Copyright © Curt Hill Stacks An Useful Abstract Data Type

Examples Come look at my desk Sock drawers Cafeteria plates Function data spaces –If a calls b and b calls c and c calls d –Their local variables are a stack (aka the invocation stack) Copyright © Curt Hill

Names Push down stacks –Push down lists –Push down queues Last In First Out Queue –LIFO One of several sequential ADTs Copyright © Curt Hill

Why use? Why does a cafeteria use them? Used for storage of things temporarily Things are all the same size Do not care about how long each thing is stored –Response or arrival times do not matter Easiest list to maintain All the work is at one end Copyright © Curt Hill

What Operations? Two main operations Push and Pop Push places a new item on the stack Pop removes it Others: –Determination of empty or number of items –Initialization Only the top of the stack is accessible –Top is most recently pushed item that has not been popped Copyright © Curt Hill

Example and Exercise Suppose the following operations: push 12 push 6 push 9 pop push 2 push 14 pop pop What is the resulting stack? Copyright © Curt Hill

Result Top on left After the first three pushes: After first pop: 6 12 After two more pushes: After second pop: After last pop: 6 12 Copyright © Curt Hill

Implementation Like many ADTs a stack may have several different possible implementations The underlying data structure could be –An array –A vector –Linked list Others are possible but less reasonable Each might need additional methods Copyright © Curt Hill

Interface and Implementation The same interface may exist with different implementations We will now look at an interface for an integer stack –Just the public part How this would be implemented would be in the private part and method implementations Copyright © Curt Hill

Integer Stack Code C++: class Stack { public: void push(int); int pop(); bool isEmpty(); Stack(); ~Stack(); private:... }; // Stack class Copyright © Curt Hill

Array stacks Variables: int st[STACKMAX]; int top; An additional method should be added: bool isFull(); Copyright © Curt Hill

Initialization Initialization is only setting top Set to zero –Indexes first unused item Set to -1 –Indexes first used item Which is better? The way of the C family is set to zero Other languages may choose either Copyright © Curt Hill

Push Now easy void push(int item){ if (top < STACKMAX) st[top++] = item; } // Push Error handling is also a design issue –What do we do with a stack that is full and a request for a push? Copyright © Curt Hill

Pop Also easy int pop(){ if(top>0) return st[top--]; } // Pop Again error handling needs some thought Copyright © Curt Hill

Capacity Several possibilities bool isEmpty(){ return top>0; } bool isFull(){ return top >= STACKMAX; } int size(){ return top; } Copyright © Curt Hill

Algebraic expressions Order of algebraic expressions There are several ways that an algebraic expression may be shown Everyone is familiar with infix, which is standard algebraic notation Operands surround operators –3 + 2 –5 + 3 * 4 –Requires precedence and parentheses There are also prefix and postfix Copyright © Curt Hill

The Others Prefix –Operator followed by operands –+ 3 2 –+ * Postfix –Operands followed by operator –3 2 + –5 4 3 * + –aka Reverse Polish Notation (RPN) –aka Suffix Copyright © Curt Hill

Why do I care? The older HP calculators used to use RPN Computers do not have a parenthesis, so every infix expression must be converted to postfix –The natural notation for computers Load the operands into a register and then execute the operation Copyright © Curt Hill

Conversion of infix to postfix Operators must have a priority Starting at the lowest priority this is: –end of expression –(–( –=–= –+ - (addition and subtraction) –* / (multiplication and division) –- (unary negation) Copyright © Curt Hill

Algorithm Overview Input for the infix expression Output for postfix expression Stack for operators Algorithm follows Copyright © Curt Hill

Algorithm Repeat until no more inputs What to do if you find a: –Operand Copy to output –Operator ( Push on regardless –Any operator but ) while priority(topstack) >= priority(current) write(pop()) push(current) –Operator ) Pop and write until ( found Discard ) Copyright © Curt Hill

Example –Examples 2+3*(4-5*6) (3+4*5)*(7-6) Copyright © Curt Hill

RPN calculator Evaluate an expression While not eof do For an operand push it on stack For an operator –Pop one or two things off of stack –Do the operation –Push result on stack Copyright © Curt Hill

Evaluate Infix Combining the two algorithms –Converting to RPN –Executing RPN Notes –When you write an operand then push on second stack –When you write an operator - execute it in stack fashion - pop off two, execute, push on result –When you are done the stack should contain only one item, which you pop and print Copyright © Curt Hill

Code generation for a compiler Stack machine is same as a RPN calculator Register machine (register-memory instructions) Convert to RPN Each output will be a load to a register Copyright © Curt Hill

Conclusion Stacks are the easiest to maintain linear structure All the action is at just one end –No iteration, no indexing Used as temporary storage when holding time does not matter Underlying data structure could be –Array –List –Vector Copyright © Curt Hill