1. Ex No: 1
MIN HEAP
Date:
AIM
To implement the min heap structure with insert and delete minimum operation using
Java program
ALGORITHM
Step 1: start the program by creating function with min heap property
Step 2: two functions namely insert() and deletemin() are created
Step 3: The insert () is used to insert new element in the tree structure with heap
property.
Step 4: The deletemin() is used to delete the minimum element which is usually a root
node.
Step 5: The two operations are performed satisfying heapness and completeness
property.
Step 6: End of the program.
1
2. PROGRAM:
MIN HEAP
import java.io.*;
class heapalg
{
int maxsize=100,size;
int[] h=new int[maxsize];
public int leftchild(int i)
{
return 2*i;
}
public int rightchild(int i)
{
return 2*i + 1;
}
public int parent(int i)
{
return i/2;
}
public boolean isleaf(int i)
{
return ((i<=size) && (i>size/2));
}
public void swap(int i,int j)
{
int t;
t=h[i];h[i]=h[j];h[j]=t;
}
public void display()
{
System.out.println("The heap elements are:"+"n");
for(int i=1;i<=size;i++)
System.out.println("n"+h[i]);
}
public void insert()
{
size++;
if(size>maxsize)
System.out.println("Heapfull");
else
{
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
h[size]=Integer.parseInt(din.readLine());
}
catch(Exception e){}
insertelt(size);
}
}
public void insertelt(int i)
{
while ((h[parent(i)]>h[i]))
{
int par=parent(i);
swap(par,i);
i=par;
2
5. OUTPUT:
--------
MIN HEAP 1.Insert 2.Delete Min
1
Enter the element:
42
The heap elements are:
42
press 1 to continue:
1
MIN HEAP 1.Insert 2.Delete Min
1
Enter the element:
3
The heap elements are:
3
42
press 1 to continue:
1
MIN HEAP 1.Insert 2.Delete Min
1
Enter the element:
86
The heap elements are:
3
42
86
press 1 to continue:
1
MIN HEAP 1.Insert 2.Delete Min
1
Enter the element:
2
The heap elements are:
2
3
86
42
press 1 to continue:
1
MIN HEAP 1.Insert 2.Delete Min
2
The deleted min elt:2
The heap elements are:
3
42
86
press 1 to continue:
12
.
5
6. Ex No: 2
DEAPS
Date:
AIM
To implement program for deaps structure with insert and delete operations using
Java.
ALGORITHM
Step 1: Start the program by creating Deap Structure.
Step 2: Perform insert and delete functions.
Step 3: The insert() is done with 2 methods namely maxinsert() and mininsert().
Step 4: The delete() is done with 2 methods namely deletemax() and deletemin()
Step 5: The leftChild and rightChild are compared and the appropriate element is
placed in the root node.
Step 6: After the insert and delete operation Deap elements are displayed.
Step 7: Stop of the program.
6
7. PROGRAM
DEAPS
import java.io.*;
class deapsalg
{
int maxsize=100,size;
int[] h=new int[maxsize+1];
public int leftchild(int i)
{
return 2*i;
}
public int rightchild(int i)
{
return 2*i + 1;
}
public int parent(int i)
{
return i/2;
}
public boolean isleaf(int i)
{
return ((i<=size) && (i>size/2));
}
public void swap(int i,int j)
{
int t;
t=h[i];h[i]=h[j];h[j]=t;
}
public void display()
{
System.out.println("The deaps elements are:");
for(int i=1;i<=size+1;i++)
System.out.println("n"+h[i]);
}
public int MaxHeap(int i)
{
int t=i;
while(t!=2 && t!=3)
t=t/2;
if(t==2)
{
return 0;
}
else
{
return 1;
}
}
public int MinPartner(int p)
{
int powvalue=(int) ((Math.floor(Math.log(p)/Math.log(2)))-1);
int partner=p-(int)(Math.pow(2,powvalue));
return partner;
}
public int MaxPartner(int p)
{
int powvalue=(int) ((Math.floor(Math.log(p)/Math.log(2)))-1);
7
8. int partner=p+(int)(Math.pow(2,powvalue));
if(partner>size+1)
partner/=2;
return partner;
public void MinInsert(int i)
}
{
while (parent(i)!=1 && (h[parent(i)]>h[i]))
{
int par=parent(i);
swap(par,i);
i=par;
}
public void MaxInsert(int i)
}
{
while (parent(i) !=1 && (h[parent(i)]<h[i]))
{
int par=parent(i);
swap(par,i);
i=par;
}
public void insert()
}
{
int newelt=0;
size++;
if(size>maxsize)
System.out.println("Deap full");
else
{
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
newelt=Integer.parseInt(din.readLine());
}
catch(Exception e){}
if(size==1)
{
h[2]=newelt;
return;
}
int p=size+1;
h[p]=newelt;
switch(MaxHeap(p))
{
case 1:
int partner=MinPartner(p);
if(h[partner]>h[p])
{
swap(p,partner);
MinInsert(partner);
}
else
MaxInsert(p);
break;
case 0: 8
partner=MaxPartner(p);
9. if(h[partner]<h[p])
{
swap(p,partner);
MaxInsert(partner);
}
else
MinInsert(p);
break;
default:
System.out.println("ERROR");
}
}
public void deletemin()
}
{
if(size==0)
System.out.println("Deap empty");
else
{
System.out.println("The deleted min elt:"+ h[2]);
int i;
int p=size+1;
int t=h[p];
size--;
int small;
for( i=2;2*i<=size+1;i=small)
{
if(h[rightchild(i)]<h[leftchild(i)])
small=rightchild(i);
else
small=leftchild(i);
h[i]=h[small];
}
p=i; t
h[p]=t;
for(i=2;i<=size+1;i++)
{
switch(MaxHeap(i))
{
case 1:
int partner=MinPartner(i);
if(h[partner]>h[i])
{
swap(i,partner);
MinInsert(partner);
}
else
MaxInsert(i);
break;
case 0:
partner=MaxPartner(i);
if(h[partner]<h[i])
{
swap(i,partner);
MaxInsert(partner);
}
else
MinInsert(i);
break;
default:
9
10. System.out.println("ERROR");
}
}
}
public void deletemax()
}
{
if(size==0)
System.out.println("Deap empty");
else
{
System.out.println("The deleted max elt:"+ h[3]);
int i;
int p=size+1;
int t=h[p];
size--;
int big;
for( i=3;2*i<=size+1;i=big)
{
if(h[rightchild(i)]>h[leftchild(i)])
big=rightchild(i);
else
big=leftchild(i);
h[i]=h[big];
}
p=i;
h[p]=t;
for(i=2;i<=size+1;i++)
{
switch(MaxHeap(i))
{
case 1:
int partner=MinPartner(i);
if(h[partner]>h[i])
{
swap(i,partner);
MinInsert(partner);
}
else
MaxInsert(i);
break;
case 0:
partner=MaxPartner(i);
if(h[partner]<h[i])
{
swap(i,partner);
MaxInsert(partner);
}
else
MinInsert(i);
break;
default:
System.out.println("ERROR");
}
}
}
}
public class deaps
}
{
10
12. OUTPUT:
--------
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
20
The deaps elements are:
0
20
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
5
The deaps elements are:
0
5
20
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
3
The deaps elements are:
0
3
20
5
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
7
The deaps elements are:
0
3
20
5
7
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
11
The deaps elements are:
0
3
20
5
7
11
press 1 to continue:
1
12
13. DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
55
The deaps elements are:
0
3
55
5
7
11
20
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
77
The deaps elements are:
0
3
77
5
7
55
20
11
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
88
The deaps elements are:
0
3
88
5
7
77
20
11
55
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
17
The deaps elements are:
0
3
88
5
7
77
20
11
55
13
14. 17
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
1
The deaps elements are:
0
1
88
5
3
77
20
11
55
17
7
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
1
Enter the element:
100
The deaps elements are:
0
1
100
5
3
88
20
11
55
17
7
77
press 1 to continue:
1
DEAPs 1.Insert 2.Delete Min 3.Delete Max
2
The deleted min elt:1
The deaps elements are:
0
3
100
5
7
88
77
11
55
17
20
press 1 to continue:
14
16. Ex.No:3
LEFTIST HEAP
Date:
AIM
To implement the leftist heap with insert and deletemin operation using Java.
ALGORITHM
Step 1: Start the program by defining function.
Step 2: We know heap as the root node with minimum element.
Step 3: The insert and delete operations are performed with the help of combining 2
trees.
Step 4: The insert operation is performed by combining the two leftist trees.
Step 5: The deletemin() is used to delete the minimum element in the heap.
Step 6: After the insert and delete operations leftist heap elements are displayed.
Step 7: Stop the program.
16
17. PROGRAM
LEFTIST HEAP
import java.io.*;
class node
{
public int data;
public node LC,RC;
public int shortest;
}
class minleftist
{
node root = null;
public void insert()
{
int newelt=0;
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
newelt=Integer.parseInt(din.readLine());
}
catch(Exception e){}
node temp = new node();
temp.data=newelt;
temp.LC=temp.RC=null;
temp.shortest=1;
if(root==null)
root=temp;
else
root=meld(root,temp);
}
public node meld(node a, node b)
{
if(a.data > b.data)
{
node t;
t=a;
a=b;
b=t;
}
if(a.RC==null)
a.RC=b;
else
a.RC=meld(a.RC,b);
if((a.LC==null) || (a.LC.shortest < a.RC.shortest))
{
node t=new node();
t=a.LC;
a.LC=a.RC;
a.RC=t;
}
if(a.RC==null)
a.shortest=1;
else
a.shortest=a.RC.shortest+1;
return a;
}
public void remove()
{
17
18. System.out.println("Deleted element is "+root.data+"n");
root=meld(root.LC,root.RC);
public void display()
}
{
if(root==null)
System.out.println("EMPTY");
else
{
System.out.println("nIn Order");
dispin(root);
}
}
public void dispin(node currentnode)
{
if(currentnode!=null)
{
dispin(currentnode.LC);
System.out.println(currentnode.data+" "+"SHORTEST "+currentnode.shortest);
dispin(currentnode.RC);
}
}
};
class LeftistTree
{
public static void main(String args[ ])throws IOException
{
int ch=0,cont=0;
minleftist m = new minleftist();
do
{
System.out.println("LEFTIST TREE 1. Insert 2. Delete");
DataInputStream din = new DataInputStream(System.in);
try
{
ch=Integer.parseInt(din.readLine());
}
catch(Exception e){}
if(ch==1)
{
m.insert();
m.display();
}
else if(ch==2)
{
m.remove();
m.display();
}
else
{
System.out.println("Enter the correct choice");
}
System.out.println("press 1 to continue:");
try
{
cont=Integer.parseInt(din.readLine());
}
catch(Exception e){}
18
19. }while(cont==1);
}
OUTPUT:
}
-------
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
50
In Order
50 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
8
In Order
50 SHORTEST 1
8 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
13
In Order
50 SHORTEST 1
8 SHORTEST 2
13 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
11
In Order
50 SHORTEST 1
8 SHORTEST 2
13 SHORTEST 1
11 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
20
In Order
13 SHORTEST 1
11 SHORTEST 2
20 SHORTEST 1
8 SHORTEST 2
50 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
19
20. 18
In Order
13 SHORTEST 1
11 SHORTEST 2
20 SHORTEST 1
8 SHORTEST 2
50 SHORTEST 1
18 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
2
In Order
13 SHORTEST 1
11 SHORTEST 2
20 SHORTEST 1
8 SHORTEST 2
50 SHORTEST 1
18 SHORTEST 1
2 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
1
Enter the element:
7
In Order
13 SHORTEST 1
11 SHORTEST 2
20 SHORTEST 1
8 SHORTEST 2
50 SHORTEST 1
18 SHORTEST 1
2 SHORTEST 2
7 SHORTEST 1
press 1 to continue:
1
LEFTIST TREE 1. Insert 2. Delete
2
Deleted element is 2
In Order
13 SHORTEST 1
11 SHORTEST 2
20 SHORTEST 1
8 SHORTEST 2
50 SHORTEST 1
18 SHORTEST 1
20
22. Ex no: 4
AVL TREE
Date:
AIM
To implement the AVL tree with insert & delete operations using Java.
ALGORITHM
Step 1: Start the program by defining the functions.
Step 2: Insert the elements to the AVL tree.
Step 3: Check the tree if it is balanced or not.
Step 4: The balance factor is one of 0, 1 and -1.
Step 5: If it is not balanced, balance the tree using
(i) Left-left
(ii) Left-right
(iii) Right-left
(iv) Right-right
Balancing
Step 6: And if the tree is balanced and then the insert() and the delete() operations are
performed.
Step 7: Stop the program.
22
23. PROGRAM
AVL TREE
import java.io.*;
class node
{
public int data;
public node LC,RC;
public int bf;
}
class avltree
{
node root = null;
public boolean insert()
{
int newelt=0;
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
newelt=Integer.parseInt(din.readLine());
}
catch(Exception e){}
if(root==null)
{
node y=new node();
y.data=newelt;
y.bf=0;
y.LC=null;
y.RC=null;
root=y;
return true;
}
node f,a,q,p;
node b,c;
int d;
node y=new node();
boolean found, unbalanced;
f=null;
a=root;
p=root;
q=null;
found=false;
while (p!=null && found!=true)
{
if(p.bf!=0) {a=p;f=q;}
if(newelt<p.data){q=p;p=p.LC;}
else if(newelt>p.data){q=p;p=p.RC;}
else {y=p;found=true;}
}
if(found==false)
{
y.data=newelt;
y.bf=0;
y.LC=null;
y.RC=null;
if(newelt<q.data)
q.LC=y;
else
23
33. Ex.No:5
B-TREE
Date:
AIM
To implement the b-tree with insert and delete operations using Java.
ALGORITHM
Step 1: Start the program by defining function.
Step 2: Declare the class btree
Step 3: The insert and delete operations are performed
Step 4: To insert, check if root is empty, if it is empty
insert the element as root.
Step 5: If it is greater insert it into right sub tree.
Step 6: Otherwise, insert it into left sub tree
Step 7: Use the function split, to split the nodes
Step 8: Call the function display to display
data1,data2,address and parent
Step 9: End of the program
33
37. System.out.println("B-Trees");
DataInputStream in=new DataInputStream(System.in);
btree bt=new btree();
int x,ch;
do
{
System.out.println("Enter the element");
x=Integer.parseInt(in.readLine());
bt.insert(x);
System.out.println("To continue...press 1");
ch=Integer.parseInt(in.readLine());
}while(ch==1);
}
}
37
38. OUTPUT:
--------
B-Trees
Enter the element
52
data1::52 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
45
data1::45 data2::52 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
89
data1::45 data2::0 Address::bnode@130c19b parent::bnode@923e30
data1::89 data2::0 Address::bnode@1f6a7b9 parent::bnode@923e30
data1::52 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
12
data1::12 data2::45 Address::bnode@130c19b parent::bnode@923e30
data1::89 data2::0 Address::bnode@1f6a7b9 parent::bnode@923e30
data1::52 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
56
data1::12 data2::45 Address::bnode@130c19b parent::bnode@923e30
data1::56 data2::89 Address::bnode@1f6a7b9 parent::bnode@923e30
data1::52 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
1
data1::1 data2::0 Address::bnode@7d772e parent::bnode@923e30
data1::45 data2::0 Address::bnode@11b86e7 parent::bnode@923e30
data1::56 data2::89 Address::bnode@1f6a7b9 parent::bnode@923e30
data1::12 data2::52 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
32
data1::1 data2::0 Address::bnode@7d772e parent::bnode@923e30
data1::32 data2::45 Address::bnode@11b86e7 parent::bnode@923e30
data1::56 data2::89 Address::bnode@1f6a7b9 parent::bnode@923e30
data1::12 data2::52 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
25
data1::1 data2::0 Address::bnode@7d772e parent::bnode@35ce36
data1::25 data2::0 Address::bnode@757aef parent::bnode@35ce36
data1::12 data2::0 Address::bnode@35ce36 parent::bnode@923e30
data1::45 data2::0 Address::bnode@d9f9c3 parent::bnode@9cab16
data1::56 data2::89 Address::bnode@1f6a7b9 parent::bnode@9cab16
data1::52 data2::0 Address::bnode@9cab16 parent::bnode@923e30
data1::32 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
38
39. 1
Enter the element
60
data1::1 data2::0 Address::bnode@7d772e parent::bnode@35ce36
data1::25 data2::0 Address::bnode@757aef parent::bnode@35ce36
data1::12 data2::0 Address::bnode@35ce36 parent::bnode@923e30
data1::45 data2::0 Address::bnode@d9f9c3 parent::bnode@9cab16
data1::56 data2::0 Address::bnode@1a46e30 parent::bnode@9cab16
data1::89 data2::0 Address::bnode@3e25a5 parent::bnode@9cab16
data1::52 data2::60 Address::bnode@9cab16 parent::bnode@923e30
data1::32 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
1
Enter the element
83
data1::1 data2::0 Address::bnode@7d772e parent::bnode@35ce36
data1::25 data2::0 Address::bnode@757aef parent::bnode@35ce36
data1::12 data2::0 Address::bnode@35ce36 parent::bnode@923e30
data1::45 data2::0 Address::bnode@d9f9c3 parent::bnode@9cab16
data1::56 data2::0 Address::bnode@1a46e30 parent::bnode@9cab16
data1::83 data2::89 Address::bnode@3e25a5 parent::bnode@9cab16
data1::52 data2::60 Address::bnode@9cab16 parent::bnode@923e30
data1::32 data2::0 Address::bnode@923e30 parent::null
To continue...press 1
12
RESULT:
Thus the program for b-tree using Java has been implemented.
39
40. Ex no: 6
TRIES
Date:
AIM
To implement the tries with insert & delete operations using Java.
ALGORITHM
Step 1: Start the program by defining the functions.
Step 2: First initialize the node to null
Step 3: to find the particular element use function find
check the element to root node, if it is not found check for left or right side of
the root. If its found return the element
Step 4: to insert the particular element read that elemnt and
insert the element with tag as 0 and level as 1.
Step 5: to display the elements ,display if root as null, print as
empty, otherwise call empty
Step 6: print the current node in left sub tre in the format as currentnode.data + level
and tag.
Step 7: display current node in the right sub tree
Step 8: end of the program
40
41. PROGRAM
TRIES
import java.io.*;
class node
{
public int tag,level;
starts with 1
public int data;
public node LC,RC,par;
}
class trie
{
public node cptr;
public node root=null;
public node find(int key)
{
int item=key;
node temp=root;
while(temp!=null)
{
cptr=temp;
if(temp.tag==1)
{
if((item & 1)==0)
{
temp=temp.LC;
item=item >> 1;
}
else
{
temp=temp.RC;
item=item >> 1;
}
}
else
{
if(key==temp.data)
{
return temp;
}
else break;
}
}
return null;
}
public void insert()
{
int key=0;
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
key=Integer.parseInt(din.readLine());
}
catch(Exception e){}
if(root==null)
{
root=new node();
41
47. 0 LEVEL- 2 TAG-1
4451 LEVEL- 5
TAG-0
0 LEVEL- 4 TAG-1
1243 LEVEL- 5
TAG-0
0 LEVEL- 3 TAG-1
1015 LEVEL- 5
TAG-0
0 LEVEL- 4 TAG-1
1055 LEVEL- 5
TAG-0
press 1 to continue:
12
RESULT
Thus the program for tries using Java has been implemented
47
48. Ex No: 7
Quick Sort
Date:
AIM
To write a Java program for the implementation the quick sort
ALGORITHM
Step1 :start the program
Step2: declare and initialize the array size
Step3: enter the number of elements to be quick sorted.
Step4: enter the elements using for loop
Step5: call the function quick(1,noe)
Void quick(int first,int last)
Step6: if the first element is less than the last
(a) then the first element is taken as the pivot &i=first, &j=last
(b) the condition is checked for i<j if true
Step7: set a loop to check the elements
(a)while (a[pivot]>=a[i]&&i<last)i++;
(b)while (a[pivot]>=a[j]&&j>first)j--;
Step8: if (i>j)
Swap(i,j)
Step9: sort the elements and display the sorted values.
48
49. PROGRAM
Quick Sort
import java.io.*;
class quicksortalg
{
int noe;
int[] a=new int[100];
public void sort()
{
try
{
System.out.println("Enter the number of elements:");
DataInputStream din=new DataInputStream(System.in);
noe=Integer.parseInt(din.readLine());
System.out.println("Enter the elements:");
for(int i=1;i<=noe;i++)
a[i]=Integer.parseInt(din.readLine());
System.out.println("The array:");
display();
}
catch(Exception e){}
quick(1,noe);
}
public void swap(int i,int j)
{
int t;
t=a[i];a[i]=a[j];a[j]=t;
}
public void quick(int first,int last)
{
if(first<last)
{
int pivot=first;
int i=first;
int j=last;
while(i<j)
{
while(a[pivot]>=a[i] && i<last) i++;
while(a[pivot]<=a[j] && j>first) j--;
if(i<j) swap(i,j);
}
swap(pivot,j);
quick(first,j-1);
quick(j+1,last);
}
}
public void display()
{
for(int i=1;i<=noe;i++)
49
51. OUTPUT
Enter the number of elements:
5
Enter the elements:
2
96
1
45
63
The array:
2
96
1
45
63
The sorted array:
1
2
45
63
96
RESULT:
Thus the program for quick sort has been implemented using Java and the output is
verified.
51
52. Ex No: 8
CONVEX HULL
Date:
AIM
To write a Java program for the implementation of convex hull
ALGORITHM
Step1: Start the program
Step2: Create a class convexhullalg
Step3: Read the number of points
Step4: Get the x and y co-ordinate values
Step5: Sort the values using sort function
Step6: To sort two values swap the values of i and j
Step7: Call the function display to display the boundary points
Step8: The function check id used to check whether the point is angular or
not(180▫)
Step9: End of the program
52
53. PROGRAM
CONVEX HULL
import java.io.*;
class convexhullalg
{
int x[],y[],n;
boolean status[];
void insert()
{
try
{
DataInputStream in=new DataInputStream(System.in);
System.out.println("Enter number of points:");
n=Integer.parseInt(in.readLine());
x=new int[n];
y=new int[n];
status=new boolean[n];
System.out.println("Enter x and y coordinates for ");
for(int i=0;i<n;i++)
{
System.out.println("point "+(i+1));
x[i]=Integer.parseInt(in.readLine());
y[i]=Integer.parseInt(in.readLine());
status[i]=false;
}
}
catch(Exception e){}
sort();
check(0,'L');
check(0,'H');
display();
}
void sort()
{
for(int i=0;i<n-1;i++)
{
for(int j=i+1;j<n;j++)
if((x[i]>x[j]) || ((x[i]==x[j]) && (y[i]>y[j])))
swap(i, j);
}
}
void swap(int i,int j)
{
int temp=x[i];
x[i]=x[j];
x[j]=temp;
temp=y[i];
y[i]=y[j];
y[j]=temp;
}
void display()
{
System.out.println("Boundary points are");
for(int i=0;i<n;i++)
if(status[i]==true)
System.out.println("("+x[i]+", "+y[i]+")");
}
53
55. OUTPUT:
--------
Enter number of points:
4
Enter x and y coordinates for
point 1
2
6
point 2
7
8
point 3
1
4
point 4
2
10
Boundary points are
(1, 4)
(2, 10)
(7, 8)
RESULT:
Thus the program for convex hull has been implemented using Java and the
output is verified.
55
56. Ex No: 9
0/1 KNAPSACK USING DYNAMIC PROGRAMMING
Date:
AIM
To write a Java program for the implementation of 0/1 knapsack using dynamic
programming.
ALGORITHM
Step 1: Start the program and define the function.
Step 2: Initialize the weight and profit.
Step 3: Read the number of objects that are given.
Step 4: For each objects, print the profit and weight
Step 5: Initializing is set to false.
Step 6: Display and print the item weight and profit
Step 7: Display the total cost
Step 8: End of the program.
56
57. PROGRAM
0/1 KNAPSACK USING DYNAMIC PROGRAMMING
import java.io.*;
class objects
{
int weight;
int profit;
}
public class knapsack
{
static int N,W;
static objects st[];
public static void main(String args[])throws IOException
{
DataInputStream in=new DataInputStream(System.in);
System.out.println("Enter the number of objects:");
N=Integer.parseInt(in.readLine());
System.out.println("Enter the maximum weight sack can take:");
W=Integer.parseInt(in.readLine());
st=new objects[N+1];
st[0]=new objects();st[0].weight=st[0].profit=0;
for(int i=1;i<=N;i++)
{
st[i]=new objects();
System.out.println("nFor object "+i);
System.out.print("Enter profit: ");
st[i].profit=Integer.parseInt(in.readLine());
System.out.print("Enter Weight: ");
st[i].weight=Integer.parseInt(in.readLine());
}
int [][] opt=new int[N+1][W+1];
boolean [][] sol= new boolean[N+1][W+1];
for(int n=1;n<=N;n++)
for(int w=1;w<=W;w++)
{
int option1=opt[n-1][w];
int option2=-1;
if(st[n].weight<=w)
option2=st[n].profit+opt[n-1][w-st[n].weight];
opt[n][w]=Math.max(option1, option2);
sol[n][w]=(option2 > option1);
}
boolean take[]=new boolean[N+1];
int prof=0;
for(int n=N,w=W;n>0;n--)
if(sol[n][w])
{
take[n]=true;
w=w-st[n].weight;
prof+=st[n].profit;
}
else
take[n]=false;
System.out.println("nThe optimal solution is:");
System.out.println("Item t weight t profit");
for(int n=1;n<=N;n++)
if(take[n])
System.out.println(n+" t "+st[n].weight+" tt "+st[n].profit);
System.out.println("n Total profit:"+prof); }}
57
58. OUTPUT:
------
Enter the number of objects:
3
Enter the maximum weight sack can take:
10
For object 1
Enter profit: 20
Enter Weight: 6
For object 2
Enter profit: 10
Enter Weight: 2
For object 3
Enter profit: 19
Enter Weight: 3
The optimal solution is:
Item weight profit
1 6 20
3 3 19
Total profit:39
RESULT
Thus the program for 0/1 knapsack using Java has been implemented.
58
59. Ex No: 10
GRAPH COLORING USING BACKTRACKING
Date:
AIM
To write the Java program for the implementation of graph coloring
ALGORITHM
Step 1: Start the program and define the function
Step 2: Create a class coloring
Step 3: Get the number of vertices in the graph
Step 4: Enter one if there is an edge in the graph
Step 5: And enter zero if there is no edge in the graph.
Step 6: Get the adjacency matrix of the given values
Step 7: Perform all possible combinations that are given
Step 8: Display all the combination
Step 9: End of the program
59
60. PROGRAM
GRAPH COLORING USING BACKTRACKING
import java.io.*;
class gcoloring
{
int a[][]=new int[10][10];
int x[]=new int[10];
int m, n;
void read()
{
DataInputStream in=new DataInputStream(System.in);
try
{
System.out.println("Enter number of vertices in the graph");
n=Integer.parseInt(in.readLine());
System.out.println("Enter 1 if there is an edge Otherwise 0");
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
{
System.out.println("between "+i+" and "+j);
a[i][j]=Integer.parseInt(in.readLine());
}
}
catch(Exception e){}
System.out.println("Given adjacency matrix is ");
for(int i=1;i<=n;i++)
{
for(int j=1;j<=n;j++)
System.out.print(a[i][j]+"t");
System.out.println();
}
for(int i=1;i<=n;i++)
x[i]=0;
for(int i=2;i<n;i++)
{
m=i;
System.out.println("All possible combinations for m = "+i+" are ");
mcoloring(1);
}
}
void mcoloring(int k)
{
do
{
nextvalue(k);
if(x[k]==0) break;
if(k==n)
{
for(int i=1;i<=n;i++)
System.out.print(x[i]+"t");
System.out.println();
}
else
mcoloring(k+1);
}while(true);
}
void nextvalue(int k)
{
60
61. int j;
do
{
x[k]=(x[k]+1)%(m+1);
if(x[k]==0) return;
for(j=1;j<=n;j++)
{
if((a[k][j]==1) && (x[k]==x[j]))
break;
}
if(j==n+1) return;
}while(true);
}
class Graphcoloring
}
{
public static void main(String args[ ])throws IOException
{
gcoloring g=new gcoloring();
g.read();
}
}
61
62. OUTPUT:
-------
Enter number of vertices in the graph
4
Enter 1 if there is an edge Otherwise 0
between 1 and 1
0
between 1 and 2
1
between 1 and 3
0
between 1 and 4
1
between 2 and 1
1
between 2 and 2
0
between 2 and 3
1
between 2 and 4
0
between 3 and 1
0
between 3 and 2
1
between 3 and 3
0
between 3 and 4
1
between 4 and 1
1
between 4 and 2
0
between 4 and 3
1
between 4 and 4
0
Given adjacency matrix is
0 1 0 1
1 0 1 0
0 1 0 1
1 0 1 0
All possible combinations for m = 2 are
1 2 1 2
2 1 2 1
All possible combinations for m = 3 are
1 2 1 2
1 2 1 3
1 2 3 2
1 3 1 2
1 3 1 3
1 3 2 3
2 1 2 1
2 1 2 3
2 1 3 1
2 3 1 3
2 3 2 1
62
63. 2 3 2 3
3 1 2 1
3 1 3 1
3 1 3 2
3 2 1 2
3 2 3 1
3 2 3 2
RESULT
Thus the program for graph coloring using Java has been implemented.
63
![PROGRAM:
MIN HEAP
import java.io.*;
class heapalg
{
int maxsize=100,size;
int[] h=new int[maxsize];
public int leftchild(int i)
{
return 2*i;
}
public int rightchild(int i)
{
return 2*i + 1;
}
public int parent(int i)
{
return i/2;
}
public boolean isleaf(int i)
{
return ((i<=size) && (i>size/2));
}
public void swap(int i,int j)
{
int t;
t=h[i];h[i]=h[j];h[j]=t;
}
public void display()
{
System.out.println("The heap elements are:"+"n");
for(int i=1;i<=size;i++)
System.out.println("n"+h[i]);
}
public void insert()
{
size++;
if(size>maxsize)
System.out.println("Heapfull");
else
{
try
{
System.out.println("Enter the element:");
DataInputStream din=new DataInputStream(System.in);
h[size]=Integer.parseInt(din.readLine());
}
catch(Exception e){}
insertelt(size);
}
}
public void insertelt(int i)
{
while ((h[parent(i)]>h[i]))
{
int par=parent(i);
swap(par,i);
i=par;
2](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)