify(3)
QWE[R]TYUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
6 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[E]RTYUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[E]RTYUIOPASDFG
Q
W
E
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Y
A
S
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[Y]RTEUIOPASDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
E
A
S
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[Y]RTEUIOPASDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
E
A
S
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[Y]RTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(2)
QW[Y]RTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
7 / 25
Making the array satisfy the max-heap property
heapify(1)
Q[W]YRTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
8 / 25
Making the array satisfy the max-heap property
heapify(1)
Q[W]YRTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
8 / 25
Making the array satisfy the max-heap property
heapify(0)
[Q]WYRTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
9 / 25
Making the array satisfy the max-heap property
heapify(0)
[Q]WYRTSUIOPAEDFG
Q
W
Y
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
9 / 25
Making the array satisfy the max-heap property
heapify(0)
[Y]WQRTSUIOPAEDFG
Y
Q
W
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
9 / 25
Making the array satisfy the max-heap property
heapify(0)
[Y]WQRTSUIOPAEDFG
Y
Q
W
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
S
A
E
Heapsort example
U
D
F
February 1, 2015
G
9 / 25
Making the array satisfy the max-heap property
heapify(0)
[Y]WURTSQIOPAEDFG
Y
W
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
G
9 / 25
Making the array satisfy the max-heap property
heapify(0)
[Y]WURTSQIOPAEDFG
Y
W
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
G
9 / 25
End of step 1
We have a heap!
Now the array satisfies the binary max-heap property:
YWURTSQIOPAEDFG
Y
W
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
G
10 / 25
Removal of elements from the heap
We have the 14th element!
[G]WURTSQIOPAEDFY
G
W
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
GWURTSQIOPAEDFY
G
W
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WGURTSQIOPAEDFY
W
G
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WGURTSQIOPAEDFY
W
G
U
R
I
T
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WTURGSQIOPAEDFY
W
T
U
R
I
G
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WTURGSQIOPAEDFY
W
T
U
R
I
G
O
Andrej Ivaskovic (University of Cambridge)
P
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WTURPSQIOGAEDFY
W
T
U
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 14th element!
WTURPSQIOGAEDFY
W
T
U
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
F
February 1, 2015
Y
11 / 25
Removal of elements from the heap
We have the 13th element!
[F]TURPSQIOGAEDWY
F
T
U
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 13th element!
FTURPSQIOGAEDWY
F
T
U
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 13th element!
UTFRPSQIOGAEDWY
U
T
F
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 13th element!
UTFRPSQIOGAEDWY
U
T
F
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
S
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 13th element!
UTSRPFQIOGAEDWY
U
T
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 13th element!
UTSRPFQIOGAEDWY
U
T
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
D
W
February 1, 2015
Y
12 / 25
Removal of elements from the heap
We have the 12th element!
[D]TSRPFQIOGAEUWY
D
T
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
DTSRPFQIOGAEUWY
D
T
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TDSRPFQIOGAEUWY
T
D
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TDSRPFQIOGAEUWY
T
D
S
R
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TRSDPFQIOGAEUWY
T
R
S
D
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TRSDPFQIOGAEUWY
T
R
S
D
I
P
O
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TRSOPFQIDGAEUWY
T
R
S
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 12th element!
TRSOPFQIDGAEUWY
T
R
S
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
E
Heapsort example
U
W
February 1, 2015
Y
13 / 25
Removal of elements from the heap
We have the 11th element!
[E]RSOPFQIDGATUWY
E
R
S
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
T
Heapsort example
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 11th element!
ERSOPFQIDGATUWY
E
R
S
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
T
Heapsort example
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 11th element!
SREOPFQIDGATUWY
S
R
E
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
T
Heapsort example
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 11th element!
SREOPFQIDGATUWY
S
R
E
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
Q
F
A
T
Heapsort example
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 11th element!
SRQOPFEIDGATUWY
S
Q
R
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
A
T
Heapsort example
E
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 11th element!
SRQOPFEIDGATUWY
S
Q
R
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
A
T
Heapsort example
E
U
W
February 1, 2015
Y
14 / 25
Removal of elements from the heap
We have the 10th element!
[A]RQOPFEIDGSTUWY
A
Q
R
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
ARQOPFEIDGSTUWY
A
Q
R
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RAQOPFEIDGSTUWY
R
Q
A
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RAQOPFEIDGSTUWY
R
Q
A
O
I
P
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RPQOAFEIDGSTUWY
R
Q
P
O
I
A
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RPQOAFEIDGSTUWY
R
Q
P
O
I
A
D
Andrej Ivaskovic (University of Cambridge)
G
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RPQOGFEIDASTUWY
R
Q
P
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
A
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 10th element!
RPQOGFEIDASTUWY
R
Q
P
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
A
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
15 / 25
Removal of elements from the heap
We have the 9th element!
[A]PQOGFEIDRSTUWY
A
Q
P
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 9th element!
APQOGFEIDRSTUWY
A
Q
P
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 9th element!
QPAOGFEIDRSTUWY
Q
P
A
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 9th element!
QPAOGFEIDRSTUWY
Q
P
A
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
F
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 9th element!
QPFOGAEIDRSTUWY
Q
P
F
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 9th element!
QPFOGAEIDRSTUWY
Q
P
F
O
I
G
D
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
16 / 25
Removal of elements from the heap
We have the 8th element!
[D]PFOGAEIQRSTUWY
D
P
F
O
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
DPFOGAEIQRSTUWY
D
P
F
O
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
PDFOGAEIQRSTUWY
P
D
F
O
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
PDFOGAEIQRSTUWY
P
D
F
O
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
POFDGAEIQRSTUWY
P
O
F
D
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
POFDGAEIQRSTUWY
P
O
F
D
I
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
POFIGAEDQRSTUWY
P
O
F
I
D
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 8th element!
POFIGAEDQRSTUWY
P
O
F
I
D
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
17 / 25
Removal of elements from the heap
We have the 7th element!
[D]OFIGAEPQRSTUWY
D
O
F
I
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 7th element!
DOFIGAEPQRSTUWY
D
O
F
I
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 7th element!
ODFIGAEPQRSTUWY
O
D
F
I
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 7th element!
ODFIGAEPQRSTUWY
O
D
F
I
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 7th element!
OIFDGAEPQRSTUWY
O
I
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 7th element!
OIFDGAEPQRSTUWY
O
I
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
E
U
W
February 1, 2015
Y
18 / 25
Removal of elements from the heap
We have the 6th element!
[E]IFDGAOPQRSTUWY
E
I
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 6th element!
EIFDGAOPQRSTUWY
E
I
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 6th element!
IEFDGAOPQRSTUWY
I
E
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 6th element!
IEFDGAOPQRSTUWY
I
E
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 6th element!
IGFDEAOPQRSTUWY
I
G
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 6th element!
IGFDEAOPQRSTUWY
I
G
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
A
S
T
Heapsort example
O
U
W
February 1, 2015
Y
19 / 25
Removal of elements from the heap
We have the 5th element!
[A]GFDEIOPQRSTUWY
A
G
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 5th element!
AGFDEIOPQRSTUWY
A
G
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 5th element!
GAFDEIOPQRSTUWY
G
A
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 5th element!
GAFDEIOPQRSTUWY
G
A
F
D
P
E
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 5th element!
GEFDAIOPQRSTUWY
G
E
F
D
P
A
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 5th element!
GEFDAIOPQRSTUWY
G
E
F
D
P
A
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
20 / 25
Removal of elements from the heap
We have the 4th element!
[A]EFDGIOPQRSTUWY
A
E
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
21 / 25
Removal of elements from the heap
We have the 4th element!
AEFDGIOPQRSTUWY
A
E
F
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
21 / 25
Removal of elements from the heap
We have the 4th element!
FEADGIOPQRSTUWY
F
E
A
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
21 / 25
Removal of elements from the heap
We have the 4th element!
FEADGIOPQRSTUWY
F
E
A
D
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
21 / 25
Removal of elements from the heap
We have the 3rd element!
[D]EAFGIOPQRSTUWY
D
E
A
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
22 / 25
Removal of elements from the heap
We have the 3rd element!
DEAFGIOPQRSTUWY
D
E
A
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
22 / 25
Removal of elements from the heap
We have the 3rd element!
EDAFGIOPQRSTUWY
E
D
A
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
22 / 25
Removal of elements from the heap
We have the 3rd element!
EDAFGIOPQRSTUWY
E
D
A
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
22 / 25
Removal of elements from the heap
We have the 2nd element!
[A]DEFGIOPQRSTUWY
A
D
E
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
23 / 25
Removal of elements from the heap
We have the 2nd element!
ADEFGIOPQRSTUWY
A
D
E
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
23 / 25
Removal of elements from the heap
We have the 2nd element!
DAEFGIOPQRSTUWY
D
A
E
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
23 / 25
Removal of elements from the heap
We have the 2nd element!
DAEFGIOPQRSTUWY
D
A
E
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
23 / 25
Removal of elements from the heap
We have the 1st element!
[A]DEFGIOPQRSTUWY
A
D
E
F
P
G
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
24 / 25
Removal of elements from the heap
We have the 1st element!
ADEFGIOPQRSTUWY
A
D
E
G
F
P
Q
Andrej Ivaskovic (University of Cambridge)
R
I
S
T
Heapsort example
O
U
W
February 1, 2015
Y
24 / 25
We are done!
What we get in the end is sorted:
ADEFGIOPQRSTUWY
Andrej Ivaskovic (University of Cambridge)
Heapsort example
February 1, 2015
25 / 25