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Chapter 7 – Stacks. 1. Main Index. Contents. Stacks Further Stack Examples Pushing/Popping a Stack Class Stack (3 slides) Using a Stack to Create a Hex # Uncoupling Stack Elt’s (6 slides) Activation Records RPN. Infix Notation Summary Slides (4 slides). Stacks.
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Chapter 7 – Stacks 1 Main Index Contents • Stacks • Further Stack Examples • Pushing/Popping a Stack • Class Stack (3 slides) • Using a Stack to Create a Hex # • Uncoupling Stack Elt’s (6 slides) • Activation Records • RPN • Infix Notation • Summary Slides (4 slides)
Stacks • A stack is a sequence of items that are accessible at only one end of the sequence.
3 Main Index Contents Further Stack Examples
Pushing/Popping a Stack • Because a pop removes the item last added to the stack, we say that a stack has LIFO (last-in/first-out) ordering.
CLASS stack CLASS stack <stack> <stack> Constructor Operations stack(); Create an empty stack bool empty(); const Check whether the stack is empty. Return true if it is empty and false otherwise. 5 Main Index Contents
CLASS stack <stack> Operations void pop(); Remove the item from the top of the stack. Precondition: The stack is not empty. Postcondition: Either the stack is empty or the stack has a new topmost item from a previous push. void push(const T& item); Insert the argument item at the top of the stack. Postcondition: The stack has a new item at the top. 6 Main Index Contents
CLASS stack <stack> Operations int size() const; Return the number of items on the stack. T& top() const; Return a reference to the value of the item at the top of the stack. Precondition: The stack is not empty. const T& top() const; Constant version of top(). 7 Main Index Contents
8 Main Index Contents Using a Stack to Create a Hex Number
9 Main Index Contents Uncoupling Stack Elements
10 Main Index Contents Uncoupling Stack Elements
11 Main Index Contents Uncoupling Stack Elements
12 Main Index Contents Uncoupling Stack Elements
13 Main Index Contents Uncoupling Stack Elements
14 Main Index Contents Uncoupling Stack Elements
15 Main Index Contents
16 Main Index Contents
Precedence Symbol Input precedence Stack precedence Rank + - 1 1 -1 * / % 2 2 -1 ^ 4 3 -1 ( 5 -1 0 ) 0 0 0 17 Main Index Contents Infix Expression Rules The figure below gives input precedence, stack precedence, and rank used for the operators +, -, *, /, %, and ^, along with the parentheses. Except for the exponential operator ^, the other binary operators are left-associative and have equal input and stack precedence.
18 Main Index Contents Summary Slide 1 §- Stack - Storage Structure with insert (push) and erase (pop) operations occur at one end, called the top of the stack. - The last element in is the first element out of the stack, so a stack is a LIFO structure.
19 Main Index Contents Summary Slide 2 §- Recursion - The system maintains a stack of activation records that specify: 1) the function arguments 2) the local variables/objects 3) the return address - The system pushes an activation record when calling a function and pops it when returning.
20 Main Index Contents Summary Slide 3 §- Postfix/RPN Expression Notation - places the operator after its operands - easy to evaluate using a single stack to hold operands. - The rules: 1) Immediately push an operand onto the stack. 2) For a binary operator, pop the stack twice, perform the operation, and push the result onto the stack. 3) At the end a single value remains on the stack. This is the value of the expression.
21 Main Index Contents Summary Slide 4 §- Infix notation - A binary operator appears between its operands. - More complex than postfix, because it requires the use of operator precedence and parentheses. - In addition, some operators are left-associative, and a few are right-associative.
