Fibonacci Heaps

Stella Lau

March 3, 2015

Stella Lau Fibonacci Heaps March 3, 2015 1 / 60

Inserting 29

29

Stella Lau Fibonacci Heaps March 3, 2015 2 / 60

Inserting 28

28 29

Stella Lau Fibonacci Heaps March 3, 2015 3 / 60

Inserting 27

27 29 28

Stella Lau Fibonacci Heaps March 3, 2015 4 / 60

Inserting 26

26 29 28 27

Stella Lau Fibonacci Heaps March 3, 2015 5 / 60

Inserting 25

25 29 28 27 26

Stella Lau Fibonacci Heaps March 3, 2015 6 / 60

Extracting min: 25

26

27 28

29

Stella Lau Fibonacci Heaps March 3, 2015 7 / 60

Cutting 29

−1 26

27 28

Stella Lau Fibonacci Heaps March 3, 2015 8 / 60

Inserting 24

24 26

27 28

Stella Lau Fibonacci Heaps March 3, 2015 9 / 60

Inserting 23

23 26

27 28

24

Stella Lau Fibonacci Heaps March 3, 2015 10 / 60

Inserting 22

22 26

27 28

24 23

Stella Lau Fibonacci Heaps March 3, 2015 11 / 60

Inserting 21

21 26

27 28

24 23 22

Stella Lau Fibonacci Heaps March 3, 2015 12 / 60

Inserting 20

20 26

27 28

24 23 22 21

Stella Lau Fibonacci Heaps March 3, 2015 13 / 60

Extracting min: 20

21

22 26

27 28

23

24

Stella Lau Fibonacci Heaps March 3, 2015 14 / 60

Cutting 24

−1 21

22 26

27 28

23

Stella Lau Fibonacci Heaps March 3, 2015 15 / 60

Cutting 22

−1 21

26

27 28

23

Stella Lau Fibonacci Heaps March 3, 2015 16 / 60

Inserting 19

19 21

26

27 28

23

Stella Lau Fibonacci Heaps March 3, 2015 17 / 60

Inserting 18

18 21

26

27 28

23

19

Stella Lau Fibonacci Heaps March 3, 2015 18 / 60

Inserting 17

17 21

26

27 28

23

19 18

Stella Lau Fibonacci Heaps March 3, 2015 19 / 60

Inserting 16

16 21

26

27 28

23

19 18 17

Stella Lau Fibonacci Heaps March 3, 2015 20 / 60

Inserting 15

15 21

26

27 28

23

19 18 17 16

Stella Lau Fibonacci Heaps March 3, 2015 21 / 60

Extracting min: 15

16

17 21

26

27 28

23

18

19

Stella Lau Fibonacci Heaps March 3, 2015 22 / 60

Cutting 19

−1 16

17 21

26

27 28

23

18

Stella Lau Fibonacci Heaps March 3, 2015 23 / 60

Cutting 17

−1 16

21

26

27 28

23

18

Stella Lau Fibonacci Heaps March 3, 2015 24 / 60

Inserting 14

14 16

21

26

27 28

23

18

Stella Lau Fibonacci Heaps March 3, 2015 25 / 60

Inserting 13

13 16

21

26

27 28

23

18

14

Stella Lau Fibonacci Heaps March 3, 2015 26 / 60

Inserting 12

12 16

21

26

27 28

23

18

14 13

Stella Lau Fibonacci Heaps March 3, 2015 27 / 60

Inserting 11

11 16

21

26

27 28

23

18

14 13 12

Stella Lau Fibonacci Heaps March 3, 2015 28 / 60

Inserting 10

10 16

21

26

27 28

23

18

14 13 12 11

Stella Lau Fibonacci Heaps March 3, 2015 29 / 60

Extracting min: 10

11

12 16

21

26

27 28

23

18

13

14

Stella Lau Fibonacci Heaps March 3, 2015 30 / 60

Cutting 14

−1 11

12 16

21

26

27 28

23

18

13

Stella Lau Fibonacci Heaps March 3, 2015 31 / 60

Cutting 12

−1 11

16

21

26

27 28

23

18

13

Stella Lau Fibonacci Heaps March 3, 2015 32 / 60

Inserting 9

9 11

16

21

26

27 28

23

18

13

Stella Lau Fibonacci Heaps March 3, 2015 33 / 60

Inserting 8

8 11

16

21

26

27 28

23

18

13

9

Stella Lau Fibonacci Heaps March 3, 2015 34 / 60

Inserting 7

7 11

16

21

26

27 28

23

18

13

9 8

Stella Lau Fibonacci Heaps March 3, 2015 35 / 60

Inserting 6

6 11

16

21

26

27 28

23

18

13

9 8 7

Stella Lau Fibonacci Heaps March 3, 2015 36 / 60

Inserting 5

5 11

16

21

26

27 28

23

18

13

9 8 7 6

Stella Lau Fibonacci Heaps March 3, 2015 37 / 60

Extracting min: 5

6

7 11

16

21

26

27 28

23

18

13

8

9

Stella Lau Fibonacci Heaps March 3, 2015 38 / 60

Cutting 9

−1 6

7 11

16

21

26

27 28

23

18

13

8

Stella Lau Fibonacci Heaps March 3, 2015 39 / 60

Cutting 7

−1 6

11

16

21

26

27 28

23

18

13

8

Stella Lau Fibonacci Heaps March 3, 2015 40 / 60

Inserting 4

4 6

11

16

21

26

27 28

23

18

13

8

Stella Lau Fibonacci Heaps March 3, 2015 41 / 60

Inserting 3

3 6

11

16

21

26

27 28

23

18

13

8

4

Stella Lau Fibonacci Heaps March 3, 2015 42 / 60

Inserting 2

2 6

11

16

21

26

27 28

23

18

13

8

4 3

Stella Lau Fibonacci Heaps March 3, 2015 43 / 60

Inserting 1

1 6

11

16

21

26

27 28

23

18

13

8

4 3 2

Stella Lau Fibonacci Heaps March 3, 2015 44 / 60

Inserting 0

0 6

11

16

21

26

27 28

23

18

13

8

4 3 2 1

Stella Lau Fibonacci Heaps March 3, 2015 45 / 60

Extracting min: 0

1

2 6

11

16

21

26

27 28

23

18

13

8

3

4

Stella Lau Fibonacci Heaps March 3, 2015 46 / 60

Cutting 4

−1 1

2 6

11

16

21

26

27 28

23

18

13

8

3

Stella Lau Fibonacci Heaps March 3, 2015 47 / 60

Cutting 2

−1 1

6

11

16

21

26

27 28

23

18

13

8

3

Stella Lau Fibonacci Heaps March 3, 2015 48 / 60

Cutting 3

−1 1

6

11

16

21

26

27 28

23

18

13

8

Stella Lau Fibonacci Heaps March 3, 2015 49 / 60

Cutting 8

−1 1

6

11

16

21

26

27 28

23

18

13

Stella Lau Fibonacci Heaps March 3, 2015 50 / 60

Cutting 13

−1 1

6

11

16

21

26

27 28

23

18

Stella Lau Fibonacci Heaps March 3, 2015 51 / 60

Cutting 18

−1 1

6

11

16

21

26

27 28

23

Stella Lau Fibonacci Heaps March 3, 2015 52 / 60

Cutting 23

−1 1

6

11

16

21

26

27 28

Stella Lau Fibonacci Heaps March 3, 2015 53 / 60

Cutting 28

−1 1

6

11

16

21

26

27

Stella Lau Fibonacci Heaps March 3, 2015 54 / 60

Cutting 27

−1 1

6

11

16

21

26

Stella Lau Fibonacci Heaps March 3, 2015 55 / 60

Cascading cut 26

−1 26 1

6

11

16

21

Stella Lau Fibonacci Heaps March 3, 2015 56 / 60

Cascading cut 21

−1 21 26 1

6

11

16

Stella Lau Fibonacci Heaps March 3, 2015 57 / 60

Cascading cut 16

−1 16 21 26 1

6

11

Stella Lau Fibonacci Heaps March 3, 2015 58 / 60

Cascading cut 11

−1 11 16 21 26 1

6

Stella Lau Fibonacci Heaps March 3, 2015 59 / 60

Cascading cut 6

−1 6 11 16 21 26 1

Stella Lau Fibonacci Heaps March 3, 2015 60 / 60