Stacks in algorithems & data structure
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The document discusses stacks as a data structure. It defines a stack as a list where all insertions and deletions are made at one end, called the top. Stacks follow the LIFO (last in, first out) principle. The document provides examples of stack implementations using arrays in C++ and describes the basic stack operations like push, pop, peek, and isEmpty. It also gives examples of real-world stacks like stacks of books, chairs, and cups.
![Arrays
An array is a finite ordered collection of homogeneous data
elements which provides direct access (or random access) to any
of its elements.
An array as a data structure is defined as a set of pairs (index,
value) such that with each index a value is associated.
index — indicates the location of an element in an array.
value - indicates the actual value of that data element.
Declaration of an array in ‘C++’:
int Array_A[20];
Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012
6](https://image.slidesharecdn.com/stacks-141027184640-conversion-gate01/85/Stacks-in-algorithems-data-structure-6-320.jpg)
![Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012
13
……….. C B A
top
The elements are stored in the stack from the first location onwards
The first element is stored at 0th location of the array ‘Stack’ which means at
STACK[0], the second element at STACK[1], ith element at Stack [i–1], and nth
element at Stack[n–1]
Associated with the array will be an integer variable, top, which points to the top
element in the stack
The initial value of top is −1, when the stack is empty
It can hold elements from index 0 and maximum it can grow up to n−1 as this is the
static stack using arrays](https://image.slidesharecdn.com/stacks-141027184640-conversion-gate01/85/Stacks-in-algorithems-data-structure-13-320.jpg)
![14
Implementation of Stack
Stack Class
class STACK
{
private:
int Stack[50];
int MaxCapacity;
int top;
public:
STACK( ) { MaxCapacity= 50; top=-1;}
int GetTop( );
int Pop( );
void Push( int Element);
int Empty( );
int CurrSize( );
int IsFull ();
};
Data Structures in C++ by
Dr. Varsha Patil Oxford University Press © 2012 14](https://image.slidesharecdn.com/stacks-141027184640-conversion-gate01/85/Stacks-in-algorithems-data-structure-14-320.jpg)
![15
Implementation of Stack
GetTop, Pop, Empty
int STACK :: GetTop ()
{
if (!Empty())
return (Stack[top]);
}
int STACK :: Pop ()
{
if (!Empty())
return (Stack[top--]);
}
int STACK :: Empty ()
{
if (top==-1)
return 1;
else
return 0;
}
Data Structures in C++ by
Dr. Varsha Patil Oxford University Press © 2012 15](https://image.slidesharecdn.com/stacks-141027184640-conversion-gate01/85/Stacks-in-algorithems-data-structure-15-320.jpg)
![16
Implementation of Stack
IsFull, CurrSize, Push
int STACK :: IsFull ()
{
if (top==MaxCapacity-1)
return 1;
else
return 0;
}
int STACK :: CurrSize()
{
return(top+1);
}
void STACK :: Push (int Element)
{
if (!IsFull())
Stack[++top]=Element;
}
Data Structures in C++ by
Dr. Varsha Patil Oxford University Press © 2012 16](https://image.slidesharecdn.com/stacks-141027184640-conversion-gate01/85/Stacks-in-algorithems-data-structure-16-320.jpg)
Stacks in algorithems & data structure
- 1. AAllggoorriitthhmmss aanndd DDaattaa SSttrruuccttuurreess Ahmad Khan Lecture 4 Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012
- 2. Stack Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 2
- 3. Objectives Understand all the aspects of a stack as data type including : Last In, First Out (LIFO) data access Push, Pop, and other stack operations Contiguous implementation of a stack Learn realization of stack using arrays(: Contiguous stack) Learn to choose appropriate realization suitable for practical applications Learn and implement the multi-stacks Use of stacks in expression conversion, recursion, reversing data and many more Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 3
- 4. A stack is an ordered list in which all insertions and deletions Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 4 are made at one end, called the top In computer programming processing of function calls and their terminations uses stack. Stack is used to remember the place where the call was made; so that it can return there after the function is complete
- 5. Following are some examples in which where we need to use stacks are generally used: Handling function calls in programs very often restricts the access only at one end. In such implementation we need to use stacks. We can keep track of the return address to earlier function after furnishing/finishing a function call using stacks If we intend to store a group of data together in a sequential manner in computer’s memory, then arrays can be one of the possible data structures. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 5
- 6. Arrays An array is a finite ordered collection of homogeneous data elements which provides direct access (or random access) to any of its elements. An array as a data structure is defined as a set of pairs (index, value) such that with each index a value is associated. index — indicates the location of an element in an array. value - indicates the actual value of that data element. Declaration of an array in ‘C++’: int Array_A[20]; Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 6
- 7. Examples of Stacks Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 7 Following figure shows some examples of stack 1.Stack of Book 2.Stack of chairs 3.Stack of cups
- 8. Primitive Operations Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 8 1) The Stack Full Condition (Stack Capacity =3)
- 9. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 9 2) The Pop Operation
- 10. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 10 3) The Empty Stack
- 11. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 11 4) The Get Top Operation
- 12. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 12 Representation Of Stack S Using Sequential Organization (Arrays)
- 13. Oxford University Data Structures Using C++ by Dr Varsha Patil Press © 2012 13 ……….. C B A top The elements are stored in the stack from the first location onwards The first element is stored at 0th location of the array ‘Stack’ which means at STACK[0], the second element at STACK[1], ith element at Stack [i–1], and nth element at Stack[n–1] Associated with the array will be an integer variable, top, which points to the top element in the stack The initial value of top is −1, when the stack is empty It can hold elements from index 0 and maximum it can grow up to n−1 as this is the static stack using arrays
- 14. 14 Implementation of Stack Stack Class class STACK { private: int Stack[50]; int MaxCapacity; int top; public: STACK( ) { MaxCapacity= 50; top=-1;} int GetTop( ); int Pop( ); void Push( int Element); int Empty( ); int CurrSize( ); int IsFull (); }; Data Structures in C++ by Dr. Varsha Patil Oxford University Press © 2012 14
- 15. 15 Implementation of Stack GetTop, Pop, Empty int STACK :: GetTop () { if (!Empty()) return (Stack[top]); } int STACK :: Pop () { if (!Empty()) return (Stack[top--]); } int STACK :: Empty () { if (top==-1) return 1; else return 0; } Data Structures in C++ by Dr. Varsha Patil Oxford University Press © 2012 15
- 16. 16 Implementation of Stack IsFull, CurrSize, Push int STACK :: IsFull () { if (top==MaxCapacity-1) return 1; else return 0; } int STACK :: CurrSize() { return(top+1); } void STACK :: Push (int Element) { if (!IsFull()) Stack[++top]=Element; } Data Structures in C++ by Dr. Varsha Patil Oxford University Press © 2012 16
- 17. STACK S; S.Push(1); S.Push(2); cout<<"t Top element of stack = "<<S.GetTop()<<endl; cout<<"t After pop = "<<S.Pop()<<endl; cout<<"t After pop = "<<S.Pop()<<endl; getch(); 17 Implementation of Stack main int main( ) { } Data Structures in C++ by Dr. Varsha Patil Oxford University Press © 2012 17