Computer Notes - Data Structures - 5

8/3/2019 Computer Notes - Data Structures - 5

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Class No.05

Data Structures

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Josephus Problem

#include "CList.cpp"void main(int argc, char *argv[])

{

CList list;

int i, N=10, M=3;

for(i=1; i 1 ) {

for(i=1; i


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Josephus Problem

Using a circularly-linked list made the solutiontrivial.



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Josephus Problem


The solution would have been more difficult ifan array had been used.

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Josephus Problem



This illustrates the fact that the choice of theappropriate data structures can significantlysimplify an algorithm. It can make the algorithmmuch faster and efficient.

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Josephus Problem




Later we will see how some elegant datastructures lie at the heart of major algorithms.

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Josephus Problem




Later we will see how some elegant datastructures lie at the heart of major algorithms. An entire CS course Design and Analysis of

Algorithms is devoted to this topic.http://ecomputernotes.com
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Abstract Data Type

We have looked at four differentimplementations of the List data structures: Using arrays

Singly linked list Doubly linked list

Circularly linked list.

The interface to the List stayed the same, i.e.,

add(), get(), next(), start(), remove() etc.

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Abstract Data Type

We have looked at four differentimplementations of the List data structures: Using arrays

Singly linked list Doubly linked list

Circularly linked list.

The interface to the List stayed the same, i.e.,

add(), get(), next(), start(), remove() etc. The list is thus an abstract data type; we use it

without being concerned with how it isimplemented.

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Abstract Data Type

What we care about is the methods that areavailable for use with the List ADT.

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Abstract Data Type


We will follow this theme when we develop

other ADT.

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Abstract Data Type



other ADT. We will publish the interface and keep the

freedom to change the implementation of ADTwithout effecting users of the ADT.

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Abstract Data Type



other ADT. We will publish the interface and keep the

freedom to change the implementation of ADTwithout effecting users of the ADT.

The C++ classes provide us the ability to createsuch ADTs.

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Stacks

Stacks in real life: stack of books, stack ofplates

Add new items at the top

Remove an item at the top

Stack data structure similar to real life:

collection of elements arranged in a linearorder.

Can only access element at the top



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Stack Operations

Push(X) insert X as the top element ofthe stack

Pop() remove the top element of thestack and return it.

Top() return the top element withoutremoving it from the stack.

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Stack Operations

push(2)

top 2

push(5)

top

2

5

push(7)

top

2

5

7

push(1)

top

2

5

7

1

1 pop()

top

2

57

push(21)

top

2

57

21

21 pop()

top

2

57

7 pop()

2

5top

5 pop()

2top

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Stack Operation

The last element to go into the stack is thefirst to come out: LIFO Last In First Out.

What happens if we call pop() and there is

no element? Have IsEmpty() boolean function that

returns true if stack is empty, false

otherwise. Throw StackEmpty exception: advanced

C++ concept.

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Stack Implementation: Array

Worst case for insertion and deletion froman array when insert and delete from thebeginning: shift elements to the left.

Best case for insert and delete is at theend of the array no need to shift anyelements.

Implement push() and pop() by insertingand deleting at the end of an array.

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Stack using an Array

top

2

5

7

12 5 7 1

0 1 32 4

top = 3



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Stack using an Array

In case of an array, it is possible that thearray may fill-up if we push enoughelements.

Have a boolean function IsFull() whichreturns true is stack (array) is full, falseotherwise.

We would call this function before callingpush(x).

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Stack Operations with Array

int pop()

{

return A[current--];

}

void push(int x)

{A[++current] = x;

}

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Stack Using Linked List

We can avoid the size limitation of a stackimplemented with an array by using alinked list to hold the stack elements.

As with array, however, we need to decidewhere to insert elements in the list andwhere to delete them so that push and pop

will run the fastest.


Computer Notes - Data Structures - 5

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