Final DAA_prints.pdf

1
/*Assignment 01 :- write a program to implement GCD and LCM Lab:DAA */
#include<iostream.h>
#include<conio.h>
void main()
{
clrscr();
int a,b;
cout<<"Enter Two Numbers For Finding GCD :n";
cin>>a>>b;
int p=a*b;
while(a!=b)
{
if(a>b)
a=a-b;
else
b=b-a;
}
cout<<"GCD = "<<a;
cout<<"nLCM = "<<p/a;
getch();
}
/* OUTPUT :-
Enter two number to find GCD & LCM :
6
4
GCD=2
LCM=12
*/

2
/*Assignment 02 :- Program for finding Maximum using rules removal of recursion Lab:DAA*/
#include <iostream.h>
#include <conio.h>
#include<stdlib.h>
#include<time.h>
int a[200],n,k;
class maximum
{
private:
int i;
public:
void read();
int max(int);
void print();
};
void maximum::read()
{
cout<<"...Program for finding Maximum using rules removal of recursion...";
cout<<"nnEnter the number of element :- ";
cin>>n;
for(int p=1;p<=n;p++)
{
if(p%9==0)
cout<<endl;
a[p]=rand();
cout<<a[p]<<"t";
}
}
int maximum::max(int i)
{
int add;
int top=0,st[400],j;
l1:
if(i<n)
{
top=top+1;
st[top]=i;
top=top++;
st[top]=2;
i=i+1;
goto l1;
l2:
j=st[top];
top=top-1;
if(a[i]>a[j])
k=i;
else
k=j;
}
else
k=n;

3
if(top==0)
return k;
else
add=st[top];
top=top-1;
i=st[top];
top=top-1;
top=top+1;
st[top]=k;
if(add==2)
goto l2;
}
void maximum::print()
{
cout<<"n Max Position :- "<<k<<endl;
cout<<"n Max Element :- "<<a[k];
}
main()
{
clrscr();
maximum m;
m.read();
m.max(1);
m.print();
getch();
return 0;
}
/* OUTPUT :-
...Program for finding Maximum using rules removal of recursion...
Enter the number of element :- 10
346 130 10982 1090 11656 7117 17595 6415
22948 31126
Max Position :- 10
Max Element :- 31126
*/

4
/* Assignment 03:- Program for Searching An element Using Rules Of Removal Of Recursion.
Lab:DAA*/
#include<conio.h>
#include<stdlib.h>
#include<time.h>
class array
{
private:
int *a,size,*stack,top,p,item;
public:
array()
{
cout<<"n Enter the number of elements :- ";
cin>>size;
a=new int[size];
stack=new int[size*2];
top=-1;
}
void getdata();
void display();
int search(int);
};
void array::getdata()
{
for(int i=0;i<size;i++)
{
if(i%8==0)
cout<<"n";
a[i]=random(100);
cout<<a[i]<<" ";
}
cout<<"n Enter the initial Position :-";
cin>>p;
cout<<"n Enter the item to be search :-";
cin>>item;
}
int array::search(int b)
{
int pos,addr,i;
while(b<size)
{
top++;
stack[top]=b;
top++;
stack[top]=2;
b++;
}
pos=-1;
do
{

5
addr=stack[top];
top--;
i=stack[top];
top--;
if(addr==2 && a[i]==item)
{
if(pos== -1)
cout<<"n Element is found at Position :";
else
cout<<" , ";
pos=i+1;
cout<<pos;
}
}while(top>0);
return pos;
}
void array::display()
{
if(search(p-1) == -1)
cout<<"n Item Is not Found In the array...";
}
void main()
{
clrscr();
clock_t e,s;
array obj;
obj.getdata();
s=clock();
obj.display();
e=clock();
cout<<"n The Time Complexity is :-"<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
Program for Searching An element Using Rules Of Removal Of Recurssion.
Enter the number of elements :- 10
1 0 33 3 35 21 53 19
70 94 27 44 10 69 56 4
16 81 68 76 82 95 21 42
95 83 92 81 45 60 66 59
54 72 11 40 12 67 47 49
56 34 86 26 17 42 69 16
53 64 62 0 78 26 46 38
37 58 60 27 17 80 29 33
40 24 41 5 49 98 0 40
6 7 25 97 35 40 19 19
21 24 75 88 90 73 46 53
3 13 45 48 59 25 11 70
64 88 87 4

6
Enter the initial Position :-1
Enter the item to be search :-94
Element is found at Position :10
The Time Complexity is :-0
*/

7
/*Assignment 04:- Program For Binomial Co-efficient .. Lab:DAA */
#include<conio.h>
int binomial(int a,int b)
{
if((a==b) || (b==0))
return 1;
else
return(binomial(a-1,b-1)+binomial(a-1,b));
}
void main()
{
clrscr();
int n;
cout<<"Program For Binomial Co-efficient ..nn";
cout<<"Enter level :-";
cin>>n;
for(int i=0;i<=n;i++)
cout<<binomial(n,i)<<"t";
getch();
}
/* OUTPUT
Program For Binomial Co-efficient ..Enter level :-2
1 2 1
*/

8
/*Assignment 05 :- Implement program for Binomial Coefficent by Using rules of removal of recursion
Lab:DAA */
#include<conio.h>
int b=0;
class bin
{
int n,m,top;
public:
void read();
int binomial(int n,int m);
int topcheck();
};
void bin::read()
{
cout<<"nprogram for Binomial Coefficent by Using rules of removal of recursionnn";
cout<<"n Enter the Value n:-";
cin>>n;
cout<<"n Enter the Value m :-";
cin>>m;
binomial(n,m);
cout<<endl<<"Binomial Coefficint Is :-"<<b;
}
int bin::topcheck()
{
if(top==0)
return(1);
return(0);
}
int bin::binomial(int n,int m)
{
int st[100];
top=0;
L1:
if((n==m)||(m==0))
{
b=b+1;
if(topcheck())
{
return(b);
}
else
goto L2;
}
else
{
top=top+1;

9
st[top]=n;
top=top+1;
st[top]=m;
n=n-1;
m=m-1;
goto L1;
}
L2:
m=st[top];
top--;
n=st[top];
top--;
n--;
goto L1;
}
void main()
{
bin b1;
clrscr();
b1.read();
getch();
}
/* OUTPUT:-
program for Binomial Coefficent by Using rules of removal of recursion
Enter the Value n:-3
Enter the Value m :-2
Binomial Coefficint Is :-3
*/

10
/* Assignment 06 :- Write a program for Max heap insert.. Lab :DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
class heap
{
private:
int a[1000],n;
public:
void getdata();
void insert();
void disp();
};
void heap::getdata()
{
cout<<"n...Program for Max Heap Insert...nn";
cout<<"Enter the Size := " ;
cin>>n;
{
a[i]=random(20000);
}
}
void heap::insert()
{
for(int j=1;j<=n;j++)
{
int i=j;
int item=a[i];
while((i>1) && (a[i/2]<item))
{
a[i]=a[i/2];
i=i/2;
}
a[i]=item;
}
}
void heap::disp()
{
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void main()
{
clrscr();

11
clock_t e,s;
heap h;
h.getdata();
cout<<"nn Befor Insert :: ";
h.disp();
s=clock();
h.insert();
e=clock();
cout<<"nn After Insert ::n";
h.disp();
cout<<"nnThe Time Complexity is ::"<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
...Program for Max Heap Insert...
Enter the Size := 10
Befor Insert :: 211 79 6702 665 7114 4343 10739
3915 14006 18997
After Insert ::
18997 14006 7114 6702 10739 211 4343
79 3915 665
The Time Complexity is ::0
*/

12
/* Assignment 07 :- Write a program for Min Heap Insert.. Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
class heap
{
private:
int a[1000],n;
public:
void getdata();
void insert();
void disp();
};
{
cout<<"n...Program for Min Heap Insert...nn";
cout<<"Enter the Size := " ;
cin>>n;
{
a[i]=random(20000);
}
}
void heap::insert()
{
{
int i=j;
int item=a[i];
while((i>1) && (a[i/2] > item))
{
a[i]=a[i/2];
i=i/2;
}
a[i]=item;
}
}
void heap::disp()
{
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void main()
{
clrscr();
clock_t e,s;

13
heap h;
h.getdata();
cout<<"nn Befor Insert :: ";
h.disp();
s=clock();
h.insert();
e=clock();
cout<<"nn After Insert ::n";
h.disp();
cout<<"nnThe Time Complexity is ::"<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
...Program for Min Heap Insert...
Enter the Size := 10
Befor Insert :: 211 79 6702 665 7114 4343 10739
3915 14006 18997
After Insert ::
79 211 4343 665 7114 6702 10739
3915 14006 18997
The Time Complexity is ::0
*/

14
/* Assignment 08:-Program for MAX heap using Heapify/Adjust Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int a[1000],n;
class heap
{
int i,j,item;
public:
void get();
void show();
void adjust(int [],int i,int j);
void heapify(int [],int);
};
void heap::get()
{
cout<<"Program for Max Heap using Heapify/Adjust..." ;
cout<<"nnEnter the size of array :";
cin>>n;
for(i=1;i<=n;i++)
a[i]=random(1000);
}
void heap::show()
{
cout<<"n The element is:= n";
for(i=1;i<=n;i++)
cout<<a[i]<<"t";
}
void heap::adjust(int a[],int i,int n)
{
j=2*i;
item=a[i];
while(j<=n)
{
if((j<n) && (a[j]<a[j+1]))
j++;
if(item>=a[j])
break;
a[j/2]=a[j];
j=2*j;
}
a[j/2]=item;
}
void heap::heapify(int a[],int n)
{
for(i=n/2;i>=1;i--)
adjust(a,i,n);
}
void main()

15
{
clrscr();
clock_t e,s;
heap h;
h.get();
h.show();
s=clock();
h.heapify(a,n);
e=clock();
h.show();
cout<<"n The Time complexityis => "<<(e-s)/CLK_TCK;
getch();
}
/* OUTPUT :-
Program for Max Heap using Heapify/Adjust...
Enter the size of array :7
The element is:=
10 3 335 33 355 217 536
The element is:=
536 355 335 33 3 217 10
The Time complexityis => 0
*/

16
/* Assignment 09:-Program for MIN heap using Heapify/Adjust Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int a[1000],n;
class heap
{
int i,j,item;
public:
void get();
void show();
void adjust(int [],int i,int j);
void heapify(int [],int);
};
void heap::get()
{
cout<<"Program for Min Heap using Heapify/Adjust..." ;
cout<<"nnEnter the size of array :";
cin>>n;
for(i=1;i<=n;i++)
a[i]=random(1000);
}
void heap::show()
{
cout<<"n The element is:= n";
for(i=1;i<=n;i++)
cout<<a[i]<<"t";
}
{
j=2*i;
item=a[i];
while(j<=n)
{
if((j<n) && (a[j]>a[j+1]))
j++;
if(item<=a[j])
break;
a[j/2]=a[j];
j=2*j;
}
a[j/2]=item;
}
{
for(i=n/2;i>=1;i--)
adjust(a,i,n);
}
void main()

17
{
clrscr();
clock_t e,s;
heap h;
h.get();
h.show();
s=clock();
h.heapify(a,n);
e=clock();
h.show();
cout<<"n The Time complexityis => "<<(e-s)/CLK_TCK;
getch();
}
//OUTPUT :-
/*
Program for Min Heap using Heapify/Adjust...
Enter the size of array :7
The element is:=
10 3 335 33 355 217 536
The element is:=
3 10 217 33 355 335 536
The Time complexityis => 0
*/

18
/* Assignment 10:- Write a program for HeapSort Ascending Using Insert/Delete Lab:DAA */
#include<conio.h>
#include<time.h>
#include<stdlib.h>
class heap
{
int item,i,b[1000];
private:
int a[1000],n;
public:
void getdata();
int delheap();
void insert(int);
void adjust(int[],int,int);
void heapsort();
void disp();
void disp1();
};
{
cout<<"Program for HeapSort for Descending using Insert/Delete...n";
cout<<"nEnter Size :=";
cin>>n;
{
a[i]=random(20000);
}
}
void heap::insert(int i)
{
int item=a[i];
while((i>1) && (a[i/2]>item))
{
a[i]=a[i/2];
i=i/2;
}
a[i]=item;
}
{
int j=2*i;
item=a[i];
while(j<=n)
{
if((j<n) && (a[j] > a[j+1]))
j=j+1;
if(item<=a[j])
break;
a[j/2]=a[j];
j=2*j;

19
}
a[j/2]=item;
}
int heap::delheap()
{
if(n==0)
{
cout<<"heap is empty :";
}
int x=a[1];
a[1]=a[i];
adjust(a,1,i-1);
return x;
}
void heap::heapsort()
{
for(i=1;i<=n;i++)
insert(i);
disp();
for(i=n;i>=1;i--)
b[i]=delheap();
}
void heap::disp()
{
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void heap::disp1()
{
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<b[i]<<"t";
}
}
void main()
{
clrscr();
clock_t e,s;
heap h;
h.getdata();
cout<<"nn Before Sort :n";
s=clock();
h.heapsort();
e=clock();
cout<<"nn After Sort :n";

20
h.disp1();
cout<<"nn Time Complexity ::"<<((e-s)/(CLK_TCK));
getch();
}
/*OUTPUT :
Program for HeapSort for Descending using Insert/Delete...
Enter Size :=50
Before Sort :
79 211 2179 665 3596 3273 9020
830 2428 6889 4388 4343 6702 10739 11286
3915 2279 8123 9497 11284 9821 5288 7114
8535 12909 16790 18464 16217 13964 12094 13233
11994 10983 14400 3303 16309 13710 14006 13424
18997 15287 16552 17374 19190 5495 8461 13895
8885 10765 19051
After Sort :
19190 19051 18997 18464 17374 16790 16552
16309 16217 15287 14400 14006 13964 13895 13710
13424 13233 12909 12094 11994 11286 11284 10983
10765 10739 9821 9497 9020 8885 8535 8461
8123 7114 6889 6702 5495 5288 4388 4343
3915 3596 3303 3273 2428 2279 2179 830
665 211 79
Time Complexity ::0
*/

21
/*Assignment 11:- Write a program for HeapSort Descending Using Insert/Delete Lab:DAA */
#include<conio.h>
#include<time.h>
#include<stdlib.h>
class heap
{
int item,i,b[1000];
private:
int a[1000],n;
public:
void getdata();
int delheap();
void insert(int);
void adjust(int[],int,int);
void heapsort();
void disp();
void disp1();
};
{
cout<<"Program for HeapSort for Ascending using Insert/Delete...n";
cout<<"nEnter Size :=";
cin>>n;
{
a[i]=random(20000);
}
}
void heap::insert(int i)
{
int item=a[i];
while((i>1) && (a[i/2]<item))
{
a[i]=a[i/2];
i=i/2;
}
a[i]=item;
}
{
int j=2*i;
item=a[i];
while(j<=n)
{
if((j<n) && (a[j]<a[j+1]))
j=j+1;
if(item>=a[j])
break;
a[j/2]=a[j];
j=2*j;

22
}
a[j/2]=item;
}
int heap::delheap()
{
if(n==0)
{
cout<<"heap is empty :";
}
int x=a[1];
a[1]=a[i];
adjust(a,1,i-1);
return x;
}
void heap::heapsort()
{
for(i=1;i<=n;i++)
insert(i);
disp();
for(i=n;i>=1;i--)
b[i]=delheap();
}
void heap::disp()
{
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void heap::disp1()
{
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<b[i]<<"t";
}
}
void main()
{
clrscr();
clock_t e,s;
heap h;
h.getdata();
cout<<"nn Before Sort :n";
s=clock();
h.heapsort();
e=clock();
cout<<"nn After Sort :n";

23
h.disp1();
cout<<"nn Time Complexity ::"<<((e-s)/(CLK_TCK));
getch();
}
//OUTPUT
/*
Program for HeapSort for Ascending using Insert/Delete...
Enter Size :=50
Before Sort :
19190 18997 19051 14400 17374 18464 16217
14006 13710 16552 16309 12909 16790 11286 13233
10983 11994 8123 13424 11284 15287 5495 13895
8535 10765 2179 13964 4343 9020 8885 12094
79 3303 830 2279 3915 2428 6702 9497
665 9821 6889 10739 5288 3596 4388 8461
211 3273 7114
After Sort :
79 211 665 830 2179 2279 2428
3273 3303 3596 3915 4343 4388 5288 5495
6702 6889 7114 8123 8461 8535 8885 9020
9497 9821 10739 10765 10983 11284 11286 11994
12094 12909 13233 13424 13710 13895 13964 14006
14400 15287 16217 16309 16552 16790 17374 18464
18997 19051 19190
Time Complexity ::0
*/

24
/* Assignment 12 :- Program for Heapsort Ascending using Adjust/Heapify... Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int b[5000];
class heap
{
public:
void heapsort(int a[],int n);
void heapify(int a[],int n);
void adjust(int a[],int i, int n);
};
void heap::heapsort(int a[],int n)
{
heapify(a,n);
for(int i=n;i>=2;i--)
{
int t=a[i];
a[i]=a[1];
a[1]=t;
adjust(a,1,i-1);
}
}
{
int i;
for(i=n/2;i>=1;i--)
{
adjust(a,i,n);
}
}
{
int j=2*i;
int item=a[i];
while(j<=n)
{
if((j<n) && (a[j]<a[j+1]))
j=j+1;
if(item>=a[j])
break;
else
{
a[j/2]=a[j];
j=2*j;
}
}
a[j/2]=item;
}

25
void main()
{
clrscr();
clock_t e,s;
int n,i;
heap h;
cout<<"..Program For HeapSort Ascending using Adjust/Heapify..nn";
cout<<"n Enter Size Of The Array :->";
cin>>n;
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
b[i]=random(n);
cout<<"t"<<b[i];
}
s=clock();
h.heapsort(b,n);
e=clock();
cout<<"n After Heap Sorting : n";
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<"t"<<b[i];
}
cout<<"nn The Time Complexity Is :="<<((e-s)/CLK_TCK);
getch(); }
/*OUTPUT :-
..Program For HeapSort Ascending using Adjust/Heapify..
Enter Size Of The Array :->50
0 0 16 1 17 10 26 9
35 47 13 22 5 34 28 2
8 40 34 38 41 47 10 21
47 41 46 40 22 30 33 29
27 36 5 20 6 33 23 24
28 17 43 13 8 21 34 8
26 32
After Heap Sorting :
0 0 1 2 2 5 8 8
9 10 13 16 17 20 20 21
21 22 22 23 24 26 26 26
26 27 27 28 28 29 30 32
33 33 34 34 34 34 36 38
40 40 40 41 41 41 43 46
47 47

26
The Time Complexity Is :=0
*/

27
/* Assignment 13 :- Program for Heapsort Descending using Adjust/Heapify... Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int b[5000];
class heap
{
public:
void heapsort(int a[],int n);
void heapify(int a[],int n);
void adjust(int a[],int i, int n);
};
void heap::heapsort(int a[],int n)
{
heapify(a,n);
for(int i=n;i>=2;i--)
{
int t=a[i];
a[i]=a[1];
a[1]=t;
adjust(a,1,i-1);
}
}
{
int i;
for(i=n/2;i>=1;i--)
{
adjust(a,i,n);
}
}
{
int j=2*i;
int item=a[i];
while(j<=n)
{
if((j<n) && (a[j]>a[j+1]))
j=j+1;
if(item<=a[j])
break;
else
{
a[j/2]=a[j];
j=2*j;
}
}
a[j/2]=item;
}
void main()

28
{ clrscr();
clock_t e,s;
int n,i;
heap h;
cout<<"..Program For HeapSort Descending using Adjust/Heapify..nn";
cout<<"n Enter Size Of The Array :->";
cin>>n;
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
b[i]=random(n);
cout<<"t"<<b[i];
}
s=clock();
h.heapsort(b,n);
e=clock();
cout<<"n After Heap Sorting : n";
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<"t"<<b[i];
}
cout<<"nn The Time Complexity Is :="<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
..Program For HeapSort Descending using Adjust/Heapify..
Enter Size Of The Array :->50
0 0 16 1 17 10 26
9 35 47 13 22 5 34 28
2 8 40 34 38 41 47 10
21 47 41 46 40 22 30 33
29 27 36 5 20 6 33 23
24 28 17 43 13 8 21 34
8 26 32
After Heap Sorting :
47 47 47 46 43 41 41
40 40 38 36 35 34 34 34
33 33 32 30 29 28 28 27
26 26 24 23 22 22 21 21
20 17 17 16 13 13 10 10
9 8 8 8 6 5 5 2
1 0 0
The Time Complexity Is :=0
*/

30
/* Assignment 14 :- Program for Union And Find Lab:DAA */
#include<conio.h>
#include<stdlib.h>
int p[100];
class heap
{
int n,a,b,c,no;
public:
void menu();
void read_e();
void s_union(int,int);
int find(int);
void print();
};
void heap::menu()
{
int ch;
cout<<"...... Program for Union And Find ......nn";
cout<<"1:Read_ele 2:Simple union 3:Find 4:Print 5:Exit"<<endl;
while(ch!=5)
{
switch(ch)
{
case 1:
read_e();
break;
case 2:
cout<<"n Enter root of two set node: ";
cin>>a>>b;
s_union(a,b);
break;
case 3:
cout<<"n Find the node :";
cin>>no;
c=find(no);
cout<<"root node is :";
cout<<c;
break;
case 4:
print();
break;
case 5:
exit(0);
}
cout<<"n Enter the choice :";
cin>>ch;
}
}
void heap::read_e()
{

31
cout<<"n Enter the Number of elements :";
cin>>n;
cout<<"n Enter Elements :";
cin>>p[i];
}
void heap::s_union(int i,int j)
{
p[i]=j;
}
int heap::find(int i)
{
while(p[i]>=0)
{
i=p[i];
}
return i;
}
void heap::print()
{
cout<<"n Union of Two set :";
{
cout<<p[i]<<" ";
}
}
void main()
{
clrscr();
heap h;
h.menu();
getch();
}
/* OUTPUT :-
...... Program for Union And Find ......
1:Read_ele 2:Simple union 3:Find 4:Print 5:Exit
Enter the choice :1
Enter the Number of elements :6
Enter Elements :-1 1 1 -1 4 4
Enter the choice :2
Enter root of two set node: 1 4
Enter the choice :4
Union of Two set :4 1 1 -1 4 4
Enter the choice :3
Find the node :6
root node is :4
Enter the choice :5

33
/* Assignment 15:- Program for Weighted Union & Collapsing Find. Lab:DAA */
#include<conio.h>
#include<process.h>
class TreeOp
{
int a[100],n,i,j,k,l,r;
public:
void get()
{
cout<<".... Program for Weighted Union & Collapsing Find.... nn ";
cout<<"Enter The size :";
cin>>n;
cout<<"Enter the Elements :";
for(i=1;i<=n;i++)
{
cin>>a[i];
}
cout<<"n";
for(i=1;i<=n;i++)
{
cout<<a[i]<<" ";
}
}
void wunion()
{
cout<<"n Enter the two roots for union :n";
cin>>j>>k;
int temp;
temp=a[j]+a[k];
if(a[j]>a[k])
{
a[j]=k;
a[k]=temp;
}
else
{
a[k]=j;
a[j]=temp;
}
cout<<"n";
for(i=1;i<=n;i++)
{
cout<<a[i]<<" ";
}
}
void wfind()
{
cout<<"n Enter the element to find root :";
cin>>l;

34
r=l;
while(a[r]>0)
{
r=a[r];
}
cout<<"Root is : "<<r;
while(l!=r)
{
int s=a[l];
a[l]=r;
l=s;
}
}
};
void main()
{
TreeOp t;
clrscr();
t.get();
int ch;
while(ch!=3)
{
cout<<"n 1: Weighted Union 2: Collapsing Find 3: Exit ";
cout<<"nEnter your choice :";
cin>>ch;
switch(ch)
{
case 1:t.wunion();
break;
case 2:t.wfind();
break;
case 3:exit(0);
break;
}
}
getch();
}
/*OUTPUT :-
.... Program for Weighted Union & Collapsing Find....
Enter The size :10
Enter the Elements : -4 1 -4 1 3 2 3 5 -2 9
-4 1 -4 1 3 2 3 5 -2 9
1: Weighted Union 2: Collapsing Find 3: Exit
Enter your choice :2
Enter the element to find root :8
Root is : 3
Enter the two roots for union :

35
1 3
-8 1 1 1 3 2 3 3 -2 9
*/

36
/* Assignment 16 :- Program for searching element from given array using Binary Search. Lab:DAA*/
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int a[1000];
class binary
{
int n,l,h,mid,x;
public:
void get();
void put();
int bsearch(int x);
void sort();
};
void binary::get()
{
cout<<"n Enter the number of elements :" ;
cin>>n;
a[i]=random(20000);
}
void binary::put()
{
{
if(i%8==0)
cout<<endl;
cout<<a[i]<<'t';
}
}
int binary::bsearch(int x)
{
l=1;
h=n;
while(l<=h)
{
mid=(l+h)/2;
if(x<a[mid])
h=mid-1;
else if(x>a[mid])
l=mid+1;
else
{
return mid;
}
}
return 0;
}
void binary::sort()

37
{
for(int i=j;i<=n;i++)
{
if(a[i]<a[j])
{
int temp=a[i];
a[i]=a[j];
a[j]=temp;
}
}
}
void main()
{
clrscr();
cout<<"n*** Program for Binary Search ***n";
int x,y,i,yes,no;
clock_t e,s;
binary b;
b.get();
b.sort();
cout<<"n Sorted elements are :"<<endl;
b.put();
cout<<"n Enter elements You want to find :"<<endl;
cin>>x;
s=clock();
y=b.bsearch(x);
cout<<"find at Position : "<<y<<endl;
b.put();
e=clock();
cout<<"n Time Complexity is :- "<<((e-s)/CLK_TCK);
getch();
}
/* Output :-
*** Program for Binary search ***
Enter the number of elements :10
Sorted elements are :
79 211 665 3915 4343 6702 7114
10739 14006 18997
Enter elements You want to find :
79
find at Position : 1
79 211 665 3915 4343 6702 7114
10739 14006 18997
Time Complexity is :- 0
*/

38
/* Assignment 17 :- Program for to find maximum and minimum from a given array using maxmin.
Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int max,min,n;
class sai
{
int a[100];
public:
int j,i;
void get();
void put();
void maxmin(int,int,int &,int &);
void show();
};
void sai::get()
{
cout<<"n Enter the Size of array :- ";
cin>>n;
for(i=1;i<=n;i++)
{
a[i]=random(1000);
}
}
void sai::put()
{
cout<<"n show The Element of array :- n";
for(i=1;i<=n;i++)
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void sai::maxmin(int i,int j,int &max,int &min)
{
int mid,max1,min1,max2,min2;
if(i==j)
{
max=min=a[i];
}
else if(i==j-1)
{
// cout<<a[i]<<" "<<a[j];
if(a[i]<a[j])
{
max=a[j];

39
min=a[i];
}
else
{
max=a[i];
min=a[j];
}
}
else
{
mid=(i+j)/2;
maxmin(i,mid,max1,min1);
maxmin(mid+1,j,max2,min2);
max=max1>max2?max1:max2;
min=min1<min2?min1:min2;
}
}
void sai::show()
{
cout<<"n The maximum element is :- "<<max;
cout<<"n The Minimum element is :- "<<min;
}
void main()
{
clrscr();
cout<<"nt*** Program for to find maximum and minimum from a given array using maxmin ***nt";
sai s;
clock_t e,l;
s.get();
s.put();
e=clock();
s.maxmin(1,n,max,min);
l=clock();
s.show();
cout<<"n The Time Complexity is :- "<<(l-e)/CLK_TCK;
getch();
}
/* OUTPUT :-
*** Program for to find maximum and minimum from a given array using max
min ***
Enter the Size of array :- 5
show The Element of array :-

40
10 3 335 33 355
The maximum element is :- 355
The Minimum element is :- 3
The Time Complexity is :- 0
*/

41
/* Assignment 18 :- Program for Ascending Merge Sort ... Lab :DAA */
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int n;
class Merge
{
int a[1000],i,j;
public:
void read();
void merge_sort(int l,int h);
void merge1(int l,int m,int h);
void disp();
};
void Merge::read()
{
for(i=0;i<n;i++)
{
a[i]=random(20000);
}
}
void Merge::merge_sort(int l,int h)
{
int m1;
if(l<h)
{
m1=int((l+h)/2);
merge_sort(l,m1);
merge_sort(m1+1,h);
merge1(l,m1,h);
}
}
void Merge::merge1(int l,int m,int h)
{
int h1=l,b[1800];
int i=l;
j=m+1;
while((h1<=m)&&(j<=h))
{
if(a[h1]<=a[j])
{
b[i]=a[h1];
i++;
h1++;
}
else
{
b[i]=a[j];

42
i++;
j++;
}
}
if(h1<=m)
{
while(h1<=m)
{
b[i]=a[h1];
i++;
h1++;
}
}
else
{
while(j<=h)
{
b[i]=a[j];
i++;
j++;
}
}
for(int k=l;k<=h;k++)
a[k]=b[k];
}
void Merge::disp()
{
for(i=0;i<n;i++)
{
cout<<a[i]<<"t";
if((i+1)%9==0)
cout<<endl;
}
}
void main()
{
clrscr();
randomize();
clock_t s,e;
int l,h;
Merge m;
cout<<"Program for Ascending Merge Sort ...nn";
cout<<"Enter the Element:";
cin>>n;
h=n-1;
l=0;
m.read();
cout<<"nnDisplay the ArrayElement=nn";
m.disp();
s=clock();
m.merge_sort(l,h);

43
e=clock();
cout<<"nAfter Sorting=n";
m.disp();
cout<<"nTime Complexity is:= "<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
Program for Ascending Merge Sort ...
Enter the Element:20
Display the ArrayElement=
1217 2426 16497 2396 1635 1326 17865 18869 9981
18029 3826 1749 9149 5263 17811 5421 3775 19800
6145 17186
After Sorting=
1217 1326 1635 1749 2396 2426 3775 3826 5263
5421 6145 9149 9981 16497 17186 17811 17865 18029
18869 19800
Time Complexity is:= 0
*/

44
/* Assignment 19 :- Program for Descending Merge Sort ... Lab:DAA */
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int n;
class Merge
{
int a[1000],i,j;
public:
void read();
void merge_sort(int l,int h);
void merge1(int l,int m,int h);
void disp();
};
void Merge::read()
{
for(i=0;i<n;i++)
{
a[i]=random(20000);
}
}
void Merge::merge_sort(int l,int h)
{
int m1;
if(l<h)
{
m1=int((l+h)/2);
merge_sort(l,m1);
merge_sort(m1+1,h);
merge1(l,m1,h);
}
}
void Merge::merge1(int l,int m,int h)
{
int h1=l,b[1800];
int i=l;
j=m+1;
while((h1<=m)&&(j<=h))
{
if(a[h1]>=a[j])
{
b[i]=a[h1];
i++;
h1++;
}
else
{
b[i]=a[j];
i++;

45
j++;
}
}
if(h1<=m)
{
while(h1<=m)
{
b[i]=a[h1];
i++;
h1++;
}
}
else
{
while(j<=h)
{
b[i]=a[j];
i++;
j++;
}
}
for(int k=l;k<=h;k++)
a[k]=b[k];
}
void Merge::disp()
{
for(i=0;i<n;i++)
{
cout<<a[i]<<"t";
if((i+1)%9==0)
cout<<endl;
}
}
void main()
{
clrscr();
randomize();
clock_t s,e;
int l,h;
Merge m;
cout<<"Program For Descending Merge Sort ....nn";
cout<<"Enter the Element:";
cin>>n;
h=n-1;
l=0;
m.read();
cout<<"nnDisplay the ArrayElement=nn";
m.disp();
s=clock();
m.merge_sort(l,h);
e=clock();

46
cout<<"nAfter Sorting=n";
m.disp();
cout<<"nTime Com.= "<<((e-s)/CLK_TCK);
getch();
}
/* OUTPUT :-
Program For Descending Merge Sort ....
Enter the Element:20
Display the ArrayElement=
10358 1643 9472 3864 102 5807 4162 15154 16666
9315 15129 6801 8252 4668 8776 12038 2719 966
5570 6927
After Sorting=
16666 15154 15129 12038 10358 9472 9315 8776 8252
6927 6801 5807 5570 4668 4162 3864 2719 1643
966 102
Time Com.= 0
*/

47
/* Assignment 20:- Program for Ascending Quick Sort. Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int n,a[1000];
class q_sort
{
public:
void get();
void put();
void quick_sort(int,int);
int partition(int,int);
};
void q_sort::get()
{
cout<<"n Enter the Size Of Array := ";
cin>>n;
{
a[i]=random(2000);
}
}
void q_sort::put()
{
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void q_sort::quick_sort(int p,int q)
{
int j;
if(p<q)
{
j=partition(p,q);
quick_sort(p,j-1);
quick_sort(j+1,q);
}
}
int q_sort::partition(int m,int p)
{
int v=a[m];
int i=m+1;
int j=p;
while(i<=j)
{
while(a[i]<=v)
i=i+1;

48
while(a[j]>=v)
j=j-1;
if(i<j)
{
p=a[i];
a[i]=a[j];
a[j]=p;
}
}
a[m]=a[j];
a[j]=v;
return j;
}
void main()
{
clrscr();
clock_t e,s;
q_sort q;
cout<<"n.... Program For Ascending Quick Sort ......nn";
q.get();
cout<<"n Display the element of array before sort :=nn";
q.put();
s=clock();
q.quick_sort(1,n);
e=clock();
cout<<"n Display the element of array before sort :=n";
q.put();
cout<<"n The time Complexity :="<<(e-s)/CLK_TCK;
getch();
}
/*OUTPUT :-
.... Program For Ascending Quick Sort ......
Enter the Size Of Array := 10
Display the element of array before sort :=
21 7 670 66 711 434 1073
391 1400 1899
7 21 66 391 434 670 1073
711 1400 1899
The time Complexity :=0
*/

49
/* Assignment 20:- Program for Descending Quick Sort. Lab:DAA */
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int n,a[1000];
class q_sort
{
public:
void get();
void put();
void quick_sort(int,int);
int partition(int,int);
};
void q_sort::get()
{
cout<<"n Enter the Size Of Array := ";
cin>>n;
{
a[i]=random(2000);
}
}
void q_sort::put()
{
{
if(i%8==0)
cout<<"n";
cout<<a[i]<<"t";
}
}
void q_sort::quick_sort(int p,int q)
{
int j;
if(p<q)
{
j=partition(p,q);
quick_sort(p,j-1);
quick_sort(j+1,q);
}
}
int q_sort::partition(int m,int p)
{
int v=a[m];
int i=m+1;
int j=p;
while(i<=j)
{
while(a[i]>=v)
i=i+1;

50
while(a[j]<=v)
j=j-1;
if(i<j)
{
p=a[i];
a[i]=a[j];
a[j]=p;
}
}
a[m]=a[j];
a[j]=v;
return j;
}
void main()
{
clrscr();
clock_t e,s;
q_sort q;
cout<<"n.... Program For Descending Quick Sort ......nn";
q.get();
cout<<"n Display the element of array before sort :=nn";
q.put();
s=clock();
q.quick_sort(1,n);
e=clock();
cout<<"n Display the element of array before sort :=n";
q.put();
cout<<"n The time Complexity :="<<(e-s)/CLK_TCK;
getch();
}
/*OUTPUT :-
.... Program For Descending Quick Sort ......
Enter the Size Of Array := 10
21 7 670 66 711 434 1073
391 1400 1899
1899 1400 1073 670 711 434 391
66 21 7
The time Complexity :=0
*/

51
/* Assignment 22 :- Program for Strasans matrix multiplication. Lab:DAA */
#include<conio.h>
#include<time.h>
class mmu1
{
int a[3][3],b[3][3],c[3][3],p,q,r,s,t,u,v,i,j;
public:
void get();
void put();
void formula();
};
void mmu1::get()
{
cout<<"nEnter the matrix 1 :- ";
for(i=1;i<=2;i++)
for(j=1;j<=2;j++)
cin>>a[i][j];
cout<<"nEnter the matrix 2 :- ";
for(i=1;i<=2;i++)
for(j=1;j<=2;j++)
cin>>b[i][j];
}
void mmu1::formula()
{
p=((a[1][1]+a[2][2])*(b[1][1]+b[2][2]));
q=((a[2][1]+a[2][2])*(b[1][1]));
r=((a[1][1])*(b[1][2]-b[2][2]));
s=((a[2][2])*(b[2][1]-b[1][1]));
t=((a[1][1]+a[1][2])*(b[2][2]));
u=((a[2][1]-a[1][1])*(b[1][1]+b[1][2]));
v=((a[1][2]-a[2][2])*(b[2][1]+b[2][2]));
c[1][1]=p+s - t+v;
c[1][2]=r+t;
c[2][1]=q+s;
c[2][2]=p+r - q+u;
}
void mmu1::put()
{
for(int i=1;i<=2;i++)
{
for(int j=1;j<=2;j++)
cout<<c[i][j]<<" ";
cout<<"n";
}
}
void main()
{
clrscr();
cout<<"nt*** Program for Stranssen's Matrix Multiplication ***nt";

52
mmu1 m;
clock_t e,s;
m.get();
s=clock();
m.formula();
cout<<"nOutput :- "<<endl;
m.put();
e=clock();
cout<<"n Time complexity :- "<<((e-s)/CLK_TCK);
getch();
}
/*OUTPUT :-
*** Program for Stranssen's Matrix Multiplication ***
Enter the matrix 1 :-
1 1
1 1
Enter the matrix 2 :-
2 2
2 2
Output :-
4 4
4 4
Time complexity :- 0 */

53
/* Assignment 23 :- Program for Knapsack solutions. Lab:DAA */
#include<conio.h>
#include<time.h>
int m,n;
class knapsack
{
float p[20],w[20],x[20],i,j,sum;
public:
void get();
void order();
void knap(int,int);
void show();
};
void knapsack::get()
{
cout<<"nEnter the element size & sack size :- n";
cin>>n>>m;
cout<<"nEnter the profit :- n";
for(i=1;i<=n;i++)
cin>>p[i];
cout<<"nEnter the weight :- n";
for(i=1;i<=n;i++)
cin>>w[i];
}
void knapsack::order()
{
for(i=1;i<=n;i++)
for(j=1;j<n;j++)
{
if((p[j]/w[j])<=(p[j+1]/w[j+1]))
{
int temp=p[j];
p[j]=p[j+1];
p[j+1]=temp;
temp=w[j];
w[j]=w[j+1];
w[j+1]=temp;
}
}
}
void knapsack::knap(int m,int n)
{
int u;
sum=0.0;
for(i=1;i<=n;i++)
x[i]=0.0;
u=m;

54
for(i=1;i<=n;i++)
{
if(w[i]>u)
break;
x[i]=1.0;
u=u-w[i];
}
if(i<=n)
x[i]=u/w[i];
for(i=1;i<=n;i++)
sum=sum+(p[i]*x[i]);
}
void knapsack::show()
{
for(i=1;i<=n;i++)
cout<<x[i]<<" ";
cout<<"n---------------------n";
cout<<"Profit :- "<<sum<<"n";
cout<<"n---------------------n";
}
void main()
{
clrscr();
cout<<"nt*** Program for Knapsack Solution ***nt";
knapsack k;
k.get();
k.order();
k.knap(m,n);
k.show();
getch();
}
/* OUTPUT :-
*** Program for Knapsack Solution ***
Enter the element size & sack size :-
7 15
Enter the profit :-
10 5 15 7 6 8 3
Enter the weight :-
2 3 5 7 1 4 1
1 1 1 1 1 0.666667 0
---------------------
Profit :- 45.333332
---------------------
*/

55
/* Assignment 24:-Minmum cost spanning tree using prims algorithm Lab:DAA */
#include<conio.h>
int g[100][100],tree[100],n;
class spanning
{
public:
void get()
{
cout<<"Enter the number of nodes :";
cin>>n;
cout<<"n Enter the graph n";
{
{
cin>>g[i][j];
}
}
}
void dis()
{
cout<<"n The Graph Is :n";
{
cout<<"n";
{
cout<<g[i][j]<<" ";
}
}
}
void prims()
{
int total=0,v1,v2;
for(int l=1;l<=n;l++)
{
tree[l]=0;
}
tree[1]=1;
cout<<"n V1 V2 min_dist : ";
for(int k=2;k<=n;k++)
{
int min_dist=30000;
{
{
if(g[i][j] && ((tree[i] && !tree[j])||(!tree[i]&&tree[j])))
{

56
if(g[i][j]<min_dist)
{
min_dist=g[i][j];
v1=i;
v2=j;
}
}
}
}
cout<<"n"<<v1<<" "<<v2<<" "<<min_dist;
tree[v1]=1;
tree[v2]=1;
total=total+min_dist;
}
cout<<"n Cost of spanning tree is : "<<total;
}
};
void main()
{
spanning s;
clrscr();
cout<<"nt. Program For Minimum cost spanning tree Usin Prims Algorithm .tnn";
s.get();
s.dis();
s.prims();
getch();
}
/* OUTPUT :-
Enter the number of nodes :6
Enter the graph
0 3 0 0 2 0
3 0 2 4 0 0
0 2 0 0 5 2
0 4 0 0 1 0
2 0 5 1 0 6
0 0 2 0 6 0
The Graph Is :
0 3 0 0 2 0
3 0 2 4 0 0
0 2 0 0 5 2
0 4 0 0 1 0
2 0 5 1 0 6
0 0 2 0 6 0
V1 V2 min_dist :
1 5 2
4 5 1
1 2 3
2 3 2

57
3 6 2
Cost of spanning tree is : 10
*/

58
/* Assignment 25 :- Program for demonstrate Kruskal Algorithm. Lab:DAA */
#include<conio.h>
#define INFINITY 999
typedef struct Graph
{
int v1;
int v2;
int cost;
}GR;
GR G[20];
int tot_edges,tot_nodes;
void create();
void spanning_tree();
int Minimum(int);
void main()
{
clrscr();
cout<<"nt Graph Creation by adjacency matrix ";
create();
spanning_tree();
getch();
}
void create()
{
int k;
cout<<"n Enter Total number of nodes: ";
cin>>tot_nodes;
cout<<"n Enter Total number of edges: ";
cin>>tot_edges;
for(k=1;k<=tot_edges;k++)
{
cout<<"n Enter Edge in (V1 V2)form ";
cin>>G[k].v1>>G[k].v2;
cout<<"n Enter Corresponding Cost ";
cin>>G[k].cost;
}
}
void spanning_tree()
{
int count,k,v1,v2,i,j,tree[10][10],pos,parent[10];
int sum;
int Find(int v2,int parent[]);
void Union(int i,int j,int parent[]);
count=0;
k=1;
sum=0;
for(i=1;i<=tot_nodes;i++)
parent[i]=i;
while(count!=tot_nodes-1)
{

59
pos=Minimum(tot_edges);//finding the minimum cost edge
if(pos==-1)//Perhaps no node in the graph
break;
v1=G[pos].v1;
v2=G[pos].v2;
i=Find(v1,parent);
j=Find(v2,parent);
if(i!=j)
{
tree[k][1]=v1;//storing the minimum edge in array tree[]
tree[k][2]=v2;
k++;
count++;
sum+=G[pos].cost;//accumulating the total cost of MST
Union(i,j,parent);
}
G[pos].cost=INFINITY;
}
if(count==tot_nodes-1)
{
cout<<"n Spanning tree is...";
cout<<"n--------------------------n";
for(i=1;i<=tot_nodes-1;i++)
{
cout<<tree[i][1];
cout<<" - ";
cout<<tree[i][2];
cout<<"]";
}
cout<<"n--------------------------";
cout<<"nCost of Spanning Tree is = "<<sum;
}
else
{
cout<<"There is no Spanning Tree";
}
}
int Minimum(int n)
{
int i,small,pos;
small=INFINITY;
pos=-1;
for(i=1;i<=n;i++)
{
if(G[i].cost<small)
{
small=G[i].cost;
pos=i;
}
}
return pos;

60
}
int Find(int v2,int parent[])
{
while(parent[v2]!=v2)
{
v2=parent[v2];
}
return v2;
}
void Union(int i,int j,int parent[])
{
if(i<j)
parent[j]=i;
else
parent[i]=j;
}
/* Output :-
Enter Edge in (V1 V2)form 1 4
Enter Corresponding Cost 4
Spanning tree is...
--------------------------
2 - 3]1 - 3]2 - 4]
--------------------------
Cost of Spanning Tree is = 6
*/

61
/* Assignment 26 :- Program for single source shortest path. Lab:DAA */
#include<conio.h>
int n;
class single
{
int v,cost[10][10],i,j,s[10];
float dist[10];
public:
void get();
void sisource();
void display();
};
void single::get()
{
cout<<"nEnter the no. of vertices :- n";
cin>>n;
cout<<"nEnter the adjency matrix :- n";
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
cin>>cost [i][j];
if(cost [i][j]==-1)
cost [i][j]=9999;
}
}
void single::sisource()
{
v=1;
for(i=1;i<=n;i++)
{
s[i]=0;
dist[i] = cost [v][i];
}
s[v]=1;
dist[v]=0.0;
int minu,u;
for(int num=2;num<=n;num++)
{
for(i=1;i<=n;i++)
if(s[i]==0)
minu=dist[i];
for(i=1;i<=n;i++)
{
if(s[i]==0 && dist[i]<minu)
{
minu=dist[i];
u=i;
}
}
s[u]=1;

62
for(i=1;i<=n;i++)
{
if(cost [u][i]>0 && cost [u][i] < 9999 && s[i]==0) {
if(dist[i] > (dist [u] + cost[u][i]))
{
dist [i]= dist [u] + cost [u][i];
}
}
}
}
}
void single::display()
{
cout<<endl;
for(i=1;i<=n;i++)
{
cout<<"distance from 1------------>"<<i<<"t";
cout<<dist[i]<<" ";
cout<<endl;
}
}
void main()
{
clrscr();
single g;
g.get();
g.sisource();
g.display();
getch();
}
/* Output :-
Enter the no. of vertices :- 6
Enter the adjency matrix :-
0 50 45 10 -1 -1
-1 0 10 15 -1 -1
-1 -1 0 -1 30 -1
20 -1 -1 0 15 -1
-1 20 35 -1 0 -1
-1 -1 -1 -1 3 0
distance from 1------------>1 0
distance from 1------------>2 45
distance from 1------------>3 45
distance from 1------------>4 10
distance from 1------------>5 25
distance from 1------------>6 9999
*/

64
/* Assignment 27 :- Implementation of 0/1 knapsack. Lab:DAA */
#include<conio.h>
#include<stdlib.h>
int table[10][10];
int w[100],v[100];
int W,n;
class knap
{
public:
knap()
{
cout<<"ntt 0/1 Knapsack Problem using Dynamic Programming"; /*initialization of table*/
{
for(int j=0;j<=W;j++)
{
table[i][j]=0;
}
}
}
void get()
{
cout<<"n Enter how many products you want to declare :- n"; cin>>n;
cout<<"n Enter Knapsack size :n";
cin>>W;
cout<<"n Enter "<<n<<" products weight and profit :- n"; for(int i=1;i<=n;i++)
{ cout<<"n Enter Product "<<i<<" weight :- t";
cin>>w[i];
cout<<"n Enter Product "<<i<<" profit :- t";
cin>>v[i];
}
}
int max(int a,int b)
{
if(a>b)
return a;
else
return b;
}
void find_item(int i,int k,int w[5])
{
cout<<"nFor the Knapsack...n";
while(i>0 && k>0)
{
if(table[i][k]!=table[i-1][k])
{
cout<<"nItem "<<i<<" is selectedn";
k=k-w[i];
i=i-1;
}

65
else
i=i-1;
}
}
void DKP(int n,int W,int w[5],int v[5])
{
int i,j;
int val1,val2;
for(i=0;i<=n;i++)
{
for(j=0;j<=W;j++)
{
table[i][0]=0;
table[0][j]=0;
}
}
for(i=1;i<=n;i++)
{
for(j=1;j<=W;j++)
{
if(w[i]<=j)
{
val1=table[i-1][j];
val2=v[i]+table[i-1][j-w[i]];
table[i][j]=max(val1,val2);
}
else
table[i][j]=table[i-1][j];
}
}
cout<<"n Table constructed using dynamic programming is...n";
for(i=0;i<=n;i++)
{
for(j=0;j<=W;j++)
cout<<table[i][j]<<"t";
cout<<"n";
}
find_item(n,W,w);
}
};
void main()
{
knap k;
clrscr();
k.get();
k.DKP(n,W,w,v);
getch();
}
/* Output :-
Enter how many products you want to declare :- 4

66
Enter knapsack size :- 5
Enter 4 product weight and profit :-
Enter product 1 weight :- 2
Enter product 1 weight :- 3
Enter Product 2 weight :- 3
Enter Product 2 profit :- 4
Table constructed using dynamic programming is...
0 0 0 0 0 0
0 0 3 3 3 3
0 0 3 4 4 7
0 0 3 4 5 7
0 0 3 4 5 7
For the Knapsack...
Item 2 is selected
Item 1 is selected
*/

67
/* Assignment 28 :- Program for longest common subsequence. Lab:DAA */
#include<conio.h>
#include<string.h>
#include<stdio.h>
void print_lcs(char b[][20],char x[],int i,int j)
{
if(i==0 || j==0)
return;
if(b[i][j]=='c')
{
print_lcs(b,x,i-1,j-1);
cout<<x[i-1]<<"t";
}
else
if(b[i][j]=='u')
print_lcs(b,x,i-1,j);
else
print_lcs(b,x,i,j-1);
}
void lcs_length(char x[],char y[])
{
int m,n,i,j,c[20][20];
char b[20][20];
m=strlen(x);
n=strlen(y);
for(i=0;i<=m;i++)
c[i][0]=0;
for(i=0;i<=n;i++)
c[0][i]=0;
for(i=1;i<=m;i++)
for(j=1;j<=n;j++)
{
if(x[i-1]==y[j-1])
{
c[i][j]=c[i-1][j-1]+1;
b[i][j]='c'; //c stands for left up cross
}
else
if(c[i-1][j]>=c[i][j-1])
{
c[i][j]=c[i-1][j];
b[i][j]='u'; //u stands for upright or above
}
else
{
c[i][j]=c[i][j-1];
b[i][j]='l'; //l stands for left
}
}
print_lcs(b,x,m,n);

68
}
void lcs()
{
int i,j;
char x[20],y[20];
cout<<"1st sequence :- ";
gets(x);
cout<<"2nd sequence :- ";
gets(y);
cout<<"nLCS are :- ";
lcs_length(x,y);
cout<< "n";
// lcs_length(y,x);
}
void main()
{
clrscr();
char ch;
do
{
lcs();
cout<<"nContinue(y/n) :- ";
cin>>ch;
}
while(ch=='y'||ch=='Y');
getch();
}
/*Output :-
1st sequence :- BAAADC
2nd sequence :- ABAADC
LCS are :- B A A D C
Continue(y/n) :- n
*/

69
/* Assignment 29 :- Implentation of matrix chain multiplication. Lab:DAA */
#include<conio.h>
#define INF 30000
int p[100],m[100][100],s[100][100],k,n,j,q,i,l;
class matrix_chain
{
public:
void get()
{
cout<<"n Enter total matrix count :n";
cin>>n;
cout<<"n Enter Matrix Orders :n";
{
cout<<"nP["<<i<<"]=";
cin>>p[i];
}
matrix_chain1(p,n);
}
void matrix_chain1(int p[],int n)
{
for (i=1;i<=n;i++)
m[i][i]=0;
for (l=2;l<=n;l++)
{
for (i=1;i<=n-l+1;i++)
{
j=i+l-1;
m[i][j]=INF;
for (k=i;k<=j-1;k++)
{
q=m[i][k]+m[k+1][j]+p[i-1]*p[k]*p[j];
if(q<m[i][j])
{
m[i][j]=q;
s[i][j]=k;
}
}
}
}
cout<<"n Total Optimal Scalar Multiplication needed are :- "<<m[1][n];
cout<<"n Array M[i][j] is n";
for(i=1;i<=n;i++)
{
cout<<"n";
for(j=1;j<=n;j++)
cout<<m[i][j]<<"t";
}
cout<<"n Array S[i][j] is :- n";
for(i=1;i<=n;i++)

70
{
cout<<"n";
for(j=1;j<=n;j++)
cout<<s[i][j]<<"t";
}
}
void print_optimal(int i,int j)
{
if (i==j)
cout<<" A "<<i;
else
{
cout<<" ( ";
print_optimal(i,s[i][j]);
print_optimal(s[i][j]+1,j);
cout<<" ) ";
}
}
};
void main()
{
clrscr();
matrix_chain m1;
m1.get();
m1.print_optimal(1,n);
getch();
}
/* Output :-
Enter total matrix count :- 3
Enter Matrix Orders :
P[0]=10
P[1]=100
P[2]=5
P[3]=50
Total Optimal Scalar Multiplication needed are :- 7500
Array M[i][j] is
0 5000 7500
0 0 25000
0 0 0
Array S[i][j] is :-
0 1 2
0 0 2
0 0 0

71
optimal sequence is :-
( ( A 1 A 2 ) A 3 )
*/

72
/* Assignment 30 :- Program for All pair shortest path. Lab:DAA */
#include<conio.h>
class all
{
int s[10][10],a[10][10],i,j,k,n,m;
public:
void get();
int min(int,int);
void find();
void display();
};
int all::min(int m,int n)
{
return(m<n ?m:n);
}
void all::get()
{
cout<<"n Enter the size of element :- n";
cin>>n;
cout<<"nEnter the element in array :- n";
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
cin>>a[i][j];
if(a[i][j]==-1)
{
s[i][j]=9999;
}
else
{
s[i][j]=a[i][j];
}
}
}
}
void all::find()
{
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
for(k=1;k<=n;k++)
{
if(i==j)
{
s[i][j]=0;
}
else
s[i][j]=min(s[i][j],s[i][k]+s[k][j]);
if(s[i][j]>=9999)

73
s[i][j]=0;
}
}
void all::display()
{
cout<<"n display the element after perform operation find :- n";
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
cout<<s[i][j]<<"t";
}
cout<<endl;
}
}
void main()
{
clrscr();
all a;
a.get();
a.find();
a.display();
getch();
}
/*Output :-
Enter the size of element :- 3
Enter the element in array :-
0 4 11
6 0 2
3 -1 0
display the element after perform operation find :-
0 4 6
5 0 2
3 7 0
*/

74
/* Assignment 31 :- Program to demonstrate breath first traversal. Lab:DAA */
#include<conio.h>
class bfstree
{
int reach[20],a[20][20],q[20],n,i,j,f,r,index;
public:
bfstree()
{
f=r=0;
index=1;
}
void get();
void bfs(int);
};
void bfstree::get()
{
cout<<"nEnter number of vertices :- ";
cin>>n;
cout<<"nEnter Adjacency matrix :- ";
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
reach[i]=0;
cin>>a[i][j];
}
for(i=1;i<=n;i++)
if(reach[i]==0)
bfs(i);
}
void bfstree::bfs(int index)
{ f=r=0;
reach[index]=1;
f++;
r++;
q[r]=index;
while(f<=r)
{
index=q[f];
f++;
cout<<index<<"t";
for(j=1;j<=n;j++)
{
if(a[index][j]==1 && reach[j]!=1)
{
reach[j]=1;
r++;
q[r]=j;
}
}
}

75
}
void main()
{
clrscr();
bfstree b;
b.get();
getch();
}
/* Output :-
Enter number of vertices :- 6
Enter Adjacency matrix :-
0 1 1 0 0 0
1 0 0 1 0 0
1 0 0 0 0 1
0 1 0 0 1 1
0 0 0 1 0 0
0 0 1 1 0 0
1 2 3 4 6 5
*/

76
/* Assignment 32 :- Program to demonstrate depth fisrt traversal. Lab:DAA */
#include<conio.h>
class dfstree
{
int a[20][20], visited[20],n,i,j;
public:
void dfs(int);
void get();
};
void dfstree::get()
{
cout<<"nEnter the number of node :- ";
cin>>n;
for(i=1;i<=n;i++)
visited[i]=0;
cout<<"nEnter the adjancy matrix :- ";
for(i=1;i<=n;i++)
{ for(j=1;j<=n;j++)
cin>>a[i][j];
}
for(i=1;i<=n;i++)
if(visited[i]==0)
dfs(i);
}
void dfstree::dfs(int v)
{
int k;
visited[v]=1;
cout<<"t"<<v;
for(k=1;k<=n;k++)
if(a[v][k]==1)
if(visited[k]==0)
dfs(k);
}
void main()
{ clrscr();
dfstree d;
d.get();
getch();
}
/*Output :-
Enter the number of node :- 5
Enter the adjancy matrix :-
0 1 1 0 0
1 0 0 1 1
1 0 0 1 0
0 1 1 0 1
0 1 0 1 0
1 2 4 3 5

78
/* Assignment 33 :- Program for demonstrate Topological sort. Lab:DAA */
#include<conio.h>
class top
{
public :
int
cost[10][10],n1,n,indeg[10],q[10],visit[10],i,j;
int f,r,count;
top()
{
f=r=0;
}
void get ()
{
cout<<"nEnter number of vertices :- ";
cin>>n;
cout<<"nEnter matrix :- n";
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
cin>>cost[i][j];
for(i=1;i<=n;i++)
{
indeg[i]=0;
visit[i]=0;
}
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{ if(cost[i][j]==1)
indeg[j]=indeg[j]+1;
}
cout<<"n Indegree :- n";
cout<<"n";
for(int k=1;k<=n;k++)
{
cout<<"Indgeree of NODE"<<k<<"Is"<<indeg[k]<<"t"<<"n";
}
}
void topo()
{
for(i=1;i<=n;i++)
{
if(indeg[i]==0 && visit[i]!=1)
{
if(f==0 && r==0)
{
f++;
r++;
}
else

79
r++;
q[r]=i;
visit[i]=1;
}
}
while(f<=r)
{
n1=q[f];
f++;
cout<<" "<<n1;
for(j=1;j<=n;j++)
{ if(cost[n1][j]==1 && visit[j]!=1) {
indeg[j]=indeg[j]-1;
if(indeg[j]==0)
{
r++;
q[r]=j;
visit[j]=1;
}
}
}
}
}
};
void main()
{
clrscr();
top p;
p.get();
p.topo();
getch();
}
/* Output :-
Enter number of vertices :- 7
Enter matrix
0 1 1 0 0 0 0
0 0 0 0 1 0 1
0 0 0 0 0 1 0
1 0 0 0 0 1 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 1 1 0
Indegree :
Indgeree of NODE 1 Is :- 1

80
4 1 2 3 7 5 6
*/

81
/* Assignment 34 :- program for n Queen for all solution
Lab:DAA
*/
#include<conio.h>
#include<math.h>
int x[100],n;
class nqueen
{
int z;
public:
void get();
void show();
void queen(int,int);
int place(int,int);
};
void nqueen::get()
{
cout<<"Enter the no of queens :- n";
cin>>n;
x[i]=0;
z=0;
queen(1,n);
}
void nqueen::queen(int k,int n)
{
{
if(place(k,i))
{
x[k]=i;
if(k==n)
{
cout<<endl;z++; cout<<z<<":->";
for( i=1;i<=n;i++)
cout<<x[i]<<"t";
}
else
queen(k+1,n);
}
}
}
int nqueen::place(int k,int i)
{
for(int j=1;j<=k-1;j++)
{
if((x[j]==i) || abs(x[j]-i)==(abs(j-k)))
return 0;
}
return 1;

82
}
void main()
{
clrscr();
nqueen n;
n.get();
getch();
}
/* OutPut :-
Enter the no of queens :-
4
1:->2 4 1 3
2:->3 1 4 2
*/

83
/* Assignment 35 :- program for n Queen for in equivalent solution Lab:DAA */
#include<conio.h>
#include<math.h>
class nqueen
{
int n,x[200],cnt;
public :
nqueen(int);
void putdata();
int place(int);
void NQueen();
};
nqueen :: nqueen(int no)
{
n = no;
cnt = 0;
for(int i = 1;i <= n;i++)
x[i] = 0;
}
void nqueen :: putdata()
{
cout<<"n";
for(int j = 1;j <= n;j++)
{
cout<<x[j]<<"t";
}
}
void nqueen :: NQueen()
{
int k = 1;
x[k] = 0;
while(k > 0)
{
x[k] = x[k] + 1;
if( k == 1 && x[k] > (n/2) )
{
break;
}
while( x[k] <= n && place(k) == 0)
{
x[k] = x[k] + 1;
}
if(x[k] <= n)
{
if( k == n)
{
cnt++;
cout<<"nSolution Number "<<cnt<<" : n";
putdata();

84
}
else
{
k++;
x[k] = 0;
}
}
else
{
k--;
}
}
}
int nqueen :: place(int k)
{
for(int j = 1;j < k;j++)
{
if( x[j] == x[k] || abs(x[j] - x[k]) == abs(j - k) )
return(0);
}
return(1);
}
void main()
{
clrscr();
int no;
cout<<"nEnter number of queen : ";
cin>>no;
if( no == 2 || no == 3)
{
cout<<"nSolution is not possible.";
}
else
{
nqueen n(no);
n.NQueen();
}
getch();
}
/* OUTPUT :-
Enter number of queen : 4
Solution Number 1 :
2 4 1 3
*/

85
/* Assignment 36 :- program for graph coloring Lab:DAA */
#include<conio.h>
#include<time.h>
int c[10][10],n,m;
class graph
{
int i,j,x[100];
public:
void get();
void color(int);
void show();
void nextvalue(int);
};
void graph::get()
{
cout<<"Enter the size of arrayn";
cin>>n;
cout<<"Enter the color for graphn";
cin>>m;
cout<<"Enter the adjancy matrixn";
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
cin>>c[i][j];
}
}
for(i=1;i<=n;i++)
x[i]=0;
color(1);
}
void graph::nextvalue(int k)
{
do
{
x[k]=((x[k]+1)%(m+1));
if(x[k]==0)
return ;
for(j=1;j<=n;j++)
if((c[k][j]!=0)&&(x[k]==x[j]))
break;
if(j==n+1)
return;
}while(1);
}
void graph::color(int k)
{
do
{
nextvalue(k);

86
if(x[k]==0)
return;
if(k==n)
{
cout<<"nColour of graph is :";
for(i=1;i<=n;i++)
cout<<x[i]<<"t";
}
else
color(k+1);
}while(1);
}
void main()
{
clrscr();
graph g;
g.get();
getch();
}
/*OUTPUT :-
Enter the size of array
3
Enter the color for graph
2
Enter the adjancy matrix
0 1 0
1 0 1
0 1 0
Colour of graph is :1 2 1
Colour of graph is :2 1 2
*/

87
/*Assignment 37 :- Program for code 1 using postfix expression Lab:DAA */
#include<conio.h>
class node
{
public:
node *left,*right;
char data[30];
};
class code
{
private:
char expr[30];
node *n,*root;
int f;
public:
void get();
int Isoperand(char);
node *create_tree();
void print(char *);
void mycode(node *,int);
};
void code::get()
{
cout<<"nEnter The Postfix Expresion:";
cin>>expr;
root = create_tree();
mycode(root,0);
}
int code::Isoperand(char c)
{
if((c >= 'A' && c <= 'Z') || (c >= 'a' && c <= 'z'))
return 1;
else
return 0;
}
void code::print(char *t)
{
switch(t[0])
{
case '+':cout<<"ADD ";break;
case '-':cout<<"SUB ";break;
case '*':cout<<"MPY ";break;
case '/':cout<<"DIV ";break;
default:cout<<t;
}
}
node* code::create_tree()
{
int i=0;
node *stack[10];

88
int top = -1;
while(expr[i] != '0')
{
n = new node;
n->data[0] = expr[i];
n->data[1] = '0';
n->left = NULL;
n->right = NULL;
if(Isoperand(expr[i]))
stack[++top] = n;
else
{
n->right = stack[top--];
n->left = stack[top--];
stack[++top] = n;
}
i++;
}
return stack[top];
}
void code::mycode(node *t,int i)
{
if(t->left == NULL && t->right == NULL)
{
cout<<"nLOAD "<<t->data;
return;
}
f = 0;
if(t->right->left != NULL && t->right->right != NULL)
{
mycode(t->right,i);
i++;
cout<<"nSTORE T"<<i;
t->right->data[0] = 'T';
t->right->data[1] = '1';
t->right->data[2] = '0';
f = 1;
}
mycode(t->left,i);
if(f == 1)
{
cout<<"n";
print(t->data);
cout<<"T"<<i;
i--;
}
else
{
cout<<"n";
print(t->data);
cout<<" ";

89
print(t->right->data);
}
}
void main()
{
clrscr();
char ch;
do
{
code obj;
obj.get();
cout<<"nAre You Want To Continue(Y/N):";
cin>>ch;
}while(ch == 'Y' || ch == 'y');
getch();
}
/* OUTPUT :-
Enter The Postfix Expresion:ab+
LOAD a
ADD b
Are You Want To Continue(Y/N):n
*/

90
/* Assignment 38 :- Program for Code 2 Lab:DAA */
#include<conio.h>
#include<stdio.h>
#include<ctype.h>
class vcode2
{
private:
int i,n,cnt,itop,istack[50],icnt;
char prefix[50],top,ch[100];
struct tree
{
char data;
int mr;
tree *left,*right,*parent;
};
public:
struct tree *ltemp,*rtemp,*temp,*root,*current,*stack[20];
vcode1()
{
top=-1;
itop=-1;
cnt=0;
cnt=1;
}
void spush(tree*);
void spop();
int ipop();
void ipush(int);
char *data(tree*);
void findmr(tree *);
void read();
void cal();
void print();
void inorder(tree*);
void preorder(tree*);
void code2(tree*,int);
};
void vcode2::read()
{
cout<<"nENTER THE PREFIX EXPRESSION :";
cin>>prefix;
cout<<"nENTER THE NUMBER OF REGISTERS :";
cin>>n;
}
void vcode2::spush(tree *ele)
{
stack[++top]=ele;
}
void vcode2::spop()
{

91
istack[top--];
}
void vcode2::ipush(int c)
{
istack[++top]=c;
}
int vcode2::ipop()
{
return(istack[itop--]);
}
void vcode2::cal()
{
root=NULL;
for(i=0;prefix[i]!='0';i++)
{
if(root==NULL)
{
root=new tree;
root->data=prefix[i];
root->left=root->right=NULL;
spush(root);
if(isalpha(prefix[i+1]) && isalpha(prefix[i+2]))
{
ltemp=new tree;
ltemp->data=prefix[i+1];
ltemp->left=ltemp->right=NULL;
rtemp=new tree;
rtemp->data=prefix[i+2];
rtemp->left=rtemp->right=NULL;
root->left=ltemp;
root->right=rtemp;
spop();
i++;i++;
}
}
else
if(!(isalpha(prefix[i])))
{
temp= new tree;
temp->data=prefix[i];
temp->left=temp->right=NULL;
current=stack[top];
if(current->left!=NULL)
{
current->right=temp;
spop();
}
else
current->left=temp;
spush(temp);
if(isalpha(prefix[i+1]) && isalpha(prefix[i+2]))

92
{
ltemp=new tree;
ltemp->data=prefix[i+1];
ltemp->left=ltemp->right=NULL;
rtemp=new tree;
rtemp->data=prefix[i+2];
rtemp->left=rtemp->right=NULL;
current=stack[top];
current->left=ltemp;
current->right=rtemp;
spop();
i++;i++;
}
}
else
if(isalpha(prefix[i]))
{
temp= new tree;
temp->data=prefix[i];
temp->left=temp->right=NULL;
current=stack[top];
if(current->left!=NULL)
{
current->right=temp;
spop();
}
else
current->left=temp;
}
}
}
void vcode2::preorder(tree *r)
{
if(r!=NULL)
{
r->left->parent=r;
preorder(r->left);
findmr(r);
cout<<" "<<r->data;
r->right->parent=r;
preorder(r->right);
findmr(r);
}
}
void vcode2::inorder(tree *r)
{
if(r!=NULL)
{
inorder(r->left);
cout<<" "<<r->mr;
inorder(r->right);

93
}
}
void vcode2::findmr(tree *p)
{
int l1,l2;
if(p->left==NULL && p->right==NULL && p->parent->right==p)
p->mr=0;
else
if(p->left==NULL && p->right==NULL && p->parent->left==p)
p->mr=1;
else
if((l1=p->left->mr)!=(l2=p->right->mr))
p->mr=((l1>l2)?l1:l2);
else
if((l1=p->left->mr)==(l2=p->right->mr))
p->mr=l1+1;
}
void vcode2::print()
{
root->parent->data='=';
cout<<"INFIX :";
preorder(root);
cout<<endl;
cout<<"MR VALUES :";
inorder(root);
cout<<endl<<endl;
code2(root,1);
}
void vcode2::code2(tree *t,int icnt)
{
tree *lc,*rc;
if((t->left==NULL) && (t->right==NULL)&& t->parent->left==t)
{
cout<<"LOAD "<<t->data<<" R "<<icnt<<endl;
return;
}
lc=t->left;
rc=t->right;
if(rc->mr==0)
{
code2(lc,icnt);
cout<<data(t)<<" R "<<icnt<<","<<rc->data<<",R"<<icnt<<endl;
}
else
if(lc->mr >=n && rc->mr >=n)
{
code2(rc,icnt);
ipush(++cnt);
cout<<"STORE R"<<icnt<<",T"<<cnt<<endl;
code2(lc,icnt);
cout<<data(t)<<" R"<<icnt<<",T"<<cnt<<" ,R"<<icnt<<endl;

94
cnt=ipop();
}
else
if(lc->mr< rc->mr)
{
code2(rc,icnt);
code2(lc,icnt+1);
cout<<data(t)<<" R"<<icnt+1<<" ,R"<<icnt<<" ,R"<<icnt<<endl;
}
else
//if(lc->mr >=rc->mr &&rc->mr <n)
{
code2(lc,icnt);
code2(rc,icnt+1);
cout<<data(t)<<" R"<<icnt<<" ,R"<<icnt+1<<" ,R"<<icnt<<endl;
}
}
char* vcode2::data(tree *t1)
{
switch(t1->data)
{
case '+': return ("ADD");
case '-': return ("SUB");
case '*': return ("MPY");
case '/': return ("DIV");
}
return 0;
}
main()
{
vcode2 c;
clrscr();
c.read();
c.cal();
c.print();
getch();
return 0;
}
/* OUTPUT :-
ENTER THE PREFIX EXPRESSION :+ab
ENTER THE NUMBER OF REGISTERS :1
INFIX : a + b
MR VALUES : 1 1 0
LOAD a R 1
ADD R 1,b,R1
Null pointer assignment
*/

Final DAA_prints.pdf

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Final DAA_prints.pdf