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Stack Implementation

Stack Implementation. Stacks can be Implemented by:. Static Arrays Fixed size Good is size is known. Dynamic Arrays Flexible Good if insertion and deletion is infrequent. Linked Lists Flexible Dynamic. Stack Implementation. All versions have common operations (STL) Void pop()

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Stack Implementation

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  1. Stack Implementation Stacks can be Implemented by: Static Arrays Fixed size Good is size is known Dynamic Arrays Flexible Good if insertion and deletion is infrequent Linked Lists Flexible Dynamic

  2. Stack Implementation All versions have common operations (STL) Void pop() // pop & removes the top item from the stack Void push(const T & item) //pushes/ adds items on top of stack Bool empty() const //returns true if stack is empty Int size() const //returns number of items in stack T&top() //returns a reference to the top of the stack without removing it Const T& top() const // constant version of top Destructors (for linked list and dynamic arrays)

  3. Stack Errors Stack underflow //condition resulting from trying to access an item from an empty stack Stack overflow //condition resulting from trying to push/ add an item onto a full stack

  4. Postfix Expression - Introduction • aka Reverse Polish Notation (RPN) after Polish mathematician Jan Lukasiewwicz • Calculators use this format extensively • Postfix Format: an operator is entered in the expression as soon as 2 operands are available • e.g. 8 + (4* 12 + 5%2) / 3 contains: • Operands: (8, 4, 12, 5, 2, 3) • Operators: (+, *, %, /) • Parenthesis: subexpressions

  5. Infix a + b * c (a + b) * c (a*b+c)/d + e a*b – c/d a*b*c*d*e*f (b*b-4*a*c)/(2*a) Postfix abc*+ ab+c* ab*c+d/e+ ab*cd/- ab*c*d*e*f* bb*4a*c*-2a*/ Infix vs. Postfix

  6. Postfix Evaluation Algorithm • Scan each term of the expression from left to right • Use a single stack to hold the operands • If a term is an operand, push it onto the stack • If a term is a binary operator, evaluate its result because its 2 operands are already on stack on the 2 top positions • Pop the stack to retrieve the operands • Evaluate the expression • Push the result back onto the stack

  7. Postfix Evaluation Algorithm • Consider the expression 4 3 5 *+ • Its postfix requires 7 steps Step 1 Step 2 Step 5 Step 6 Step 7 Step 3 Step 4 • Read * operator • Pop first 2 operands on stack • Compute 5*3 = 15 • Read + operator • Pop first 2 operands on stack • Compute 15+4 = 19 5 3 3 15 4 4 4 4 19 Push 3 Push 15 Push 19 Push 4 Push 5

  8. Postfix - Detecting Errors • Errors can occur during the evaluation of a postfix expression • At each step in the algorithm, the state of the stack allows us to identify when an error occurs and the cause of the error • e.g. 38+*9 ERROR • Too many successive operators • * is missing a second operand • e.g. 98+7 ERROR • Too many operands • What to do with 7?

  9. Designing Postfix Evaluation Class for Implementation d_rpn.h Class postfixEval { public: postfix Eval(); // default constructor // postfix expression is a NULL string string getPostfixExp() const; // access member function which enables a programmer to retrieve the current expression void setPostfixExp(const string& postfixExp); // operation which takes a string argument containing the postfix expression int evalaute(); // key member function which attempts to compute the value of the postfix expression // if successful, it returns the value of the expression // if the expression contains an error, the function throws the expressionError exception

  10. Designing Postfix Evaluation Class for Implementation d_rpn.h private: String postfixExpression; // the characters in the string include operands, operators, and white space characters // such as blanks, tabs //These are scanned by the evaluate() function Stack<int> operandStack; // stack pf operands stored during operations and used by evaluate() function void getOperands (int& left, int& right); // pops the left and right operands from stack // precondition: checks that the stack is not empty and has at least 2 entries before each pop operation // an empty stack prior to pop() operations indicates that there are too many operators and the // function throws an expressionError exception int compute (int left, int right, char op) const; // evalautes an operations // pushes result onto a stack // for (/) and remainder (%) operators, compute() checks the RH operator to see if it is 0 // If it is 0, the function throws an exressionError exception with the message “Divide by 0” // for the exponentail operator (^), compute() checks for (0,0) and throws an ExpressionError exception Bool isOPerator (char ch) const; // determines whether a character is one of the valid operators (+, -, *, /, %, ^) }; Utility functions to implement algorithm

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