Lecture 5 Stack Sandy Ardianto & Erick Pranata © Sekolah Tinggi Teknik Surabaya 1

Data Structure

Lecture 5Stack

Sandy Ardianto & Erick Pranata© Sekolah Tinggi Teknik Surabaya

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» In computer science, a stack is a last-in first-out (LIFO) data structure.

» A stack can have any data type as an element, but is characterized by only two fundamental operations, the push and pop.

Stack

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» The push operation adds to the top of the list, hiding any items already on the stack, or initializing the stack if it is empty.˃ Push is implemented by a

procedure.

» The pop operation removes an item from the top of the stack, and returns this value to the caller. ˃ Pop is implemented by a

function

Push and Pop Operations


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Stack History» Stack was first proposed in 1955, and

then patented in 1957, by the German Friedrich L. Bauer.

» The same concept was developed independently, at around the same time, by the Australian Charles Leonard Hamblin.

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Other Operations of Stack» In modern computer languages, the

stack is usually implemented with more operations than just push and pop.

» Some implementations have a function which returns the current length of the stack.

» Another typical helper operation, peek, can return the current top element of the stack without removing it from the stack. 5


Stack Implementation» In most high level languages, a stack can

easily implemented either through an array or a linked list.

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Stack Implementation Using Array» The array implementation aims to

create an array where the zero-offset position is the bottom. That is, array[0] is the bottom.

» The program keeps track of which offset index corresponds to the top. This index changes as the stack shrinks and grows in size.

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Stack Implementation Using Arraypublic class STACK {const int STACK_SIZE = 1000;

public int top; public int[] items(STACK_SIZE);

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Stack Implementation Using Arraypublic STACK() { top = -1;}

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Stack Implementation Using Arraypublic bool IsEmpty() {return s.top == -1;

}

public bool IsFull() {return s.top == STACKSIZE – 1;

}

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Stack Implementation Using Arraypublic void Push(int x) {if (IsFull(s)) { throw

new Exception("stack overflow");} else { top = top + 1; items(top) = x;}

}

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Stack Implementation Using Arraypublic int Pop() { if (IsEmpty()) { throw

new Exception("stack underflow");} else { int data = items(top); top = top – 1; return data;}

}

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Stack Implementation Using Arraypublic int Pop() { if (IsEmpty()) { throw

new Exception("stack underflow");} else { int data = items(top); top = top – 1; return data;}

}

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Peek()

The Stack<T> Class» The stack data structure

˃ Elements are from the same type T˃ T can be any type, e.g. Stack<int> ˃ Size is dynamically increased as needed

» Basic functionality:˃ Push(T) – inserts elements to the stack˃ Pop() – removes and returns the top

element from the stack

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The Stack<T> Class» Basic functionality:

˃ Peek() – returns the top element of the stack without removing it

˃ Count – returns the number of elements˃ Clear() – removes all elements˃ Contains(T) – determines whether given

element is in the stack˃ ToArray() – converts the stack to an array˃ TrimExcess() – sets the capacity to

the actual number of elements 15


Stack<T> – Examplestatic void Main(){ Stack<string> stack = new Stack<string>(); stack.Push("1. Ivan"); stack.Push("2. Nikolay"); stack.Push("3. Maria"); stack.Push("4. George"); Console.WriteLine("Top = {0}", stack.Peek()); while (stack.Count > 0) { string personName = stack.Pop(); Console.WriteLine(personName); }}

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Stack<T> – Matching Brackets» We are given an arithmetical expression

with brackets that can be nested» Goal: extract all sub-expressions in

brackets» Example:

˃ 1 + (2 - (2+3) * 4 / (3+1)) * 5» Result:

˃ (2+3) | (3+1) | (2 - (2+3) * 4 / (3+1))» Algorithm:

˃ For each '(' push its index in a stack˃ For each ')' pop the corresponding start index

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Stack<T> – Matching Bracketsstring expression = "1 + (2 - (2+3) * 4 / (3+1)) * 5";Stack<int> stack = new Stack<int>();for (int index = 0; index < expression.Length; index++){ char ch = expression[index]; if (ch == '(') { stack.Push(index); } else if (ch == ')') { int startIndex = stack.Pop(); int length = index - startIndex + 1; string contents =

expression.Substring(startIndex, length); Console.WriteLine(contents); }}

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Stack Applications» Calculator

˃ Convert an expression (infix notation) into a postfix notation.

˃ Calculate a postfix expression.˃ These two processes need a stack.

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Expression Notations» There are three notations of

expressions: infix, prefix, and postfix.

Infix : 1 + 5 * 3 + 2 1 + (2 + 3)Prefix : + + 1 * 5 3 2 + 1 + 2 3Postfix : 1 5 3 * + 2 + 1 2 3 + +

» Infix can contain parentheses, but prefix and postfix cannot (never need parentheses).

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Calculation of postfix» Push when encountering an operand.» Pop two operands and evaluate the

value when encountering an operator, and then push the result.

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Stack Applications» Conversion from a decimal (base-10)

number system to another number system˃ Examples: from decimal to binary (base-2),

from decimal to octal (base-8), and from decimal to hexadecimal (base-16).

˃ Suppose to convert the decimal number 156 to binary (base-2).

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Stack Applications» Write the integer answer (quotient)

under the long division symbol, and write the remainder (0 or 1) to the right of the dividend. This remainder must be pushed into a stack.

2 ) 156 0 78

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Stack Applications» Continue downwards, dividing each

new quotient by two and writing the remainders to the right of each dividend (pushing the remainders into a stack). Stop when the quotient is 0.

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Stack Applications2 ) 156 02 ) 78 02 ) 39 12 ) 19 12 ) 9 12 ) 4 02 ) 2 02 ) 1 1 0

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Pop all elements from the stack to get a sequence of binary digits.

10011100

Homework» Write an essay describing source code

which is used to calculate infix notation.˃ Submit the printed version @ my office.˃ Due: Friday, 11 April 2014 at 5 pm.

» Inappropriate essay will be returned unmarked.

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