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Doubly Linked Lists-Computer Programming-Assignment Solution, Exercises of Aeronautical Engineering

Biju Patnaik University of Technology Aeronautical Engineering

This is solution to assignment for Aeronautical Engineering and Computer Programming course. It was submitted to Prof. Chitraksh Gavde at Biju Patnaik University of Technology, Rourkela. It includes: List, Doubly, Linked, Problem, Pointer, Programming, Procdure,Postcondition, Precondition, Loop, Else, Return

Typology: Exercises

2011/2012

Uploaded on 07/20/2012

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CP5_6

The problems in this problem set cover lectures C5 and C6.

1.

a. What are doubly linked lists? What is the record declaration for a node in a doubly

linked list?

10 11 13

head

Figure 1. Sample Doubly Linked List

Doubly linked lists have two pointers instead of the single pointer seen in singly linked

lists. The pointers point to both the previous node in the list as well as the next node in

the list. type Listnode is

record

Element : Elementtype;

Next : Listptr;

Prev : Listptr; -- this is the change made to singly linked lists

end record;

b. Write an algorithm to insert a node into a sorted doubly linked list. Use a diagram to

show the sequence of operations that have to be performed to carry out the insertion step.

Hint: Extend the approach used in class/ notes for singly linked lists.

Preconditions:

1. User passes the list (called List) and the element to be inserted (called Element) to

the insert procedure

2. List is already sorted

Postconidtions:

1. Procedure returns the list with the element inserted in the correct position

2. List remains sorted

Algorithm:

Create three temporary Listptrs Current, Previous and NewNode

Previous := null

Current := List.Head;

NewNode := new Listnode;

NewNode.Element := Element

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Partial preview of the text

Download Doubly Linked Lists-Computer Programming-Assignment Solution and more Exercises Aeronautical Engineering in PDF only on Docsity!

CP5_

The problems in this problem set cover lectures C5 and C6.

a. What are doubly linked lists? What is the record declaration for a node in a doubly

linked list?

10 11 13

head

Figure 1. Sample Doubly Linked List

Doubly linked lists have two pointers instead of the single pointer seen in singly linked

lists. The pointers point to both the previous node in the list as well as the next node in

the list.

type Listnode is record Element : Elementtype; Next : Listptr; Prev : Listptr; -- this is the change made to singly linked lists end record;

b. Write an algorithm to insert a node into a sorted doubly linked list. Use a diagram to

show the sequence of operations that have to be performed to carry out the insertion step.

Hint: Extend the approach used in class/ notes for singly linked lists.

Preconditions:

1. User passes the list (called List) and the element to be inserted (called Element) to

the insert procedure

2. List is already sorted

Postconidtions:

1. Procedure returns the list with the element inserted in the correct position

2. List remains sorted

Algorithm:

Create three temporary Listptrs Current , Previous and NewNode

Previous := null

Current := List.Head;

NewNode := new Listnode;

NewNode.Element := Element

Loop

exit when Current = Null

exit when Current.Element > Element

Previous := Current;

Current := Current.Next;

NewNode. Next := Current;

NewNode.Prev:= Previous;

If Previous = null

L.Head := NewNode

else

Previous.Next := NewNode

If Current /= null

Current.Prev := NewNode;

Return List

Consider the doubly linked list shown in Figure 1. The insertion of a node with element

12 in the list, the insert operation is shown in Figures 2 and 3.

10 11 13

head

Initial State

10 11 13

head Previous^ Current

12

When loop is exited^ NewNode

Figure 2. Prior to Insertion

Current.Prev := NewNode

10 11 13

12

NewNode

head Previous Current

Figure 3. After Insertion Operation

c. Implement your algorithm as an Ada95 program.

Package Specification

Checking: c:/docume~1/jayaka~1/mydocu~1/16070/code/doubly_linked_list.ads (source file time stamp: 2004-03-31 20:46:40)

-- Specification for doubly-linked lists
-- Specified: Jayakanth Srinivasan
-- Last Modified: February 11, 2004
package Doubly_Linked_List is
subtype Elementtype is Integer;
type Listnode;
type Listptr is access Listnode;
type Listnode is
record
Element : Elementtype;
Next : Listptr;
Prev : Listptr; -- this is the change made to singly linked lists
end record;
type List is
record
Head : Listptr;
end record;
procedure Makeempty (
L : in out List );
-- Pre: L is defined
-- Post: L is empty
function Isempty (
L : in List )
return Boolean;
-- Pre: L is defined
-- Post: returns True if L is empty, False otherwise
procedure Display (
L : in List );
-- Pre: L may be empty
-- Post: displays the contents of L's Element fields, in the
-- order in which they appear in L
procedure Initialize (
L : in out List );
-- Pre: L may be empty
-- Post: Elements inserted into the list at correct position
procedure Insert_In_Order (
L : in out List;
Element : in Elementtype );
end Doubly_Linked_List;

54 lines: No errors

Package Implementation

Compiling: c:/docume~1/jayaka~1/mydocu~1/16070/code/doubly_linked_list.adb (source file time stamp: 2004-03-31 20:48:14)

-- Implementation for doubly-linked lists
-- Programmer: Jayakanth Srinivasan
-- Last Modified: Feb 11, 2004
with Ada.Text_Io;
with Ada.Integer_Text_Io;
with Ada.Unchecked_Deallocation;
use Ada.Text_Io;
use Ada.Integer_Text_Io;
package body Doubly_Linked_List is
-- create an instance of the free procedure
procedure Free is
new Ada.Unchecked_Deallocation(Listnode, Listptr);
-- check if list is empty. List.Head will be null
function Isempty (
L : in List )
return Boolean is

-- create a node and set the data to element
Newnode := new Listnode;
Newnode.Element:= Element;
-- check if the list is empty.
if Isempty(L)= False then
loop
-- need two separate exits, otherwise there will be
-- an execption at runtime
exit when Current = null;
exit when Current.Element >Element;
Previous := Current;
Current := Current.Next;
end loop;
end if;
-- do insertion
Newnode.Prev:= Previous;
Newnode.Next := Current;
if Previous = null then
-- list is empty
L.Head := Newnode;
else
Previous.Next := Newnode;
if Current /= null then
Current.Prev := Newnode;
end if;
end if;
end Insert_In_Order;
end Doubly_Linked_List;

108 lines: No errors

Test Program

Compiling: c:/docume~1/jayaka~1/mydocu~1/16070/code/doubly_list_test.adb (source file time stamp: 2004-03-31 20:49:02)

-- Program to test the doubly linked list package
-- Programmer: Jayakanth Srinivasan
-- Date Last Modified : Feb 11, 2004
with Doubly_Linked_List;
use Doubly_Linked_List;
procedure Doubly_List_Test is
My_List : List;
begin
-- initialize the list
Initialize(My_List);
-- insert 1,3,2,4 into the list and display at each stage
Insert_In_Order(My_List, 1);

Display(My_List);
Insert_In_Order(My_List, 3);
Display(My_List);
Insert_In_Order(My_List, 2);
Display(My_List);
Insert_In_Order(My_List, 4);
Display(My_List);
end Doubly_List_Test;

27 lines: No errors

Doubly Linked Lists-Computer Programming-Assignment Solution, Exercises of Aeronautical Engineering

Related documents

Partial preview of the text

Download Doubly Linked Lists-Computer Programming-Assignment Solution and more Exercises Aeronautical Engineering in PDF only on Docsity!

CP5_

The problems in this problem set cover lectures C5 and C6.

a. What are doubly linked lists? What is the record declaration for a node in a doubly

linked list?

Figure 1. Sample Doubly Linked List

Doubly linked lists have two pointers instead of the single pointer seen in singly linked

lists. The pointers point to both the previous node in the list as well as the next node in

the list.

b. Write an algorithm to insert a node into a sorted doubly linked list. Use a diagram to

show the sequence of operations that have to be performed to carry out the insertion step.

Hint: Extend the approach used in class/ notes for singly linked lists.

Preconditions:

1. User passes the list (called List) and the element to be inserted (called Element) to

the insert procedure

2. List is already sorted

Postconidtions:

1. Procedure returns the list with the element inserted in the correct position

2. List remains sorted

Algorithm:

Create three temporary Listptrs Current , Previous and NewNode

Previous := null

Current := List.Head;

NewNode := new Listnode;

NewNode.Element := Element

Loop

exit when Current = Null

exit when Current.Element > Element

Previous := Current;

Current := Current.Next;

NewNode. Next := Current;

NewNode.Prev:= Previous;

If Previous = null

L.Head := NewNode

else

Previous.Next := NewNode

If Current /= null

Current.Prev := NewNode;

Return List

Consider the doubly linked list shown in Figure 1. The insertion of a node with element

12 in the list, the insert operation is shown in Figures 2 and 3.

Figure 2. Prior to Insertion

Figure 3. After Insertion Operation

c. Implement your algorithm as an Ada95 program.

2. What is the Shortest Path through the graph shown below using Dijkstra’s algorithm.

Assume node A is the start node.

Show all the steps in the computation of the shortest path.

Initialize

V = {a, b, c, d, e}

E = {(a,b), (a,c), (b,e), (b,c), (c,b), (c,d), (c,e), (d,a), (d,e), (e.d)}

S = {→}

Q = {a, b, c, d, e}

D = [0, ∞, ∞,∞,∞]

Previous = [0, 0, 0, 0, 0]

Start at A

Relax (a,b,10)

Relax (a,c,5)

S = {a}

Q = {b, c, d, e}

b e

a

c d

For a graph G = (V, E). where V is a finite nonempty set of vertices and E is the set

of edges,

a. Walk

A walk is a sequence of vertices (v1, v2, …, vk) in which each adjacent vertex

pair is an edge

b. Path

A path is a walk with no repeated nodes

c. Eulerian Path

An Eulerian path in a graph is a path that uses each edge precisely once.

d. Cycle

A cycle is a path that begins and ends with the same vertex

e. Degree of a vertex

The degree of a vertex in an undirected graph is the number of edges incident

with it, except that a loop at a vertex contributes twice to the degree of that vertex

In a directed graph, the degree of the vertex is partitioned into indegree (number