1. Doubly-Linked Lists Same basic functions operate on list Each node has a forward and backward link: What advantages does a doubly-linked list offer? 88 NULL 42109 NULL head_ptr

2. Doubly-Linked Lists Same basic functions operate on list Each node has a forward and backward link: What advantages does a doubly-linked list offer? Cursor can move forwards and backwards in list. 88 NULL 42109 NULL head_ptr

4. Stacks and Queues Kruse and Ryba Ch 2 and 3

5. What is a stack? It is an ordered group of homogeneous items of elements. Elements are added to and removed from the top of the stack (the most recently added items are at the top of the stack). The last element to be added is the first to be removed (LIFO: Last In, First Out).

6. Stack Specification Definitions: (provided by the user) –MAX_ITEMS: Max number of items that might be on the stack –ItemType: Data type of the items on the stack Operations –MakeEmpty –Boolean IsEmpty –Boolean IsFull –Push (ItemType newItem) –Pop (ItemType& item) (or pop and top)

7. Push (ItemType newItem) Function: Adds newItem to the top of the stack. Preconditions: Stack has been initialized and is not full. Postconditions: newItem is at the top of the stack.

8. Pop (ItemType& item) Function: Removes topItem from stack and returns it in item. Preconditions: Stack has been initialized and is not empty. Postconditions: Top element has been removed from stack and item is a copy of the removed element.

10. Stack Implementation #include "ItemType.h" // Must be provided by the user of the class // Contains definitions for MAX_ITEMS and ItemType class StackType { public: StackType(); void MakeEmpty(); bool IsEmpty() const; bool IsFull() const; void Push(ItemType); void Pop(ItemType&); private: int top; ItemType items[MAX_ITEMS]; };

11. Stack Implementation (cont.) StackType::StackType() { top = -1; } void StackType::MakeEmpty() { top = -1; } bool StackType::IsEmpty() const { return (top == -1); }

12. Stack Implementation (cont.) bool StackType::IsFull() const { return (top == MAX_ITEMS-1); } void StackType::Push(ItemType newItem) { top++; items[top] = newItem; } void StackType::Pop(ItemType& item) { item = items[top]; top--; }

13. Stack overflow The condition resulting from trying to push an element onto a full stack. if(!stack.IsFull()) stack.Push(item); Stack underflow The condition resulting from trying to pop an empty stack. if(!stack.IsEmpty()) stack.Pop(item);

14. Implementing stacks using templates Templates allow the compiler to generate multiple versions of a class type or a function by allowing parameterized types.

15. Implementing stacks using templates template class StackType { public: StackType(); void MakeEmpty(); bool IsEmpty() const; bool IsFull() const; void Push(ItemType); void Pop(ItemType&); private: int top; ItemType items[MAX_ITEMS]; }; (cont.)

16. Example using templates // Client code StackType myStack; StackType yourStack; StackType anotherStack; myStack.Push(35); yourStack.Push(584.39); The compiler generates distinct class types and gives its own internal name to each of the types.

17. Function templates The definitions of the member functions must be rewritten as function templates. template StackType ::StackType() { top = -1; } template void StackType ::MakeEmpty() { top = -1; }

18. Function templates (cont.) template bool StackType ::IsEmpty() const { return (top == -1); } template bool StackType ::IsFull() const { return (top == MAX_ITEMS-1); } template void StackType ::Push(ItemType newItem) { top++; items[top] = newItem; }

19. Function templates (cont.) template void StackType ::Pop(ItemType& item) { item = items[top]; top--; }

20. Implementing stacks using dynamic array allocation template class StackType { public: StackType(int); ~StackType(); void MakeEmpty(); bool IsEmpty() const; bool IsFull() const; void Push(ItemType); void Pop(ItemType&); private: int top; int maxStack; ItemType *items; };

21. Implementing stacks using dynamic array allocation (cont.) template StackType ::StackType(int max) { maxStack = max; top = -1; items = new ItemType[max]; } template StackType ::~StackType() { delete [ ] items; }

22. Example: postfix expressions Postfix notation is another way of writing arithmetic expressions. In postfix notation, the operator is written after the two operands. infix: 2+5 postfix: 2 5 + Expressions are evaluated from left to right. Precedence rules and parentheses are never needed!!

23. Example: postfix expressions (cont.)

24. Postfix expressions: Algorithm using stacks (cont.)

25. Postfix expressions: Algorithm using stacks WHILE more input items exist Get an item IF item is an operand stack.Push(item) ELSE stack.Pop(operand2) stack.Pop(operand1) Compute result stack.Push(result) stack.Pop(result)

26. Write the body for a function that replaces each copy of an item in a stack with another item. Use the following specification. (this function is a client program). ReplaceItem(StackType& stack, ItemType oldItem, ItemType newItem) Function: Replaces all occurrences of oldItem with newItem. Precondition: stack has been initialized. Postconditions: Each occurrence of oldItem in stack has been replaced by newItem. (You may use any of the member functions of the StackType, but you may not assume any knowledge of how the stack is implemented).

27. { ItemType item; StackType tempStack; while (!Stack.IsEmpty()) { Stack.Pop(item); if (item==oldItem) tempStack.Push(newItem); else tempStack.Push(item); } while (!tempStack.IsEmpty()) { tempStack.Pop(item); Stack.Push(item); } 1 2 3 3 5 1 1 5 3 Stack tempStack oldItem = 2 newItem = 5

28. What is a queue? It is an ordered group of homogeneous items of elements. Queues have two ends: –Elements are added at one end. –Elements are removed from the other end. The element added first is also removed first (FIFO: First In, First Out). queue elements enter no changes of order elements exit 2341 tailhead

29. Queue Specification Definitions: (provided by the user) –MAX_ITEMS: Max number of items that might be on the queue –ItemType: Data type of the items on the queue Operations –MakeEmpty –Boolean IsEmpty –Boolean IsFull –Enqueue (ItemType newItem) –Dequeue (ItemType& item) (serve and retrieve)

30. Enqueue (ItemType newItem) Function: Adds newItem to the rear of the queue. Preconditions: Queue has been initialized and is not full. Postconditions: newItem is at rear of queue.

31. Dequeue (ItemType& item) Function: Removes front item from queue and returns it in item. Preconditions: Queue has been initialized and is not empty. Postconditions: Front element has been removed from queue and item is a copy of removed element.

32. Implementation issues Implement the queue as a circular structure. How do we know if a queue is full or empty? Initialization of front and rear. Testing for a full or empty queue.

35. Make front point to the element preceding the front element in the queue (one memory location will be wasted).

36. Initialize front and rear

37. Queue is empty now!! rear == front

38. Queue Implementation template class QueueType { public: QueueType(int); QueueType(); ~QueueType(); void MakeEmpty(); bool IsEmpty() const; bool IsFull() const; void Enqueue(ItemType); void Dequeue(ItemType&); private: int front; int rear; ItemType* items; int maxQue; };

39. Queue Implementation (cont.) template QueueType ::QueueType(int max) { maxQue = max + 1; front = maxQue - 1; rear = maxQue - 1; items = new ItemType[maxQue]; }

40. Queue Implementation (cont.) template QueueType ::~QueueType() { delete [] items; }

41. Queue Implementation (cont.) template void QueueType :: MakeEmpty() { front = maxQue - 1; rear = maxQue - 1; }

42. Queue Implementation (cont.) template bool QueueType ::IsEmpty() const { return (rear == front); } template bool QueueType ::IsFull() const { return ( (rear + 1) % maxQue == front); }

43. Queue Implementation (cont.) template void QueueType ::Enqueue (ItemType newItem) { rear = (rear + 1) % maxQue; items[rear] = newItem; }

44. Queue Implementation (cont.) template void QueueType ::Dequeue (ItemType& item) { front = (front + 1) % maxQue; item = items[front]; }

45. Queue overflow The condition resulting from trying to add an element onto a full queue. if(!q.IsFull()) q.Enqueue(item);

46. Queue underflow The condition resulting from trying to remove an element from an empty queue. if(!q.IsEmpty()) q.Dequeue(item);

47. Example: recognizing palindromes A palindrome is a string that reads the same forward and backward. Able was I ere I saw Elba We will read the line of text into both a stack and a queue. Compare the contents of the stack and the queue character-by-character to see if they would produce the same string of characters.

48. Example: recognizing palindromes

49. #include #include "stack.h" #include "queue.h“ int main() { StackType s; QueType q; char ch; char sItem, qItem; int mismatches = 0; cout << "Enter string: " << endl; while(cin.peek() != '\\n') { cin >> ch; if(isalpha(ch)) { if(!s.IsFull()) s.Push(toupper(ch)); if(!q.IsFull()) q.Enqueue(toupper(ch)); }

50. while( (!q.IsEmpty()) && (!s.IsEmpty()) ) { s.Pop(sItem); q.Dequeue(qItem); if(sItem != qItem) ++mismatches; } if (mismatches == 0) cout << "That is a palindrome" << endl; else cout << That is not a palindrome" << endl; return 0; } Example: recognizing palindromes

51. Case Study: Simulation Queuing System: consists of servers and queues of objects to be served. Simulation: a program that determines how long items must wait in line before being served.

52. Case Study: Simulation (cont.) Inputs to the simulation: (1) the length of the simulation (2) the average transaction time (3) the number of servers (4) the average time between job arrivals

53. Case Study: Simulation (cont.) Parameters the simulation must vary: (1) number of servers (2) time between arrivals of items Output of simulation: average wait time.