Programming Stack. Virendra Singh Indian Institute of Science Bangalore Lecture 7. Courtesy: Prof. Sartaj Sahni. Aug 25,2010

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1 SE-286: Data Structures and Programming g Stack Virendra Singh Indian Institute of Science Bangalore Lecture 7 Courtesy: Prof. Sartaj Sahni 1

Stacks Stacks are a special form of collection with LIFO semantics Two methods int push( Stack s, void *item ); - add item to the top of the stack void *pop( Stack s ); - remove an item

2 Stacks Stacks are a special form of collection with LIFO semantics Two methods int push( Stack s, void *item ); - add item to the top of the stack void *pop( Stack s ); - remove an item from the top of the stack Like a plate stacker Other methods int IsEmpty( Stack s ); /* Return TRUE if empty */ void *Top( Stack s ); /* Return the item at the top, without deleting it */ 2

3 Stacks Linear list. One end is called top. Other end is called bottom. Additions to and removals from the top end only. 3

4 Stack Of Cups top E top F E D D C C bottom B A bottom B A Add a cup to the stack. Remove a cup from new stack. A stack is a LIFOlist. 4

5 Parentheses Matching (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( ) Output pairs (u,v) such that the left parenthesis at position u is matched with the right parenthesis at v. (2,6) (1,13) (15,19) (21,25) (27,31) (0,32) (34,38) (a+b))*((c+d) (( ) (0,4) right parenthesis at 5 has no matching left parenthesis (8,12) left parenthesis at 7 has no matching right parenthesis 5

6 Parentheses Matching scan expression from left to right when a left parenthesis is encountered, add its position to the stack when a right parenthesis is encountered, remove matching position from stack 6

7 Example (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( )

8 Example (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( ) (2,6) (1,13) 8

9 Example (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( ) (2,6) (1,13) (15,19) 9

10 Example (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( ) (2,6) (1,13) (15,19) (21,25) 10

11 Example (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) ) ( ( ( )) ( ) 1 0 (2,6) (1,13) (15,19) (21,25)(27,31) (0,32) and so on 11

12 Towers Of Hanoi/Brahma A B C 64 gold disks to be moved from tower A to tower C each tower operates as a stack 12 cannot place big disk on top of a smaller one

13 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 13

14 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 14

15 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 15

16 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 16

17 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 17

18 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 18

19 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 19

20 Towers Of Hanoi/Brahma A B C 3-disk Towers Of Hanoi/Brahma 7 disk Aug 25,2010 moves SE286@SERC

21 Recursive Solution 1 A B C n>0gold disks to be moved from A to C using B 21 move top n-1 disks from A to B using C

22 Recursive Solution 1 A B C move top disk from A to C 22

23 Recursive Solution A B C move top n-1 disks from B to C using A 23 1

24 Recursive Solution A B C moves(n) = 0 when n = 0 moves(n) = 2*moves(n-1) + 1 = 2 n 24-1 when n > 0 1

25 Towers Of Hanoi/Brahma moves(64) = 1.8 * (approximately) Performing 10 9 moves/second, a computer would take about t570 years to complete. At 1 disk move/min, the monks will take about 3.4 * years. 25

26 Chess Story 1 grain of rice on the first square, 2 for next, 4 for next, 8 for next, and so on. Surface area needed exceeds surface area of earth. 26

27 Chess Story 1 penny for the first square, 2 for next, 4 for next, 8 for next, and so on. $3.6 * (federal budget ~ $2 * ). 27

28 Switch Box Routing Routing region

29 Routing for pins 1-3 and is confined to lower left region. Routing A 2-pin Net Routing for pins 5 through 16 is confined to upper right region. 29

30 (u,v), u<v is a 2-pin net. u is start pin. v is end pin. Routing A 2-pin Net Examine pins in clockwise order beginn- ing with pin 1. 30

31 Routing A 2-pin Net Start pin => push onto stack. End pin => start pin must be at top of stack

32 Method Invocation And Return public void a() { ; b(); } public void b() { ; c(); } public void c() { ; d(); } public void d() { ; e(); } public void e() { ; c(); } return address in d() return address in c() return address in e() return address in d() return address in c() return address in b() return address in a() 32

33 Try-Throw-Catch When you enter a try block,,push the address of this block on a stack. When an exception is thrown,,pop pthe try block that is at the top of the stack (if the stack is empty, terminate). If the popped try block has no matching catch block, go back to the preceding step. If the popped try block has a matching catch block, execute the matching catch block. 33

34 Rat In A Maze 34

35 Rat In A Maze Move order is: right, down, left, up Aug Block 25,2010 positions to SE286@SERC avoid revisit. 35

36 Rat In A Maze Move order is: right, down, left, up Block positions to avoid revisit. 36

37 Rat In A Maze Move backward until we reach a square from which h 37 a forward move is possible.

38 Rat In A Maze Move down. 38

39 Rat In A Maze Move lf left. 39

40 Rat In A Maze Move down. 40

41 Rat In A Maze Move backward until we reach a square from which h 41 a forward move is possible.

42 Rat In A Maze Move backward until we reach a square from which a forward move is possible. 42 Move downward.

43 Rat In A Maze Move right. Aug 25,2010 Backtrack. SE286@SERC 43

44 Rat In A Maze Move downward. d 44

45 Rat In A Maze Move right. 45

46 Rat In A Maze Move one down and then right. 46

47 Rat In A Maze Move one up and then right. 47

48 Rat In A Maze Move down to exit and eat cheese. Path from maze entry to current position operates as 48 a stack.

Lesson Plan for Teachers

Grade level recommendation: 8 th grade Lesson Plan for Teachers Learning goals: Problem solving Reasoning Basic algebra Exponents Recursive equations Explicit equations NCTM standards correlation: http://www.nctm.org/standards/