Data Structures and Programming 資料結構與程式設計. Topic 6 Stacks. Stacks. Stack of Cups. Stacks. top. top. bottom. bottom

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1 Data Structures and Programming 資料結構與程式設計 Topic 6 Stacks 課程編號 : EE 30 科目名稱 : 資料結構與程式設計授課教師 : 黃鼎偉時間地點 : 一 678 電機二館 229 Stacks Linear list. One end is called top. Other end is called bottom. Additions to and removals from the top end only. 2 Stack of Cups top bottom E D C B A top bottom Add a cup to the stack. Remove a cup from new stack. A stack is a LIFO (last-in first-out) list. F E D C B A Stacks template<class T> 2 class stack 3 { 4 public: 5 virtual ~stack() {} 6 virtual bool empty() const = 0; 7 virtual int size() const = 0; 8 virtual T& top() = 0; 9 virtual void pop() = 0; 0 virtual void push(const T& theelement) = 0; }; 3 stack.h 4

2 Derive From A Linear List Class arraylist chain Derive From arraylist stack top is either left end or right end of linear list empty() => arraylist::empty() O() time size() => arraylist::size() O() time top() => get(0) or get(size() ) O() time 5 6 Derive From arraylist Derive From arraylist when top is left end of linear list push(theelement) => insert(0, theelement) O(size) time pop() => erase(0) O(size) time when top is right end of linear list push(theelement) => insert(size(), theelement) O() time pop() => erase(size() ) O() time use right end of list as top of stack 7 8

3 Derive From chain firstnode Derive From chain firstnode NULL stack top is either left end or right end of linear list empty() => chain::empty() O() time size() => chain::size() O() time NULL when top is left end of linear list top() => get(0) O() time push(theelement) => insert(0, theelement) O() time pop() => erase(0) O() time 9 0 Derive From chain firstnode null when top is right end of linear list top() => get(size() ) O(size) time push(theelement) => insert(size(), theelement) O(size) time pop() => erase(size() ) O(size) time use left end of list as top of stack Derive From arraylist and its Constructor template<class T> 2 class derivedarraystack : 3 private arraylist<t>, 4 public stack<t> 5 { 6 public: 7 // code for stack methods comes here 8 9 }; 0 derivedarraystack(int initialcapacity = 0) : arraylist<t> (initialcapacity) {} derivedarraystack.h 2

4 empty() and size() bool empty() const 2 { 3 return arraylist<t>::empty(); 4 } 5 6 int size() const 7 { 8 return arraylist<t>::size(); 9 } top() T& top() 2 { 3 if (arraylist<t>::empty()) 4 throw stackempty(); 5 return get(arraylist<t>::size() ); 6 } derivedarraystack.h 3 derivedarraystack.h 4 push(theelement) void push(const T& theelement) 2 { 3 insert(arraylist<t>::size(), theelement); 4 } pop() void pop() 2 { 3 if (arraylist<t>::empty()) 4 throw stackempty(); 5 erase(arraylist<t>::size() ); 6 } derivedarraystack.h 5 derivedarraystack.h 6

5 Evaluation Merits of deriving from arraylist Code for derived class is quite simple and easy to develop. Code is expected to require little debugging. Code for other stack implementations such as a linked implementation are easily obtained. Just replace private arraylist<t> with private chain<t> For efficiency reasons we must also make changes to use the left end of the list as the stack top rather than the right end. Demerits Unnecessary work is done by the code. top() verifies that the stack is not empty before get is invoked. The index check done by get is, therefore, not needed. insert(size(), theelement) does an index check and a copy_backward. Neither is needed. pop() verifies that the stack is not empty before erase is invoked. erase does an index check and a copy. Neither is needed. So the derived code runs slower than necessary. 7 8 Evaluation Code developed from scratch will run faster but will take more time (cost) to develop. Tradeoff between software development cost and performance. Tradeoff between time to market and performance. Could develop easy code first and later refine it to improve performance. A Faster pop() if (arraylist<t>::empty()) 2 throw stackempty(); 3 erase(arraylist<t>::size() ); try 2 { erase(arraylist<t>::size() );} 3 catch (illegalindex) 4 {throw stackempty();} 9 derivedarraystack.h vs derivedarraystackwithcatch.h 20

6 Code From Scratch arraystack Use a D array stack whose data type is T. same as using array element in arraylist Use an int variable stacktop. Stack elements are in stack[0:stacktop]. Top element is in stack[stacktop]. Bottom element is in stack[0]. Stack is empty iff stacktop =. Number of elements in stack is stacktop +. Class arraystack template class<t> 2 class arraystack : public stack<t> 3 { 4 public: 5 // public methods come here 6 private: 7 int stacktop; // current top of stack 8 int arraylength; // stack capacity 9 T *stack; // element array 0 }; 2 arraystack.h 22 Constructor 2 template<class T> 3 arraystack<t>::arraystack(int initialcapacity) 4 { 5 // Constructor. 6 if (initialcapacity < ) 7 { 8 // code to throw an exception comes here 9 } 0 arraylength = initialcapacity; stack = new T[arrayLength]; 2 stacktop = ; 3 } push( ) template<class T> 2 void arraystack<t>::push(const T& theelement) 3 { 4 // Add theelement to stack. 5 if (stacktop == arraylength ) 6 { 7 // code to double capacity coms here 8 } 9 // add at stack top 0 stack[++stacktop] = theelement; } top arraystack.h 23 arraystack.h 24

7 pop() void pop() 2 { 3 if (stacktop == ) 4 throw stackempty(); 5 stack[stacktop ].~T(); // destructor for T 6 } top Code From Scratch linkedstack 4 template<class T> 5 class linkedstack : public stack<t> 6 { 7 public: 8 linkedstack(int initialcapacity = 0) 9 {stacktop = NULL; stacksize = 0;} 20 ~linkedstack(); 2 bool empty() const 22 {return stacksize == 0;} 23 int size() const 24 {return stacksize;} 25 T& top() 26 { 27 if (stacksize == 0) 28 throw stackempty(); 29 return stacktop >element; 30 } 3 void pop(); 32 void push(const T& theelement) 33 { 34 stacktop = new chainnode<t>(theelement, stacktop); 35 stacksize++; 36 } 37 private: 38 chainnode<t>* stacktop; // pointer to stack top 39 int stacksize; // number of elements in stack 40 }; arraystack.h 25 linkedstack.h 26 Performance 50,000,000 pop, push, and peek operations initial capacity Class default 50,000,000 arraystack 2.7s.5s STL stack 5.6s - derivedarraystack 7.5s 6.3s linkedstack 40.5s 40.5s derivedlinkedstack 4.0s 4.0s Applications Parentheses Matching Towers of Hanoi/Brahma Rearranging Railroad Cars Routing A 2-pin Net Method Invocation And Return Try-Throw-Catch Chess Story Eight Queens Puzzle Knight s Tour Eight Puzzle 27 28

8 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) (,3) (5,9) (2,25) (27,3) (0,32) (34,38) (a+b))*((c+d) (0,4) right parenthesis at 5 has no matching left parenthesis (8,2) left parenthesis at 7 has no matching right parenthesis 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 parenthesismatching.cpp 29 parenthesismatching.cpp 30 Example Towers of Hanoi/Brahma (((a+b)*c+d-e)/(f+g)-(h+j)*(k-l))/(m-n) 34 (2,6) (,3) (5,9) (2,25) (27,3) (0,32) and so on 64 gold disks to be moved from tower A to tower C each tower operates as a stack cannot place big disk on top of a smaller one parenthesismatching.cpp

9 Towers of Hanoi/Brahma Towers of Hanoi/Brahma disk Towers of Hanoi/Brahma 2 3-disk Towers of Hanoi/Brahma 3 hanoiusingstacks.cpp 33 hanoiusingstacks.cpp 34 Towers of Hanoi/Brahma Towers of Hanoi/Brahma disk Towers of Hanoi/Brahma disk Towers of Hanoi/Brahma hanoiusingstacks.cpp 35 hanoiusingstacks.cpp 36

10 Towers of Hanoi/Brahma Towers of Hanoi/Brahma 3-disk Towers of Hanoi/Brahma disk Towers of Hanoi/Brahma 2 hanoiusingstacks.cpp 37 hanoiusingstacks.cpp 38 Towers of Hanoi/Brahma Towers of Hanoi/Brahma 3 3-disk Towers of Hanoi/Brahma 2 3-disk Towers of Hanoi/Brahma disk moveshanoiusingstacks.cpp hanoiusingstacks.cpp 39 40

11 Recursive Solution Recursive Solution n > 0 gold disks to be moved from A to C using B move top disk from A to C move top n disks from A to B using C 4 hanoirecursive.cpp 42 Recursive Solution Recursive Solution move top n disks from B to C using A moves(n) = 0 when n = 0 moves(n) = 2*moves(n ) + = 2 n when n > 0 hanoirecursive.cpp 43 44

12 Towers of Hanoi/Brahma Rearranging Railroad Cars moves(64) =.8 * 0 9 (approximately) Performing 0 9 moves/second, a computer would take about 570 years to complete. At disk move/min, the monks will take about 3.4 * 0 3 years. [ ] Input track H H H3 9 Output track [ ] Input track Output track H H2 H3 hanoirecursive.cpp 45 railroadwithstacks.cpp 46 Switch Box Routing Routing region Routing A 2-pin Net Routing for pins -3 and 8-40 is confined to lower left region Routing for pins 5 through6 is confined to upper right region switchbox.cpp 47 switchbox.cpp 48

13 Routing A 2-pin Net Routing A 2-pin Net (u,v), u<v is a 2-pin net. u is start pin. v is end pin Examine pins in clock-wise order beginning with pin Start pin => push onto stack. End pin => start pin must be at top of stack switchbox.cpp 49 switchbox.cpp 50 Move order is: right, down, left, up Block positions to avoid revisit. maze.cpp 5 52

14 Move order is: right, down, left, up Move backward until we reach a square from which a forward move is possible. Block positions to avoid revisit Move down. Move left. maze.cpp 55 maze.cpp 56

15 Move down. Move backward until we reach a square from which a forward move is possible. maze.cpp 57 maze.cpp 58 Move backward until we reach a square from which a forward move is possible. Move right. Backtrack. Move downward. maze.cpp 59 maze.cpp 60

16 Move downward. Move right. maze.cpp 6 maze.cpp 62 Move one down and then right. Move one up and then right. maze.cpp 63 maze.cpp 64

17 Method Invocation And Return Move down to exit and eat cheese. Path from maze entry to current position operates public void a() { ; b(); } public void b() { ; c(); } public void c() { ; d(); } public void d() { ; e(); } return address in d() return address in c() return address in e() return address in d() return address in c() return address in b() public void e() { ; c(); } return address in a() as a stack. maze.cpp Try-Throw-Catch When you enter a try block, push the address of this block on a stack. When an exception is thrown, pop the 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. 67 Chess Story 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. 68

Chess Story penny for the first square, 2 for next, 4 for next, 8 for next, and so on. $3.

Eight Queens Puzzle The eight queens puzzle is the problem of placing eight chess queens on an 8 8

The queens must be placed in such a way that no two queens attack each other.

69 70 Knight s Tour The knight's tour is a mathematical problem involving a knight on a chessboard.

18 Chess Story penny for the first square, 2 for next, 4 for next, 8 for next, and so on. $3.6 * 0 7 (federal budget ~ $2 * 0 2 ). Eight Queens Puzzle The eight queens puzzle is the problem of placing eight chess queens on an 8 8 chessboard so that none of them can capture any other using the standard chess queen's moves. The queens must be placed in such a way that no two queens attack each other. Using stack to store the recursive steps of moves Knight s Tour The knight's tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once. A knight's tour is called a closed tour if the knight ends on a square attacking the square from which it began (so that it may tour the board again immediately with the same path). Otherwise the tour is open. Eight Puzzle Using Stack to store the best moves. Using stack to store the recursive steps of moves 7 72

Data Structures and Programming 資料結構與程式設計. Topic 3 Linear Lists Array. AbstractDataType linearlist. Linear List - Array Representation

Data Structures and Programming 資料結構與程式設計 Topic 3 Linear Lists Array 課程編號 :901 31900 EE 3011 科目名稱 : 資料結構與程式設計授課教師 : 黃鼎偉時間地點 : 一 678 電機二館 229 Abstract Data Type linearlist Abstract Data Type (ADT) AbstractDataType