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Algorithm Analysis and Design (Assignment –II)
Submitted in partial fulfilment of the requirements for the degree of
Master of Technology in Information TechnologyMaster of Technology in Information TechnologyMaster of Technology in Information TechnologyMaster of Technology in Information Technology
by
Vijayananda D Mohire
(Enrolment No.921DMTE0113)
Information Technology Department
Karnataka State Open University Manasagangotri, Mysore – 570006
Karnataka, India (2009)
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Algorithm Analysis and Design
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CERTIFICATECERTIFICATECERTIFICATECERTIFICATE
This is to certify that the Assignment-II entitled (Algorithm Analysis and
Design, subject code: MT13) submitted by Vijayananda D Mohire having
Roll Number 921DMTE0113 for the partial fulfilment of the requirements
of Master of Technology in Information Technology degree of Karnataka
State Open University, Mysore, embodies the bonafide work done by
him under my supervision.
Place: ________________ Place: ________________ Place: ________________ Place: ________________ Signature of the Internal SupervisorSignature of the Internal SupervisorSignature of the Internal SupervisorSignature of the Internal Supervisor
NameNameNameName
Date: ________________Date: ________________Date: ________________Date: ________________ DesignatioDesignatioDesignatioDesignationnnn
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For EvaluationFor EvaluationFor EvaluationFor Evaluation
Question Question Question Question
NumberNumberNumberNumber
Maximum MarksMaximum MarksMaximum MarksMaximum Marks Marks Marks Marks Marks
awarded awarded awarded awarded
Comments, if anyComments, if anyComments, if anyComments, if any
1 5
2 5
TOTALTOTALTOTALTOTAL 10
Evaluator’s Name and Signature Date
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PrefacePrefacePrefacePreface
This document has been prepared specially for the assignments of M.Tech – IT I
Semester. This is mainly intended for evaluation of assignment of the academic
M.Tech - IT, I semester. I have made a sincere attempt to gather and study the best
answers to the assignment questions and have attempted the responses to the
questions. I am confident that the evaluator’s will find this submission informative
and evaluate based on the provide content.
For clarity and ease of use there is a Table of contents and Evaluators section to
make easier navigation and recording of the marks. A list of references has been
provided in the last page – Bibliography that provides the source of information both
internal and external. Evaluator’s are welcome to provide the necessary comments
against each response, suitable space has been provided at the end of each
response.
I am grateful to the Infysys academy, Koramangala, Bangalore in making this a big
success. Many thanks for the timely help and attention in making this possible within
specified timeframe. Special thanks to Mr. Vivek and Mr. Prakash for their timely
help and guidance.
Candidate’s Name and Signature Date
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TTTTABLE OF ABLE OF ABLE OF ABLE OF CCCCONTENTS ONTENTS ONTENTS ONTENTS
FOR EVALUATION ................................................................................................................................................................ 4
PREFACE................................................................................................................................................................................. 5
QUESTION 1 ......................................................................................................................................................................... 9
ANSWER 1(A) ....................................................................................................................................................................... 9
ANSWER 1(B) ...................................................................................................................................................................... 12
QUESTION 2 ....................................................................................................................................................................... 15
ANSWER 2 ........................................................................................................................................................................... 15
BIBLIOGRAPHY .................................................................................................................................................................... 38
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Table of FiguresTable of FiguresTable of FiguresTable of Figures Figure 1 Figure 1 Figure 1 Figure 1 Depth First Search Algorithm Output (Schildt, 2000) ...................................................................................... 10 Figure 2 Figure 2 Figure 2 Figure 2 Depth First Search explanation (Schildt, 2000) .................................................................................................. 11 Figure 3 Figure 3 Figure 3 Figure 3 DFS Code Snippet (Schildt, 2000) ........................................................................................................................... 12 Figure 4Figure 4Figure 4Figure 4 Breadth First Search Output (Schildt, 2000) ....................................................................................................... 13 Figure 5 Figure 5 Figure 5 Figure 5 Breadth First Search Explanation (Schildt, 2000) ............................................................................................. 13 Figure 6 Figure 6 Figure 6 Figure 6 Breadth First Search Code Snippet (Schildt, 2000) .......................................................................................... 14 Figure 7 Figure 7 Figure 7 Figure 7 Merge Sort Input (Anonymous, 2009) ................................................................................................................... 15 Figure 8 Figure 8 Figure 8 Figure 8 Merge Sort Output (Anonymous, 2009) ................................................................................................................. 15
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ALGORITHMALGORITHMALGORITHMALGORITHM ANALYSIS ANDANALYSIS ANDANALYSIS ANDANALYSIS AND DESIGNDESIGNDESIGNDESIGN
RESPONSE TO ASSIGNMENT RESPONSE TO ASSIGNMENT RESPONSE TO ASSIGNMENT RESPONSE TO ASSIGNMENT –––– IIIIIIII
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Question 1Question 1Question 1Question 1 Write the C/C++ codes for DFS & BFS?
Answer 1Answer 1Answer 1Answer 1(a)(a)(a)(a) Depth First Search AlgorithmDepth First Search AlgorithmDepth First Search AlgorithmDepth First Search Algorithm
Input:
Let us now consider a problem that we will use various searches to solve.
Imagine that you are a travel agent and a rather quarrelsome customer wants
you to book a flight from New York to Los Angeles with XYZ Airlines. You try to
tell the customer that XYZ does not have a direct flight from New York to Los
Angeles, but the customer insists that XYZ is the only airline that he will fly.
XYZ's scheduled flights are as follows:
Flight DistanceFlight DistanceFlight DistanceFlight Distance
New York to Chicago 1,000 miles
Chicago to Denver 1,000 miles
New York to Toronto 800 miles
New York to Denver 1,900 miles
Toronto to Calgary 1,500 miles
Toronto to Los Angeles 1,800 miles
Toronto to Chicago 500 miles
Denver to Urbana 1,000 miles
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Denver to Houston 1,500 miles
Houston to Los Angeles 1,500 miles
Denver to Los Angeles 1,000 miles
You quickly see that there is a way to fly from New York to Los Angeles by using
XYZ if you book connecting flights, and you book the fellow his flights.
Output:
Figure Figure Figure Figure 1111 Depth First Search Algorithm Output (Schildt, 2000)
Explanation:
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Figure Figure Figure Figure 2222 Depth First Search explanation (Schildt, 2000)
If you refer to Figure 2, you see that this is indeed the first solution that would be
found by a depth-first search. It is not the optimal solution— which is New York
to Chicago to Denver to Los Angeles with a distance of 3,000 miles— but it is
not bad.
Lets looks at the key code SNIPPET as below:
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Figure Figure Figure Figure 3333 DFS Code Snippet (Schildt, 2000)
Full code available in Appendix
Answer 1(b)Answer 1(b)Answer 1(b)Answer 1(b) Breadth First Search Algorithm
Input: Same as in Depth First Search Algorithm
Output:
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Figure Figure Figure Figure 4444 Breadth First Search Output (Schildt, 2000)
Explanation:
Figure Figure Figure Figure 5555 Breadth First Search Explanation (Schildt, 2000)
Let’s look into the code snippet as below:
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Figure Figure Figure Figure 6666 Breadth First Search Code Snippet (Schildt, 2000)
Full code available in Appendix:
Evaluator’s Comments if any:
Extra code Line for BFS algorithm
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Question 2Question 2Question 2Question 2 Write the C/C++ codes for merge sort?for merge sort?for merge sort?for merge sort?
Answer 2Answer 2Answer 2Answer 2
Input:
Figure Figure Figure Figure 7777 Merge Sort Input (Anonymous, 2009) Output:
Figure Figure Figure Figure 8888 Merge Sort Output (Anonymous, 2009) Explanation:
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Full code in available in Appendix
Evaluator’s Comments if any:
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AppendixAppendixAppendixAppendix
/* Depth-first search. */
#include <stdio.h>
#include <string.h>
#include<conio.h>
#define MAX 100
/* structure of the flight database */
structstructstructstruct FL {
charcharcharchar from[20];
charcharcharchar to[20];
intintintint distance;
charcharcharchar skip; /* used in backtracking */
};
structstructstructstruct FL flight[MAX]; /* array of db structures */
intintintint f_pos = 0; /* number of entries in flight db */
intintintint find_pos = 0; /* index for searching flight db */
intintintint tos = 0; /* top of stack */
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structstructstructstruct stack {
charcharcharchar from[20];
charcharcharchar to[20];
intintintint dist;
};
structstructstructstruct stack bt_stack[MAX]; /* backtrack stack */
voidvoidvoidvoid setup(voidvoidvoidvoid), route(charcharcharchar *to);
voidvoidvoidvoid assert_flight(charcharcharchar *from, charcharcharchar *to, intintintint dist);
voidvoidvoidvoid push(charcharcharchar *from, charcharcharchar *to, intintintint dist);
voidvoidvoidvoid pop(charcharcharchar *from, charcharcharchar *to, intintintint *dist);
voidvoidvoidvoid isflight(charcharcharchar *from, charcharcharchar *to);
intintintint find(charcharcharchar *from, charcharcharchar *anywhere);
intintintint match(charcharcharchar *from, charcharcharchar *to);
intintintint main(voidvoidvoidvoid)
{
charcharcharchar from[20], to[20];
setup();
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printf("From? ");
gets(from);
printf("To? ");
gets(to);
isflight(from,to);
route(to);
getch();
returnreturnreturnreturn 0;
}
/* Initialize the flight database. */
voidvoidvoidvoid setup(voidvoidvoidvoid)
{
assert_flight("New York", "Chicago", 1000);
assert_flight("Chicago", "Denver", 1000);
assert_flight("New York", "Toronto", 800);
assert_flight("New York", "Denver", 1900);
assert_flight("Toronto", "Calgary", 1500);
assert_flight("Toronto", "Los Angeles", 1800);
assert_flight("Toronto", "Chicago", 500);
assert_flight("Denver", "Urbana", 1000);
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assert_flight("Denver", "Houston", 1500);
assert_flight("Houston", "Los Angeles", 1500);
assert_flight("Denver", "Los Angeles", 1000);
}
/* Put facts into the database. */
voidvoidvoidvoid assert_flight(charcharcharchar *from, charcharcharchar *to, intintintint dist)
{
ifififif(f_pos < MAX) {
strcpy(flight[f_pos].from, from);
strcpy(flight[f_pos].to, to);
flight[f_pos].distance = dist;
flight[f_pos].skip = 0;
f_pos++;
}
elseelseelseelse printf("Flight database full.\n");
}
/* Show the route and total distance. */
voidvoidvoidvoid route(charcharcharchar *to)
{
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intintintint dist, t;
dist = 0;
t = 0;
whilewhilewhilewhile(t < tos) {
printf("%s to ", bt_stack[t].from);
dist += bt_stack[t].dist;
t++;
}
printf("%s\n", to);
printf("Distance is %d.\n", dist);
}
/* If flight between from and to, then return
the distance of flight; otherwise, return 0. */
intintintint match(charcharcharchar *from, charcharcharchar *to)
{
registerregisterregisterregister intintintint t;
forforforfor(t=f_pos-1; t > -1; t--)
ifififif(!strcmp(flight[t].from, from) &&
!strcmp(flight[t].to, to)) returnreturnreturnreturn flight[t].distance;
returnreturnreturnreturn 0; /* not found */
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}
/* Given from, find anywhere. */
intintintint find(charcharcharchar *from, charcharcharchar *anywhere)
{
find_pos = 0;
whilewhilewhilewhile(find_pos < f_pos) {
ifififif(!strcmp(flight[find_pos].from,from) &&
!flight[find_pos].skip) {
strcpy(anywhere,flight[find_pos].to);
flight[find_pos].skip = 1; /* make active */
retureturetureturnrnrnrn flight[find_pos].distance;
}
find_pos++;
}
returnreturnreturnreturn 0;
}
/* Determine if there is a route between from and to. */
voidvoidvoidvoid isflight(charcharcharchar *from, charcharcharchar *to)
{
intintintint d, dist;
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charcharcharchar anywhere[20];
/* see if at destination */
ifififif(d=match(from, to)) {
push(from, to, d);
returnreturnreturnreturn;
}
/* try another connection */
ifififif(dist=find(from, anywhere)) {
push(from, to, dist);
isflight(anywhere, to);
}
elseelseelseelse ifififif(tos > 0) {
/* backtrack */
pop(from, to, &dist);
isflight(from, to);
}
}
/* Stack Routines */
voidvoidvoidvoid push(charcharcharchar *from, charcharcharchar *to, intintintint dist)
{
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ifififif(tos < MAX) {
strcpy(bt_stack[tos].from,from);
strcpy(bt_stack[tos].to,to);
bt_stack[tos].dist = dist;
tos++;
}
elseelseelseelse printf("Stack full.\n");
}
voidvoidvoidvoid pop(charcharcharchar *from, charcharcharchar *to, intintintint *dist)
{
ifififif(tos > 0) {
tos--;
strcpy(from,bt_stack[tos].from);
strcpy(to,bt_stack[tos].to);
*dist = bt_stack[tos].dist;
}
elseelseelseelse printf ("Stack underflow.\n");
}
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/* Breadth-first search. */
#include <stdio.h>
#include <string.h>
#include<conio.h>
#define MAX 100
/* structure of the flight database */
structstructstructstruct FL {
charcharcharchar from[20];
charcharcharchar to[20];
intintintint distance;
charcharcharchar skip; /* used in backtracking */
};
structstructstructstruct FL flight[MAX]; /* array of db structures */
intintintint f_pos = 0; /* number of entries in flight db */
intintintint find_pos = 0; /* index for searching flight db */
inininintttt tos = 0; /* top of stack */
structstructstructstruct stack {
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charcharcharchar from[20];
charcharcharchar to[20];
intintintint dist;
};
structstructstructstruct stack bt_stack[MAX]; /* backtrack stack */
voidvoidvoidvoid setup(voidvoidvoidvoid), route(charcharcharchar *to);
voidvoidvoidvoid assert_flight(charcharcharchar *from, charcharcharchar *to, intintintint dist);
voidvoidvoidvoid push(charcharcharchar *from, charcharcharchar *to, intintintint dist);
voidvoidvoidvoid pop(charcharcharchar *from, charcharcharchar *to, intintintint *dist);
voidvoidvoidvoid isflight(charcharcharchar *from, charcharcharchar *to);
intintintint find(charcharcharchar *from, charcharcharchar *anywhere);
intintintint match(charcharcharchar *from, charcharcharchar *to);
intintintint main(voidvoidvoidvoid)
{
charcharcharchar from[20], to[20];
setup();
printf("From? ");
gets(from);
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printf("To? ");
gets(to);
isflight(from,to);
route(to);
getch();
returnreturnreturnreturn 0;
}
/* Initialize the flight database. */
voidvoidvoidvoid setup(voidvoidvoidvoid)
{
assert_flight("New York", "Chicago", 1000);
assert_flight("Chicago", "Denver", 1000);
assert_flight("New York", "Toronto", 800);
assert_flight("New York", "Denver", 1900);
assert_flight("Toronto", "Calgary", 1500);
assert_flight("Toronto", "Los Angeles", 1800);
assert_flight("Toronto", "Chicago", 500);
assert_flight("Denver", "Urbana", 1000);
assert_flight("Denver", "Houston", 1500);
assert_flight("Houston", "Los Angeles", 1500);
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assert_flight("Denver", "Los Angeles", 1000);
}
/* Put facts into the database. */
voidvoidvoidvoid assert_flight(charcharcharchar *from, charcharcharchar *to, intintintint dist)
{
ifififif(f_pos < MAX) {
strcpy(flight[f_pos].from, from);
strcpy(flight[f_pos].to, to);
flight[f_pos].distance = dist;
flight[f_pos].skip = 0;
f_pos++;
}
elseelseelseelse printf("Flight database full.\n");
}
/* Show the route and total distance. */
voidvoidvoidvoid route(charcharcharchar *to)
{
intintintint dist, t;
dist = 0;
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t = 0;
whilewhilewhilewhile(t < tos) {
printf("%s to ", bt_stack[t].from);
dist += bt_stack[t].dist;
t++;
}
printf("%s\n", to);
printf("Distance is %d.\n", dist);
}
/* If flight between from and to, then return
the distance of flight; otherwise, return 0. */
intintintint match(charcharcharchar *from, charcharcharchar *to)
{
registerregisterregisterregister intintintint t;
forforforfor(t=f_pos-1; t > -1; t--)
ifififif(!strcmp(flight[t].from, from) &&
!strcmp(flight[t].to, to)) returnreturnreturnreturn flight[t].distance;
returnreturnreturnreturn 0; /* not found */
}
/* Given from, find anywhere. */
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intintintint find(charcharcharchar *from, charcharcharchar *anywhere)
{
find_pos = 0;
whilewhilewhilewhile(find_pos < f_pos) {
ifififif(!strcmp(flight[find_pos].from,from) &&
!flight[find_pos].skip) {
strcpy(anywhere,flight[find_pos].to);
flight[find_pos].skip = 1; /* make active */
returnreturnreturnreturn flight[find_pos].distance;
}
find_pos++;
}
returnreturnreturnreturn 0;
}
/* Determine if there is a route between from and to. */
voidvoidvoidvoid isflight(charcharcharchar *from, charcharcharchar *to)
{
intintintint d, dist;
charcharcharchar anywhere[20];
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whilewhilewhilewhile(dist=find(from, anywhere)) {
/* breadth-first modification */
ifififif(d=match(anywhere, to)) {
push(from, to, dist);
push(anywhere, to, d);
returnreturnreturnreturn;
}
}
/* try any connection */
ifififif(dist=find(from, anywhere)) {
push(from, to, dist);
isflight(anywhere, to);
}
elseelseelseelse ifififif(tos>0) {
pop(from, to, &dist);
isflight(from, to);
}
}
/* Stack Routines */
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voidvoidvoidvoid push(charcharcharchar *from, charcharcharchar *to, intintintint dist)
{
ifififif(tos < MAX) {
strcpy(bt_stack[tos].from,from);
strcpy(bt_stack[tos].to,to);
bt_stack[tos].dist = dist;
tos++;
}
elseelseelseelse printf("Stack full.\n");
}
voidvoidvoidvoid pop(charcharcharchar *from, charcharcharchar *to, intintintint *dist)
{
ifififif(tos > 0) {
tos--;
strcpy(from,bt_stack[tos].from);
strcpy(to,bt_stack[tos].to);
*dist = bt_stack[tos].dist;
}
elseelseelseelse printf ("Stack underflow.\n");
}
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//Merge Sort
#include <iostream.h>
#include <conio.h>
intintintint a[50];
voidvoidvoidvoid merge(intintintint,intintintint,intintintint);
voidvoidvoidvoid merge_sort(intintintint low,intintintint high)
{
intintintint mid;
ifififif(low<high)
{
mid=(low+high)/2;
merge_sort(low,mid);
merge_sort(mid+1,high);
merge(low,mid,high);
}
}
voidvoidvoidvoid merge(intintintint low,intintintint mid,intintintint high)
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{
intintintint h,i,j,b[50],k;
h=low;
i=low;
j=mid+1;
whilewhilewhilewhile((h<=mid)&&(j<=high))
{
ifififif(a[h]<=a[j])
{
b[i]=a[h];
h++;
}
elseelseelseelse
{
b[i]=a[j];
j++;
}
i++;
}
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ifififif(h>mid)
{
forforforfor(k=j;k<=high;k++)
{
b[i]=a[k];
i++;
}
}
elseelseelseelse
{
forforforfor(k=h;k<=mid;k++)
{
b[i]=a[k];
i++;
}
}
forforforfor(k=low;k<=high;k++) a[k]=b[k];
}
intintintint main()
{
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intintintint num,i;
cout<<"********************************************************"<<endl;
cout<<" MERGE SORT PROGRAM "<<endl;
cout<<"********************************************************"<<endl;
cout<<endl<<endl;
cout<<"Please Enter THE NUMBER OF ELEMENTS you want to sort [THEN
PRESS ENTER]:"<<endl;
cin>>num;
cout<<endl;
cout<<"Now, Please Enter the ( "<< num <<" ) numbers (ELEMENTS)
[THEN PRESS ENTER]:"<<endl;
forforforfor(i=1;i<=num;i++)
{
cin>>a[i] ;
}
merge_sort(1,num);
cout<<endl;
cout<<"So, the sorted list (using MERGE SORT) will be :"<<endl;
cout<<endl<<endl;
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forforforfor(i=1;i<=num;i++)
cout<<a[i]<<" ";
cout<<endl<<endl<<endl<<endl;
getch();
returnreturnreturnreturn 0;
}
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BibliographyBibliographyBibliographyBibliography Anonymous. (2009). C++ > Algorithms sample source codes, Merge Sort. Retrieved 2009, from Happy Codings:
http://www.cplusplus.happycodings.com/Algorithms/code17.html
Schildt, H. (2000). C, The Complete Reference. New York: McGraw-Hill.