Data Structures And Algorithms

Transcription

1 Data Structures And Algorithms Stacks Eng. Anis Nazer First Semester

2 Stack An Abstract data type (ADT) Accessed only on one end Similar to a stack of dishes you can add/remove on top of stack only last dish added is the first dish removed Last in first out (LIFO)

3 Stack Operations: clear(): remove all elements isempty(): check if the stack is empty push(): add an element to the stack : remove an element from the stack topel(): get the value of the top element without removing it from the stack

4 Empty stack push(5) push(13) push(7) push(19) Stack Example

5 Stack Example Empty stack push(5) push(13) push(7) push(19) 5

6 Stack Example Empty stack push(5) push(13) push(7) push(19) 13 5

7 Stack Example Empty stack push(5) push(13) push(7) push(19) 5

8 Stack Example Empty stack push(5) push(13) push(7) push(19) 7 5

9 Stack Example Empty stack push(5) push(13) push(7) push(19)

10 Stack Example Empty stack push(5) push(13) push(7) push(19) 7 5

11 Stack Example Empty stack push(5) push(13) push(7) push(19) 5

12 Stack Application delimiter matching: an expression contains ( ), { }, [ ] must be matched for correct syntax

13 Stack Application Algorithm: read character while not end of string if character is "(", "{", or "[" push character else if character ")", "}", or "]" c = pop if character does not matches c failure read next character if stack is empty success else failure

14 Example s = t[ 5 ] + u / ( v * ( w + y ) z);

15 Adding Big integers Example: R carry 0 S1 S2 SUM

16 Algorithm We need three stacks: S1, S2, SUM push digits of N1 into S1, Most significant digit first push digits of N2 into S2, Most significant digit first carry = 0 while S1 is not empty or S2 is not empty { R = S1. + S2. + carry if R >= 10 carry = 1 R = R%10 else carry = 0 SUM.push(R) } if carry == 1 push carry while SUM is not empty display SUM.

17 Stack implementation a linked list can be easily used as a stack push() is addtohead() is deletefromhead()

18 LinkedList as a Stack class LLStack : protected LinkedList { public: void push(int d); int ; bool isempty(); void clear(); int topel(); };

19 LinkedList as a Stack push(): void LLStack::push(int d) { addtohead(d); }

20 LinkedList as a Stack : int LLStack:: { return deletefromhead(); }

21 LinkedList as a Stack isempty(): bool LLStack::isEmpty() { return LinkedList::isEmpty(); }

22 LinkedList as a Stack clear(): void LLStack::clear() { while (!isempty()) { ; } }

23 LinkedList as a Stack topel(): int LLStack::topEl() { int d = ; push(d); return d; }

24 LinkedList as a Stack What about the constructor and destructor they are provided by the base class they are called automatically when you create an object of type LLStack, the constructor of LinkedList is called automatically same thing for the destructor

25 Another stack Implementation A stack can be also implemented using an array a variable top is the index of the top of stack

26 Stack using an array Empty stack A[0] A[1] A[2] A[3] A[4] top = 1

27 Stack using an array push(5) A[0] A[1] A[2] A[3] A[4] top = 0

28 Stack using an array push(13) A[0] A[1] A[2] A[3] A[4] top = 1

29 Stack using an array A[0] A[1] A[2] A[3] A[4] top = 0

30 Stack using an array push(7) A[0] A[1] A[2] A[3] A[4] top = 1

31 Stack using an array push(19) A[0] A[1] A[2] A[3] A[4] top = 2

32 Stack using an array A[0] A[1] A[2] A[3] A[4] top = 1

33 Stack using an array A[0] A[1] A[2] A[3] A[4] top = 0

34 implementation using Array class arraystack { public: arraystack(int s ); ~arraystack(); void push(int d); int ; void clear(); bool isempty(); int topel(); private: int *A; int top; };

35 implementation using Array constructor and destructor arraystack::arraystack(int s = 100 ) { top = 1; if ( s <= 0 ) s = 100; A = new int[s]; } arraystack::~arraystack() { delete [] A; }

36 implementation using Array push() void arraystack::push(int d) { // careful if stack is full... top++; A[top] = d; }

37 implementation using Array int arraystack:: { // careful if stack is empty... int d = A[top]; top ; return d; }

38 implementation using Array clear() void arraystack::clear() { top = 1; }

39 implementation using Array isempty() bool arraystack::isempty() { if ( top < 0 ) return true; else return false; }

40 implementation using Array topel() int arraystack::topel() { return A[top]; }

41 Array Vs LinkedList implementations Stack using a LinkedList: push(),, topel(), isempty() clear() O(n) Stack using an Array: O(1) push(),, topel(), isempty(), clear() disadvantage: O(1) stack size should be known beforehand, push in a full stack is O(n)

42 Stack Application Delimiter matching Adding Big integers saving function variables in function calls Others... Search for other applications where a stack is used