![13
Declaration of Stack
• For Contiguous implementation, set an array which hold the entries in the
stack and a counter.
• Create and Initializes a stack to be empty before it is first used
Data Structures & Algorithms
Push and Pop
• Stack is implemented using ‘Push’ and ‘Pop’ operations.
• Operations during implementation should be done with care;
For e.g.,
• popping an item from an empty stack
• pushing an item into a stack that is full should not be done.
[Create stack: create and initialize the stack to be empty]
void Createstack (stack sptr)
return [ sptr.top=0 ]](https://image.slidesharecdn.com/session1-180119051348/85/Data-Structures-13-320.jpg)
![14
Algorithm for push
Procedure push [s,top ,x]
[this procedure inserts an element [x] to the top of the stack.]
[check for stack overflow, maxstack is constant for maximum size]
[allowed for stacks]
if top> maxstack then
write (“Stack overflow”)
exit
[increment top]
top=top+1
[insert element]
s[top]=x
[finished]
End push
Push Operation
Data Structures & Algorithms
• First step of the algorithm checks for an overflow condition.
• Such a condition exits then the insertion cannot be performed and an
appropriate error message result.](https://image.slidesharecdn.com/session1-180119051348/85/Data-Structures-14-320.jpg)
![15
Pop Operation
Algorithm for pop
Procedure pop [s, top, x ]
[ this function removes the top element from a stack.]
[check for underflow on stack]
if top <=0 then
write (“Stack is Underflow”) exit
[Pop element from stack]
x=s [top]
[decrement pointer]
top = top-1
End pop
• First step itself checking underflow condition
• If exist an appropriate error message will display and the
procedure is terminated
Data Structures & Algorithms](https://image.slidesharecdn.com/session1-180119051348/85/Data-Structures-15-320.jpg)
![16
Other operations
[Full: returns non-zero if the stack is full]
boolean_type full(stack_type sptr)
{return sptr .top>=MAXSTACK;}
[Empty: returns non-zero if the stack is empty]
boolean - type empty (stack_type sptr)
{return sptr .top<=0;}
Data Structures & Algorithms](https://image.slidesharecdn.com/session1-180119051348/85/Data-Structures-16-320.jpg)
Data Structures
- 1. 1 Introduction to Data Structures Session I Dr. V.Umadevi M.Sc(CS &IT). M.Tech (IT)., M.Phil., PhD., D.Litt., Director, Department of Computer Science, Jairams Arts and Science College, Karur. Data Structures & Algorithms
- 2. 2 • Introduction to Data Structures • Primitive Data Structures • Types of Data structures – Stacks – Queues – Lists • Stack – Basic Operation of Stack – Operations on the Data Structures – Applications of Infix, Postfix and Prefix Data Structures & Algorithms Introduction to Data Structures
- 3. 3 Data Structures & Algorithms • A Computer is a machine that manipulates information. • Computer science studies includes: – How information is organized in a computer – How it can be manipulated – How it can be utilized Introduction to Data Structures • Data is represented by the values held temporarily in the program’s data area or recorded permanently on a file • Different data values may be related to each other which need to be organized to form a proper data structure. • Program follow certain rules to access manipulate and process the structured data. Information – Processed data given as output Data – Raw facts and figures given as input
- 4. 4 Data Structures & Algorithms • Organization of data in a computer's memory or in a file. • Proper choice of a data structure can lead to more efficient programs. • Example: Array, Stack, Queue, Linked list, Tree and Graph. • Represented as follows: Data structure=Data organization + allowed operations. Data Structure
- 5. 5 Primitive Data structure • Data structures typically are directly operated upon by the machine level instructions. • Primitive data constitute the numbers and characters, which are built into a programming language. • Examples are: Integer, Boolean and Characters. • Other data structures can be constructed from one or more primitives. • Simple data structures built from primitives are Strings, Arrays, and Records Data Structures & Algorithms
- 6. 6 Types of Data Structures – Linear data structure. – Non-Linear data structure. • Various names used for naming the elements of a data structure ( Commonly used names are data element, data item, item aggregate, node list and data object) • Various data structures are used depending upon the needs and convenience Data Structures & Algorithms
- 7. 7 Data Structures & Algorithms •Elements or items form a sequence one after the other. •Linear list can be realized in memory using either an array or a linked list structure. •Data is also stored in memory locations by means of pointers. Examples are: Arrays, Stacks, Queues and Linked list. Linear Data Structure
- 8. 8 Linear Data Structures Types • Arrays - elements stored in memory locations in a sequential order • Stack is an ordered collection of data items – inserted or deleted from one end i.e., Last In First Out (LIFO) principle. • Queue is an ordered list – inserted at one end and are retrieved from the other end i.e., First in First out (FIFO) principle. • Linked Lists -elements stored in memory locations by means of pointers (chain of structures). Data Structures & Algorithms
- 9. 9 Non-Linear Data Structures • Represents the hierarchical relationship between individual data items. • Examples are : Trees, Graphs • Tree - hierarchical relation between its elements. • Graph - collection of node and edges – Node - data element – Edge - path between two nodes. Data Structures & Algorithms
- 10. 10 Operations on the Data Structures Data Structures & Algorithms • Traversal-is a technique in which each element is processed individually and separately. • Search-is an activity in which a particular record or item is to be found. • Insertion- is a process in which a new element is added into the structure. • Deletion- is a process in which a given item is removed from the structure • Sorting-is a process in which all elements are arranged in a specific order so that each item can be retrieved easily. • Merging-is a process in which two structures are combined into a single structure.
- 11. 11 Stack • Ordered collection of items • Item may be inserted or deleted only from the top of the stack. • Works on Last In First Out (LIFO) concept. • Helps backtracking or to return to the previous state. Data Structures & Algorithms
- 12. 12 Basic Stack Operations Createstack Create and Initializes a stack to be empty before it is first used Push adds an item to a stack Pop extracts the most recently pushed item from the stack ( removing an item from the stack.) Full returns non-zero if the stack is full Empty returns non-zero if the stack is empty Data Structures & Algorithms
- 13. 13 Declaration of Stack • For Contiguous implementation, set an array which hold the entries in the stack and a counter. • Create and Initializes a stack to be empty before it is first used Data Structures & Algorithms Push and Pop • Stack is implemented using ‘Push’ and ‘Pop’ operations. • Operations during implementation should be done with care; For e.g., • popping an item from an empty stack • pushing an item into a stack that is full should not be done. [Create stack: create and initialize the stack to be empty] void Createstack (stack sptr) return [ sptr.top=0 ]
- 14. 14 Algorithm for push Procedure push [s,top ,x] [this procedure inserts an element [x] to the top of the stack.] [check for stack overflow, maxstack is constant for maximum size] [allowed for stacks] if top> maxstack then write (“Stack overflow”) exit [increment top] top=top+1 [insert element] s[top]=x [finished] End push Push Operation Data Structures & Algorithms • First step of the algorithm checks for an overflow condition. • Such a condition exits then the insertion cannot be performed and an appropriate error message result.
- 15. 15 Pop Operation Algorithm for pop Procedure pop [s, top, x ] [ this function removes the top element from a stack.] [check for underflow on stack] if top <=0 then write (“Stack is Underflow”) exit [Pop element from stack] x=s [top] [decrement pointer] top = top-1 End pop • First step itself checking underflow condition • If exist an appropriate error message will display and the procedure is terminated Data Structures & Algorithms
- 16. 16 Other operations [Full: returns non-zero if the stack is full] boolean_type full(stack_type sptr) {return sptr .top>=MAXSTACK;} [Empty: returns non-zero if the stack is empty] boolean - type empty (stack_type sptr) {return sptr .top<=0;} Data Structures & Algorithms
- 17. 17 Application of Stack Stack based Language (Re_expressing the expression) – Computers solve arithmetic expressions by restructuring them so that the order of each calculation is embedded in the expression. – Once converted, to the required notation (Either Prefix or Postfix), an expression can be solved. Types of Expression • Any expression represent in 3 ways • Infix, Prefix and Postfix. • Expression 4 + 5 * 5 is represented as follows: – Infix - Operators are embedded between operands- 4+5*5. – Prefix - Operators precede the operands- + 4 * 5 5 – Postfix - Operators follow the operands- 4 5 5 * + – Default representation of mathematical expression is Infix (or Polish) notation. Data Structures & Algorithms
- 18. 18 Conversion of Expression- • Infix to Postfix – Applying the precedence rule first for operators – Place the Operators follow the operands – For e.g., an expression A+(B*C) • A + ( B * C) -Parenthesis for emphasis • A + ( BC *) -Convert the multiplication • A (BC *) + -Convert the addition • ABC * + -Postfix Form • Infix to Prefix – Applying the precedence rule first for operators – Place operators precede the operands – For e.g., an expression A+(B*C) • A + ( B * C) -Parenthesis for emphasis • A + (* BC) -Convert the multiplication • + A ( * BC ) -Convert the addition • * + ABC -Prefix Form Data Structures & Algorithms
- 19. 19 • Scratch pad – Use to write down instructions that cannot be acted upon immediately. – Example of this is the rat-in-maze problem. – Use to solve the problem of traversing a maze. – Keep track of previously explored routes, or else an infinite loop could occur. • Text Editor – Characters are pushed on a stack as the user enters text. – Commands to delete one character or a command to delete a series of characters would also push a character on a stack. – Example, an identifier to delete one character would pop the stack once. – Example, an identifier to delete a sentence would pop all characters until the stack is empty or a period is encountered. Data Structures & Algorithms