1. Cs212: Data Structures
Computer Science Department
Lecture 6: Stacks

2. Lecture Contents Basic Stack Operation
What is Stack ?
Basic Stack Operation
Array-Based Stack Implementation
Stack Linked List Implementation
Infix, Postfix and Prefix
17-Feb-19
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3. Stacks
What is Stack ?
A Stack is a linear list in which all additions and deletions are restricted to one end ,called the top
Objects can be inserted into a stack at any time, but only the most recently inserted (that is, "last") object can be removed at any time.
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4. Stacks
What is Stack ?
If you inserted a data series into a stack and then removed it ,the order of the data would be reversed .
Data input as {5,10,15,20} would be removed as {20,15,10,5}
This reversing attribute is why stacks are known as last in first out(LIFO)
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5. Stacks
Example 1:
Internet Web browsers store the addresses of recently visited sites on a stack. Each time a user visits a new site, that site's address is "pushed" onto the stack of addresses. The browser then allows the user to "pop" back to previously visited sites using the "back" button.
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6. Stacks
Example 2:
Text editors usually provide an "undo" mechanism that cancels recent editing operations and reverts to former states of a document. This undo operation can be accomplished by keeping text changes in a stack.
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7. Abstract data types (ADTs)
abstract data type (ADT): A specification of a collection of data and the operations that can be performed on it.
Describes what a collection does, not how it does it
We don't know exactly how a stack is implemented, and we don't need to.
We just need to understand the idea of the collection and what operations it can perform.
Formally, a stack is an abstract data type (ADT) that supports the following two methods:

8. Stacks 1.Push Add new element to the top of the stack
Basic Stack Operation
1.Push
Add new element to the top of the stack
The input consists of the stack and the new element.
Prior to this operation, the stack must exist and must not be full
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9. Check for enough room, (no overflow)
Stacks
Check for enough room, (no overflow)
Data
Push
Top
Top
operation

10. Stacks 2. Pop Removes the top element of the stack.
Basic Stack Operation
2. Pop
Removes the top element of the stack.
Prior to this operation, the stack must exist and must not be empty.
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11. Check if empty, (no underflow)
Stacks
Check if empty, (no underflow)
Data
Top
Pop
Top
operation

12. Stacks Additionally, let us also define the following methods:
Other Stack Operation
Additionally, let us also define the following methods:
size(): Return the number of elements in the stack.
isEmpty(): Return a Boolean indicating if the stack is empty.
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13. Stacks Top: Returns the top element of the stack.
Other Stack Operation
Top:
Returns the top element of the stack.
Prior to this operation, the stack must exist and must not be empty.
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14. Check if empty, (no underflow)
Stacks
Check if empty, (no underflow)
Data
Top
Top
Stack top
operation

15. Exceptions
Attempting the execution of an operation of ADT may sometimes cause an error condition, called an exception
Exceptions are said to be “thrown” by an operation that cannot be executed
In the Stack ADT, operations pop and top cannot be performed if the stack is empty
Attempting the execution of pop or top on an empty stack throws an EmptyStackException
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16. Class Stack Stack<E>()
Stack<Integer> s = new Stack<Integer>();
s.push(42);
s.push(-3);
s.push(17); // bottom [42, -3, 17] top
System.out.println(s.pop()); // 17
Stack<E>()
constructs a new stack with elements of type E
push(value)
places given value on top of stack
pop()
removes top value from stack and returns it;
throws EmptyStackException if stack is empty
top()
returns top value from stack without removing it;
size()
returns number of elements in stack
isEmpty()
returns true if stack has no elements

17. Array-Based Stack Implementation
We can implement a stack by storing its elements in an array. Specifically, the stack in this implementation consists of an N-element array S plus an integer variable t that gives the index of the top element in array S.
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18. Array-Based Stack Implementation con.. 17 23 97 44
stk:
top = 3
or count = 4
If the bottom of the stack is at location 0, then an empty stack is represented by top = -1 or count = 0
To add (push) an element, either:
Increment top and store the element in stk[top], or
Store the element in stk[count] and increment count
To remove (pop) an element, either:
Get the element from stk[top] and decrement top, or
Decrement count and get the element in stk[count]

19. Array-Based Stack Implementation con..
The array implementation of a stack is simple and efficient. Nevertheless, this implementation has one negative aspect—it must assume a fixed upper bound, CAPACITY, on the ultimate size of the stack.
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20. Array-Based Stack Implementation con..
Fortunately, there is another implementation, which we discuss next, that does not have a size limitation and use space proportional to the actual number of elements stored in the stack.
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21. Linked-list implementation of stacks
Several data strucures could be used to implement a stack.
To implement linked list stack , we need two different structures , a head and a data node.
Top
(a) Conceptual
count
Head
Data nodes
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22. Linked-list implementation of stacks con..
Stack Head :require only two attributes
top pointer
count for number of elements in the stack
Stack Data Node
The rest of the data structure is a typical linked list data node
The header of the list points to the top of the stack 44 97 23 17
myStack:
Pushing is inserting an element at the front of the list
Popping is removing an element from the front of the list
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23. Infix, Postfix and Prefix
Infix, Postfix and Prefix notations are three different but equivalent ways of writing expressions.
It is easiest to demonstrate the differences by looking at examples of operators that take two operands.
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24. Infix, Postfix and Prefix
Infix notation
The operator comes between the operands
This is the usual way we write expressions X + Y .
An expression such as A * ( B + C ) / D is usually taken to mean something like: "First add B and C together, then multiply the result by A, then divide by D to give the final answer."
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25. Infix, Postfix and Prefix
Infix notation
Infix notation needs extra information to make the order of evaluation of the operators clear: rules built into the language about operator precedence and associativity, and brackets ( ) to allow users to override these rules.
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26. Infix, Postfix and Prefix
Infix notation
For example, the usual rules for associativity say that we perform operations from left to right, so the multiplication by A is assumed to come before the division by D. Similarly, the usual rules for precedence say that we perform multiplication and division before we perform addition and subtraction.
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27. Infix, Postfix and Prefix
Postfix notation
Also known as "Reverse Polish notation“
Operators are written after their operands X Y +.
The infix expression given above is equivalent to A B C + * D / 
The order of evaluation of operators is always left-to-right, and brackets cannot be used to change this order. Because the "+" is to the left of the "*" in the example above, the addition must be performed before the multiplication. 
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28. Infix, Postfix and Prefix
Postfix notation
Operators act on values immediately to the left of them. For example, the "+" above uses the "B" and "C". We can add (totally unnecessary) brackets to make this explicit:  ( (A (B C +) *) D /)  Thus, the "*" uses the two values immediately preceding: "A", and the result of the addition. Similarly, the "/" uses the result of the multiplication and the "D".
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29. Infix, Postfix and Prefix
Prefix notation
Also known as "Polish notation“
Operators are written before their operands + X Y.
The expressions given above are equivalent to / * A + B C D  As for Postfix, operators are evaluated left-to-right and brackets are superfluous. Operators act on the two nearest values on the right. I have again added (totally unnecessary) brackets to make this clear:  (/ (* A (+ B C) ) D)
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30. Infix, Postfix and Prefix
Prefix notation
Although Prefix "operators are evaluated left-to-right", they use values to their right, and if these values themselves involve computations then this changes the order that the operators have to be evaluated in.
In the example above, although the division is the first operator on the left, it acts on the result of the multiplication, and so the multiplication has to happen before the division (and similarly the addition has to happen before the multiplication). 
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31. Infix, Postfix and Prefix
Examples
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32. Infix, Postfix and Prefix
Examples
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33. End Of Chapter References: Text book, chapter4: Stacks 17-Feb-19
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