Transcript Lecture 20
CSC 205 Programming II Lecture 20 Postfix Expressions Recap: Stack Stack features Stack operations Orderly linear structure Access from one side only – top item Push – add an item to top Pop – remove the top item Peek – get the content of the top item Implementations and trade-offs Array-based Implementation Instance variables needed Collection of data – Object[] items Two auxiliary variables • Number of items on stack – int numItems • Stack capacity – int CAPACITY Selected methods pop popAll Arithmetic Expressions Three possible orders Infix: operator in between operands 2 * (3 + 4) • Widely used in normal presentation • Parentheses needed to remove ambiguity Prefix: operator proceeds operands *+342 Postfix: operator following operands 234+* Evaluating Expressions Infix 2 * (3 + 4) 2 * (3 + 4) 2 * 7 14 Prefix * + 3 4 2 * + 3 4 2 * 7 2 14 Postfix 2 3 4 + * 2 3 4 + * 2 7 * 14 Evaluating Postfix Expressions Using Stack Assumptions Correct postfix expression With arithmetic operators +, -, *, and / only The algorithm Initialize a stack Read the next input while there is one • If (the next input is a number) • Push it onto the stack • Else • Pop two numbers off the stack • Carry out the calculation & push the result onto the stack Converting Infix to Postfix Notation It’s easier to evaluate postfix expressions No need for a separate stack for operators: an operator is consumed when encountered Infix expressions can be converted into equivalent postfix ones then be evaluated Assumptions Correct infix expression +, -, *, and / only Sample Expression 1 –fully parenthesized (a – ((b + (c * d)) / e)) Converting Infix to Postfix Notation – when fully parenthesized Initialize a stack (for operators and parentheses) Read the next input while there is one If (the next input is a left parenthesis) • Push it onto the stack Else if (the next input is a number) • Write it to the output Else if (the next input is an operator) • Push it onto the stack Else • Pop and output the top item (an operator) • Pop and discard the top item (a left parenthesis) Sample Expression 2 – parenthesized as needed a – (b + c * d) / e Converting Infix to Postfix Notation – using precedence rules Initialize a stack (for operators and parentheses) Read the next input while there is one If (the next input is a left parenthesis) • Push it onto the stack Else if (the next input is a number) • Write it to the output Else if (the next input is an operator) • Pop and print operators off the stack until • Stack become empty • The next item is a left parenthesis • The next item is an operator of lower precedence • Push the new operator onto stack Else • Pop and output the top item (an operator) • Pop and discard the top item (a left parenthesis)