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Chapter 7

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Chapter 7

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  1. Chapter 7 Stacks Data Structures Using C++

  2. Chapter Objectives • Learn about stacks • Examine various stack operations • Learn how to implement a stack as an array • Learn how to implement a stack as a linked list • Discover stack applications • Learn to use a stack to remove recursion • Become aware of the STL class stack Data Structures Using C++

  3. Stacks • Definition: list of homogeneous elements, wherein the addition and deletion of elements occur only at one end, called the top of the stack • Last In First Out (LIFO) data structure • Used to implement function calls • Used to convert recursive algorithms (especially not tail recursive) into nonrecursive algorithms Data Structures Using C++

  4. Various Types of Stacks Data Structures Using C++

  5. LIFO • Last In First Out (LIFO) data structure • Top element of stack is last element to be added to stack • Elements added and removed from one end (top) • Item added last are removed first Data Structures Using C++

  6. Empty Stack Data Structures Using C++

  7. Stack Operations Data Structures Using C++

  8. Basic Operations on a Stack • initializeStack: Initializes the stack to an empty state • destroyStack: Removes all the elements from the stack, leaving the stack empty • isEmptyStack: Checks whether the stack is empty. If empty, it returns true; otherwise, it returns false Data Structures Using C++

  9. Basic Operations on a Stack • isFullStack: Checks whether the stack is full. If full, it returns true; otherwise, it returns false • push: • Add new element to the top of the stack • The input consists of the stack and the new element. • Prior to this operation, the stack must exist and must not be full Data Structures Using C++

  10. Basic Operations on a Stack • top: Returns the top element of the stack. Prior to this operation, the stack must exist and must not be empty. • pop: Removes the top element of the stack. Prior to this operation, the stack must exist and must not be empty. Data Structures Using C++

  11. Example of a Stack Data Structures Using C++

  12. Empty Stack Data Structures Using C++

  13. initializeStack and destroyStack template<class Type> void stackType<Type>::initializeStack() { stackTop = 0; }//end initializeStack template<class Type> void stackType<Type>::destroyStack() { stackTop = 0; }//end destroyStack Data Structures Using C++

  14. emptyStack and fullStack template<class Type> bool stackType<Type>::isEmptyStack() { return(stackTop == 0); }//end isEmptyStack template<class Type> bool stackType<Type>::isFullStack() { return(stackTop == maxStackSize); }//end isFullStack Data Structures Using C++

  15. Push Data Structures Using C++

  16. Push template<class Type> void stackType<Type>::push(const Type& newItem) { if(!isFullStack()) { list[stackTop] = newItem; //add newItem at the top //of the stack stackTop++; //increment stackTop } else cerr<<"Cannot add to a full stack."<<endl; }//end push Data Structures Using C++

  17. Return Top Element template<class Type> Type stackType<Type>::top() { assert(stackTop != 0); //if the stack is empty, //terminate the program return list[stackTop - 1]; //return the element of the //stack indicated by //stackTop - 1 }//end top Data Structures Using C++

  18. Pop template<class Type> void stackType<Type>::pop() { if(!isEmptyStack()) stackTop-; //decrement stackTop else cerr<<"Cannot remove from an empty stack."<<endl; }//end pop Data Structures Using C++

  19. Pop Data Structures Using C++

  20. copyStack template<class Type> void stackType<Type>::copyStack(const stackType<Type>& otherStack) { delete [] list; maxStackSize = otherStack.maxStackSize; stackTop = otherStack.stackTop; list = new Type[maxStackSize]; assert(list != NULL); //copy otherStack into this stack for(int j = 0; j < stackTop; j++) list[j] = otherStack.list[j]; }//end copyStack Data Structures Using C++

  21. Copy Constructor template<class Type> stackType<Type>::stackType(const stackType<Type>& otherStack) { list = NULL; copyStack(otherStack); }//end copy constructor Data Structures Using C++

  22. Overloading the Assignment Operator (=) template<class Type> const stackType<Type>& stackType<Type>::operator= (const stackType<Type>& otherStack) { if(this != &otherStack) //avoid self-copy copyStack(otherStack); return *this; }//end operator= Data Structures Using C++

  23. Time-Complexity of Operations of class stackType Data Structures Using C++

  24. Stack Header File //Header file: myStack.h #ifndef H_StackType #define H_StackType #include <iostream> #include <cassert> using namespace std; //Place the definition of the class template stackType, as given //previously in this chapter, here. //Place the definitions of the member functions, as discussed in //this chapter, here. #endif Data Structures Using C++

  25. Programming Example: Highest GPA Input The program reads an input file consisting of each student’s GPA, followed by the student’s name. Sample data is: 3.8 Lisa 3.6 John 3.9 Susan 3.7 Kathy 3.4 Jason 3.9 David 3.4 Jack Data Structures Using C++

  26. Programming Example: Highest GPA (Algorithm) • Declare the variables. • Open the input file. • If the input file does not exist, exit the program. • Set the output of the floating-point numbers to a fixed decimal format with a decimal point and trailing zeroes. Also, set the precision to two decimal places. • Read the GPA and student name. • highestGPA = GPA; • Initialize the stack. Data Structures Using C++

  27. Programming Example: Highest GPA (Algorithm) • while (not end of file) { 8.1 if (GPA > highestGPA) { 8.1.1 destroyStack(stack); 8.1.2 push(stack, student name); 8.1.3 highestGPA = GPA; } 8.2 else if(GPA is equal to highestGPA) push(stack, student name); 8.3 Read the GPA and student name; } Data Structures Using C++

  28. Programming Example: Highest GPA (Algorithm) • Output the highest GPA. • Output the names of the students having the highest GPA. Data Structures Using C++

  29. Programming Example: Highest GPA (Sample Run) Input File (Ch7_HighestGPAData.txt) 3.4 Holt 3.2 Bolt 2.5 Colt 3.4 Tom 3.8 Ron 3.8 Mickey 3.6 Pluto 3.5 Donald 3.8 Cindy 3.7 Dome 3.9 Andy 3.8 Fox 3.9 Minnie 2.7 Goofy 3.9 Doc 3.4 Danny Data Structures Using C++

  30. Programming Example: Highest GPA (Sample Run) Output Highest GPA = 3.90 The students holding the highest GPA are: Doc Minnie Andy Data Structures Using C++

  31. Empty and Nonempty Linked Stack Empty linked stack Nonempty linked stack Data Structures Using C++

  32. Default Constructor template<class Type> //default constructor linkedStackType<Type>::linkedStackType() { stackTop = NULL; } Data Structures Using C++

  33. Destroy Stack template<class Type> void linkedStackType<Type>::destroyStack() { nodeType<Type> *temp; //pointer to delete the node while(stackTop != NULL) //while there are elements //in the stack { temp = stackTop; //set temp to point to //the current node stackTop = stackTop->link; //advance stackTop //to the next node delete temp; //deallocate the memory //occupied by temp } }//end destroyStack Data Structures Using C++

  34. initializeStack and isStackEmpty template<class Type> void linkedStackType<Type>:: initializeStack() { destroyStack(); } template<class Type> bool linkedStackType<Type>::isEmptyStack() { return(stackTop == NULL); } template<class Type> bool linkedStackType<Type>::isFullStack() { return false; Data Structures Using C++

  35. Push Stack before the push operation Stack and newNode Data Structures Using C++

  36. Push Stack after the statement newNode->link = stackTop; executes Stack after the statement stackTop = newNode; executes Data Structures Using C++

  37. Return Top Element template<class Type> Type linkedStackType<Type>::top() { assert(stackTop != NULL); //if the stack is empty, //terminate the program return stackTop->info; //return the top element }//end top Data Structures Using C++

  38. Pop Stack before the popoperation Data Structures Using C++

  39. Pop Stack after the statements temp = stackTop; and stackTop = stackTop->link; execute Stack after the statement delete temp; executes Data Structures Using C++

  40. Application of Stacks:Postfix Expression Calculator • Prefix/Polish Notation • Suffix/Postfix/Reverse Polish Notation Data Structures Using C++

  41. Application of Stacks:Postfix Expression Calculator Data Structures Using C++

  42. Application of Stacks:Postfix Expression Calculator Stack after pushing 6 Stack after retrieving the top two elements and popping twice Stack after pushing 3 Stack after pushing the result of op1 + op2, which is 9 Data Structures Using C++

  43. Application of Stacks:Postfix Expression Calculator Stack after pushing 2 Stack after pushing the result of op1 * op2, which is 18 Stack after retrieving the top two elements and popping twice Stack after popping the element Data Structures Using C++

  44. Postfix Expression Calculator (Main Algorithm) Data Structures Using C++

  45. Nonrecursive Algorithm to Print Linked List current = first; //Line 1 while(current != NULL) //Line 2 { stack.push(current); //Line 3 current = current->link; //Line 4 } Data Structures Using C++

  46. List After Execution of Statementcurrent = first; Data Structures Using C++

  47. Repeated Execution of:stack.push(current);current = current->link; Data Structures Using C++

  48. STL class stack (Stack Container Adapter) • Standard Template Library (STL) provides a class to implement a stack in a program • Name of the class defining a stack is stack • Name of the header file containing the definition of the class stack is stack Data Structures Using C++

  49. Operations on a stack Object Data Structures Using C++

  50. Chapter Summary • Stack Data Structure • Last In First Out (LIFO) • Stacks Implemented as Arrays • Stacks Implemented as Linked Lists • Postfix Expression Calculator • Nonrecursive Algorithm to Print Linked List • STL class stack Data Structures Using C++