Stacks and Queues

2 struct Node{ double data; Node* next; }; class List { public: List(); // constructor List(const List& list); // copy constructor ~List(); // destructor List& operator=(const List& list); // assignment operator bool empty() const; // boolean function void addHead(double x); // add to the head double deleteHead(); // delete the head and get the head element // List& rest(); // get the rest of the list with the head removed // double headElement() const; // get the head element void addEnd(double x); // add to the end double deleteEnd(); // delete the end and get the end element // double endElement(); // get the element at the end bool searchNode(double x); // search for a given x void insertNode(double x); // insert x in a sorted list void deleteNode(double x); // delete x in a sorted list … void print() const; // output int length() const; // count the number of elements private: Node* head; }; More complete list ADT

3 Stack Overview * Stack ADT * Basic operations of stack n Pushing, popping etc. * Implementations of stacks using n array n linked list

4 Stack * A stack is a list in which insertion and deletion take place at the same end n This end is called top n The other end is called bottom * Stacks are known as LIFO (Last In, First Out) lists. n The last element inserted will be the first to be retrieved

5 Push and Pop * Primary operations: Push and Pop * Push n Add an element to the top of the stack * Pop n Remove the element at the top of the stack top empty stack A top push an element top push another A B top pop A

6 Implementation of Stacks * Any list implementation could be used to implement a stack n Arrays (static: the size of stack is given initially) n Linked lists (dynamic: never become full) * We will explore implementations based on array and linked list

7 class Stack { public: Stack(); // constructor Stack(const Stack& stack); // copy constructor ~Stack(); // destructor bool empty() const; void push(const double x); double pop(); // change the stack double top() const; // keep the stack unchanged // bool full(); // optional // void print() const; private: … }; Stack ADT update, ‘logical’ constructor/destructor, composition/decomposition ‘physical’ constructor/destructor Compare with List, see that it’s ‘operations’ that define the type! inspection, access

8 Using Stack int main(void) { Stack stack; stack.push(5.0); stack.push(6.5); stack.push(-3.0); stack.push(-8.0); stack.print(); cout << "Top: " << stack.top() << endl; stack.pop(); cout << "Top: " << stack.top() << endl; while (!stack.empty()) stack.pop(); stack.print(); return 0; } result

9 struct Node{ public: double data; Node* next; }; class Stack { public: Stack(); // constructor Stack(const Stack& stack); // copy constructor ~Stack(); // destructor bool empty() const; void push(const double x); double pop(); // change the stack bool full(); // unnecessary for linked lists double top() const; // keep the stack unchanged void print() const; private: Node* top; }; Stack using linked lists

10 void List::addHead(int newdata){ Nodeptr newPtr = new Node; newPtr->data = newdata; newPtr->next = head; head = newPtr; } void Stack::push(double x){ Node* newPtr = new Node; newPtr->data = x; newPtr->next = top; top = newPtr; } From ‘addHead’ to ‘push’ Push (addHead), Pop (deleteHead)

11 Implementation based on ‘existing’ linked lists * Optional to learn * Good to see that we may ‘re-use’ linked lists

12 * Now let’s implement a stack based on a linked list  To make the best out of the code of List, we implement Stack by inheriting List To let Stack access private member head, we make Stack as a friend of List class List { public: List() { head = NULL; }// constructor ~List();// destructor bool empty() { return head == NULL; } Node* insertNode(int index, double x); int deleteNode(double x); int searchNode(double x); void printList(void); private: Node* head; friend class Stack; };

13 class Stack : public List { public: Stack() {} ~Stack() {} double top() { if (head == NULL) { cout << "Error: the stack is empty." << endl; return -1; } else return head->data; } void push(const double x) { InsertNode(0, x); } double pop() { if (head == NULL) { cout << "Error: the stack is empty." << endl; return -1; } else { double val = head->data; DeleteNode(val); return val; } void printStack() { printList(); } }; Note: the stack implementation based on a linked list will never be full. from List

14 Stack using arrays class Stack { public: Stack(int size = 10);// constructor ~Stack() { delete [] values; }// destructor bool empty() { return top == -1; } void push(const double x); double pop(); bool full() { return top == maxTop; } double top(); void print(); private: int maxTop;// max stack size = size - 1 int top;// current top of stack double* values;// element array };

15  Attributes of Stack maxTop : the max size of stack top : the index of the top element of stack values : point to an array which stores elements of stack  Operations of Stack empty : return true if stack is empty, return false otherwise full : return true if stack is full, return false otherwise top : return the element at the top of stack push : add an element to the top of stack pop : delete the element at the top of stack print : print all the data in the stack

16 Allocate a stack array of size. By default, size = 10. Initially top is set to -1. It means the stack is empty. When the stack is full, top will have its maximum value, i.e. size – 1. Stack::Stack(int size /*= 10*/) { values=new double[size]; top=-1; maxTop=size - 1; } Although the constructor dynamically allocates the stack array, the stack is still static. The size is fixed after the initialization. Stack constructor

17 * void push(const double x); n Push an element onto the stack n Note top always represents the index of the top element. After pushing an element, increment top. void Stack::push(const double x) { if (full()) // if stack is full, print error cout << "Error: the stack is full." << endl; else values[++top] = x; }

18 * double pop() n Pop and return the element at the top of the stack n Don’t forgot to decrement top double Stack::pop() { if (empty()) { //if stack is empty, print error cout << "Error: the stack is empty." << endl; return -1; } else { return values[top--]; }

19 * double top() n Return the top element of the stack n Unlike p op, this function does not remove the top element double Stack::top() { if (empty()) { cout << "Error: the stack is empty." << endl; return -1; } else return values[top]; }

20 * void print() n Print all the elements void Stack::print() { cout "; for (int i = top; i >= 0; i--) cout << "\t|\t" << values[i] << "\t|" << endl; cout << "\t| |" << endl; }

21 Stack Application: Balancing Symbols * To check that every right brace, bracket, and parentheses must correspond to its left counterpart n e.g. [( )] is legal, but [( ] ) is illegal * How? n Need to memorize n Use a counter, several counters, each for a type of parenthesis …

22 Balancing Symbols using a stack * Algorithm (1) Make an empty stack. (2) Read characters until end of file i. If the character is an opening symbol, push it onto the stack ii. If it is a closing symbol, then if the stack is empty, report an error iii. Otherwise, pop the stack. If the symbol popped is not the corresponding opening symbol, then report an error (3) At end of file, if the stack is not empty, report an error

23 Stack Application: postfix, infix expressions and calculator * Postfix expressions n a b c * + d e * f + g * + n Operands are in a stack * Convert infix to postfix n a+b*c+(d*e+f)*g  a b c * + d e * f + g * + n Operators are in a stack * Calculator n Adding more operators …

24 Stack Application: function calls and recursion * Take the example of factorial! And run it. #include using namespace std; int fac(int n){ int product; if(n <= 1) product = 1; else product = n * fac(n-1); return product; } void main(){ int number; cout << "Enter a positive integer : " << endl;; cin >> number; cout << fac(number) << endl; }

25 Stack Application: function calls and recursion * Take the example of factorial! And run it. #include using namespace std; int fac(int n){ int product; if(n <= 1) product = 1; else product = n * fac(n-1); return product; } void main(){ int number; cout << "Enter a positive integer : " << endl;; cin >> number; cout << fac(number) << endl; }

26 Assume the number typed is 3. fac(3): has the final returned value 6 3<=1 ? No. product 3 = 3*fac(2) product 3 =3*2=6, return 6, fac(2): 2<=1 ? No. product 2 = 2*fac(1) product 2 =2*1=2, return 2, fac(1): 1<=1 ? Yes. return 1 Tracing the program …

27 fac(3)prod3=3*fac(2) prod2=2*fac(1)fac(2) fac(1)prod1=1 Call is to ‘push’ and return is to ‘pop’! top

28 Static and dynamic objects * ‘dynamic’ is relative * ‘static variables’ are from a Stack * ‘dynamic variables’ are from a heap (seen later …)

29 Array versus linked list implementations * push, pop, top are all constant-time operations in both array and linked list implementation n For array implementation, the operations are performed in very fast constant time

30 Queue Overview * Queue ADT * Basic operations of queue n Enqueuing, dequeuing etc. * Implementation of queue n Linked list n Array

31 Queue * A queue is also a list. However, insertion is done at one end, while deletion is performed at the other end. * It is “First In, First Out (FIFO)” order. n Like customers standing in a check-out line in a store, the first customer in is the first customer served.

32 Enqueue and Dequeue * Primary queue operations: Enqueue and Dequeue * Like check-out lines in a store, a queue has a front and a rear. * Enqueue – insert an element at the rear of the queue * Dequeue – remove an element from the front of the queue Insert (Enqueue) Remove (Dequeue) rearfront

33 Implementation of Queue * Just as stacks can be implemented as arrays or linked lists, so with queues. * Dynamic queues have the same advantages over static queues as dynamic stacks have over static stacks

34 class Queue { public: Queue(); Queue(Queue& queue); ~Queue(); bool empty(); void enqueue(double x); double dequeue(); void print(void); // bool full(); // optional private: … }; Queue ADT ‘physical’ constructor/destructor ‘logical’ constructor/destructor

35 Using Queue int main(void) { Queue queue; cout << "Enqueue 5 items." << endl; for (int x = 0; x < 5; x++) queue.enqueue(x); cout << "Now attempting to enqueue again..." << endl; queue.enqueue(5); queue.print(); double value; value=queue.dequeue(); cout << "Retrieved element = " << value << endl; queue.print(); queue.enqueue(7); queue.print(); return 0; }

36 Struct Node { double data; Node* next; } class Queue { public: Queue(); Queue(Queue& queue); ~Queue(); bool empty(); void enqueue(double x); double dequeue(); // bool full(); // optional void print(void); private: Node* front;// pointer to front node Node* rear;// pointer to last node int counter;// number of elements }; Queue using linked lists

37 class Queue { public: Queue() {// constructor front = rear = NULL; counter= 0; } ~Queue() {// destructor double value; while (!empty()) dequeue(value); } bool empty() { if (counter) return false; else return true; } void enqueue(double x); double dequeue(); // bool full() {return false;}; void print(void); private: Node* front;// pointer to front node Node* rear;// pointer to last node int counter;// number of elements, not compulsary }; Implementation of some online member functions …

38 Enqueue (addEnd) void Queue::enqueue(double x) { Node* newNode = new Node; newNode->data = x; newNode->next = NULL; if (empty()) { front= newNode; } else { rear->next =newNode; } rear = newNode; counter++; } 8 rear newNode 5 58

39 Dequeue (deleteHead) double Queue::dequeue() { double x; if (empty()) { cout << "Error: the queue is empty." << endl; exit(1); // return false; } else { x = front->data; Node* nextNode = front->next; delete front; front= nextNode; counter--; } return x; } front

40 Printing all the elements void Queue::print() { cout "; Node* currNode=front; for (int i = 0; i < counter; i++) { if (i == 0) cout << "\t"; elsecout << "\t\t"; cout data; if (i != counter - 1) cout << endl; else cout << "\t<-- rear" << endl; currNode=currNode->next; }

41 Queue using Arrays * There are several different algorithms to implement Enqueue and Dequeue * Naïve way n When enqueuing, the front index is always fixed and the rear index moves forward in the array. front rear Enqueue(3) 3 front rear Enqueue(6) 3 6 front rear Enqueue(9) 3 6 9

42 * Naïve way (cont’d) n When dequeuing, the front index is fixed, and the element at the front the queue is removed. Move all the elements after it by one position. (Inefficient!!!) Dequeue() front rear 6 9 Dequeue() front rear 9 rear = -1 front

43 * A better way n When enqueued, the rear index moves forward. n When dequeued, the front index also moves forward by one element XXXXOOOOO (rear) OXXXXOOOO (after 1 dequeue, and 1 enqueue) OOXXXXXOO (after another dequeue, and 2 enqueues) OOOOXXXXX (after 2 more dequeues, and 2 enqueues) (front) The problem here is that the rear index cannot move beyond the last element in the array.

44 Using Circular Arrays * Using a circular array * When an element moves past the end of a circular array, it wraps around to the beginning, e.g. n OOOOO7963  4OOOO7963 (after Enqueue(4)) * How to detect an empty or full queue, using a circular array algorithm? n Use a counter of the number of elements in the queue.

45 class Queue { public: Queue(int size = 10);// constructor Queue(Queue& queue); // not necessary! ~Queue() { delete [] values; }// destructor bool empty(void); void enqueue(double x); // or bool enqueue(); double dequeue(); bool full(); void print(void); private: int front;// front index int rear;// rear index int counter;// number of elements int maxSize;// size of array queue double* values;// element array }; full() is not essential, can be embedded

46  Attributes of Queue front/rear : front/rear index counter : number of elements in the queue maxSize : capacity of the queue values : point to an array which stores elements of the queue  Operations of Queue empty : return true if queue is empty, return false otherwise full : return true if queue is full, return false otherwise enqueue : add an element to the rear of queue dequeue : delete the element at the front of queue print : print all the data

47 Queue constructor * Queue(int size = 10) n Allocate a queue array of size. By default, size = 10. n front is set to 0, pointing to the first element of the array n rear is set to -1. The queue is empty initially. Queue::Queue(int size /* = 10 */) { values=new double[size]; maxSize=size; front=0; rear=-1; counter=0; }

48 Empty & Full  Since we keep track of the number of elements that are actually in the queue: counter, it is easy to check if the queue is empty or full. bool Queue::empty() { if (counter==0)return true; elsereturn false; } bool Queue::full() { if (counter < maxSize)return false; elsereturn true; }

49 Enqueue void Queue::enqueue(double x) { if (full()) { cout << "Error: the queue is full." << endl; exit(1); // return false; } else { // calculate the new rear position (circular) rear = (rear + 1) % maxSize; // insert new item values[rear]= x; // update counter counter++; // return true; } Or ‘bool’ if you want

50 Dequeue double Queue::dequeue() { double x; if (empty()) { cout << "Error: the queue is empty." << endl; exit(1); // return false; } else { // retrieve the front item x= values[front]; // move front front= (front + 1) % maxSize; // update counter counter--; // return true; } return x; }

51 Printing the elements void Queue::print() { cout "; for (int i = 0; i < counter; i++) { if (i == 0) cout << "\t"; elsecout << "\t\t"; cout << values[(front + i) % maxSize]; if (i != counter - 1) cout << endl; else cout << "\t<-- rear" << endl; }

52 Using Queue int main(void) { Queue queue; cout << "Enqueue 5 items." << endl; for (int x = 0; x < 5; x++) queue.enqueue(x); cout << "Now attempting to enqueue again..." << endl; queue.enqueue(5); queue.print(); double value; value=queue.dequeue(); cout << "Retrieved element = " << value << endl; queue.print(); queue.enqueue(7); queue.print(); return 0; }

53 Results Queue implemented using linked list will be never full! based on array based on linked list

54 Queue applications * When jobs are sent to a printer, in order of arrival, a queue. * Customers at ticket counters …