function []=simpson13(x, f)
[x0,xn]=size(x)
[y0,yn]=size(f)
if((x0<>1)|(y0<>1)) then
error('x of f,or both , not column vector(s)')
abort;
end;
if((xn<>yn)) then
error('x and f are not of the same length');
abort;
end;
if(modulo(xn-1,2)<>0) then
disp(xn-1,"list size=");
error('list size must be an even number');
abort;
end;
n=xn;
h=x(2)-x(1);
I=f(1,1)+f(1,n);
for j=2:n-1
if(modulo(j,2)==0) then
I=I+4*f(1,j);
else
I=I+2*f(1,j);
end;
end;
I=(h/3.0)*I
printf('Integration by simpson 1/3 rd rule =%f',I);
endfunction
Output:
-->x=(0:0.1:1.6);
-->simpson13(x,sin(x))
Integration by simpson 1/3 rd rule =1.029200
8 Comments
// Practical 1: Write a program to perform insertion, deletion, searching and traversal in 1D array.
ReplyDelete#include iostream.h
#include conio.h
void traverseArray(int arr[], int size)
{
int i;
cout << "Array elements: ";
for (i = 0; i < size; i++)
cout << arr[i] << " ";
cout << endl;
}
void insertElement(int arr[], int &size, int capacity, int element, int position)
{
int i;
if (size == capacity || position < 0 || position > size)
{
cout << "Insertion failed!" << endl;
return;
}
for (i = size; i > position; i--)
arr[i] = arr[i - 1];
arr[position] = element;
size++;
cout << "Element inserted successfully!" << endl;
}
void deleteElement(int arr[], int &size, int position)
{
int i;
if (position < 0 || position >= size)
{
cout << "Invalid position!" << endl;
return;
}
for (i = position; i < size - 1; i++)
arr[i] = arr[i + 1];
size--;
cout << "Element deleted successfully!" << endl;
}
void searchElement(int arr[], int size, int element)
{
int i;
for (i = 0; i < size; i++)
{
if (arr[i] == element)
{
cout << "Element " << element << " found at position " << i << "." << endl;
return;
}
}
cout << "Element not found." << endl;
}
void main()
{
const int capacity = 100;
int arr[capacity], size = 0;
int choice, element, position;
clrscr();
do
{
cout << "\nMenu:\n1.Traverse 2.Insert 3.Delete 4.Search 5.Exit";
cout << "\nEnter choice: ";
cin >> choice;
switch (choice)
{
case 1:
traverseArray(arr, size);
break;
case 2:
cout << "Element to insert: ";
cin >> element;
cout << "Position (0-based): ";
cin >> position;
insertElement(arr, size, capacity, element, position);
break;
case 3:
cout << "Position to delete: ";
cin >> position;
deleteElement(arr, size, position);
break;
case 4:
cout << "Element to search: ";
cin >> element;
searchElement(arr, size, element);
break;
case 5:
cout << "Exiting...";
break;
default:
cout << "Invalid choice!";
}
} while (choice != 5);
getch();
}
// Practical 2: Implement stack using arrays with push, pop, peek and display operations.
ReplyDelete#include iostream.h
#include conio.h
#define MAX 100
class Stack
{
int arr[MAX];
int top;
public:
Stack()
{
top = -1;
}
int isEmpty()
{
if (top == -1)
return 1;
else
return 0;
}
int isFull()
{
if (top == MAX - 1)
return 1;
else
return 0;
}
void push(int x)
{
if (isFull())
{
cout << "Stack Overflow! Cannot push " << x << endl;
return;
}
arr[++top] = x;
cout << x << " pushed to stack." << endl;
}
void pop()
{
if (isEmpty())
{
cout << "Stack Underflow! Nothing to pop." << endl;
return;
}
cout << arr[top--] << " popped from stack." << endl;
}
void peek()
{
if (isEmpty())
{
cout << "Stack is empty." << endl;
return;
}
cout << "Top element is: " << arr[top] << endl;
}
void display()
{
int i;
if (isEmpty())
{
cout << "Stack is empty." << endl;
return;
}
cout << "Stack elements from top to bottom: ";
for (i = top; i >= 0; i--)
cout << arr[i] << " ";
cout << endl;
}
};
void main()
{
Stack s;
int choice, value;
clrscr();
do
{
cout << "\nStack Operations Menu\n";
cout << "1. Push\n2. Pop\n3. Peek\n4. Display\n5. Exit\n";
cout << "Enter choice: ";
cin >> choice;
switch (choice)
{
case 1:
cout << "Enter value to push: ";
cin >> value;
s.push(value);
break;
case 2:
s.pop();
break;
case 3:
s.peek();
break;
case 4:
s.display();
break;
case 5:
cout << "Exiting program...";
break;
default:
cout << "Invalid choice!";
}
} while (choice != 5);
getch();
}
// Practical 3: Write a program to convert an infix expression into postfix and evaluate it.
ReplyDelete#include iostream.h
#include conio.h
#include ctype.h
#include string.h
#define MAX 100
char stackOp[MAX];
int topOp = -1;
int stackVal[MAX];
int topVal = -1;
void pushOp(char x)
{
stackOp[++topOp] = x;
}
char popOp()
{
return stackOp[topOp--];
}
char peekOp()
{
return stackOp[topOp];
}
int isEmptyOp()
{
if (topOp == -1)
return 1;
else
return 0;
}
void pushVal(int x)
{
stackVal[++topVal] = x;
}
int popVal()
{
return stackVal[topVal--];
}
int precedence(char op)
{
if (op == '+' || op == '-')
return 1;
if (op == '*' || op == '/')
return 2;
if (op == '^')
return 3;
return 0;
}
void infixToPostfix(char infix[], char postfix[])
{
int i, k = 0;
char ch;
for (i = 0; infix[i] != '\0'; i++)
{
ch = infix[i];
if (isdigit(ch))
{
postfix[k++] = ch;
}
else if (ch == '(')
{
pushOp(ch);
}
else if (ch == ')')
{
while (!isEmptyOp() && peekOp() != '(')
{
postfix[k++] = popOp();
}
popOp();
}
else
{
while (!isEmptyOp() && precedence(peekOp()) >= precedence(ch))
{
postfix[k++] = popOp();
}
pushOp(ch);
}
}
while (!isEmptyOp())
{
postfix[k++] = popOp();
}
postfix[k] = '\0';
}
int evaluatePostfix(char postfix[])
{
int i, a, b, res;
char ch;
for (i = 0; postfix[i] != '\0'; i++)
{
ch = postfix[i];
if (isdigit(ch))
{
pushVal(ch - '0');
}
else
{
b = popVal();
a = popVal();
switch (ch)
{
case '+': pushVal(a + b); break;
case '-': pushVal(a - b); break;
case '*': pushVal(a * b); break;
case '/': pushVal(a / b); break;
case '^':
res = 1;
while (b > 0)
{
res = res * a;
b--;
}
pushVal(res);
break;
}
}
}
return popVal();
}
void main()
{
char infix[50], postfix[50];
int result;
clrscr();
cout << "Enter infix expression (single digit operands): ";
cin >> infix;
infixToPostfix(infix, postfix);
cout << "Postfix: " << postfix << endl;
result = evaluatePostfix(postfix);
cout << "Result: " << result;
getch();
}
// Practical 4: Implement queue using arrays with enqueue, dequeue and display operations.
ReplyDelete#include iostream.h
#include conio.h
#define MAX 100
class Queue
{
int arr[MAX];
int front, rear, capacity;
public:
Queue(int size)
{
capacity = size;
front = -1;
rear = -1;
}
int isFull()
{
if (rear == capacity - 1)
return 1;
else
return 0;
}
int isEmpty()
{
if (front == -1 || front > rear)
return 1;
else
return 0;
}
void enqueue(int val)
{
if (isFull())
{
cout << "Queue Overflow. Cannot insert " << val << endl;
return;
}
if (isEmpty())
front = 0;
arr[++rear] = val;
cout << val << " enqueued to queue." << endl;
}
void dequeue()
{
if (isEmpty())
{
cout << "Queue Underflow. No element to dequeue." << endl;
return;
}
cout << arr[front++] << " dequeued from queue." << endl;
if (front > rear)
{
front = rear = -1;
}
}
void display()
{
int i;
if (isEmpty())
{
cout << "Queue is empty." << endl;
return;
}
cout << "Queue elements: ";
for (i = front; i <= rear; i++)
cout << arr[i] << " ";
cout << endl;
}
};
void main()
{
int size, choice, val;
clrscr();
cout << "Enter queue capacity: ";
cin >> size;
Queue q1(size);
do
{
cout << "\n1. Enqueue\n2. Dequeue\n3. Display\n4. Exit";
cout << "\nEnter choice: ";
cin >> choice;
switch (choice)
{
case 1:
cout << "Enter value to enqueue: ";
cin >> val;
q1.enqueue(val);
break;
case 2:
q1.dequeue();
break;
case 3:
q1.display();
break;
case 4:
cout << "Exiting...";
break;
default:
cout << "Invalid choice!";
}
} while (choice != 4);
getch();
}
// Practical 5: Implement circular queue using arrays.
ReplyDelete#include iostream.h
#include conio.h
#define MAX 20
class CircularQueue
{
int arr[MAX];
int front, rear, capacity;
public:
CircularQueue(int size)
{
capacity = size;
front = -1;
rear = -1;
}
int isFull()
{
if (front == (rear + 1) % capacity)
return 1;
else
return 0;
}
int isEmpty()
{
if (front == -1)
return 1;
else
return 0;
}
void enqueue(int val)
{
if (isFull())
{
cout << "Overflow: Cannot insert " << val << endl;
return;
}
if (isEmpty())
front = rear = 0;
else
rear = (rear + 1) % capacity;
arr[rear] = val;
cout << val << " enqueued." << endl;
}
void dequeue()
{
if (isEmpty())
{
cout << "Underflow: No element to dequeue." << endl;
return;
}
cout << arr[front] << " dequeued." << endl;
if (front == rear)
front = rear = -1;
else
front = (front + 1) % capacity;
}
void display()
{
int i;
if (isEmpty())
{
cout << "Queue is empty." << endl;
return;
}
cout << "Queue elements: ";
i = front;
while (1)
{
cout << arr[i] << " ";
if (i == rear)
break;
i = (i + 1) % capacity;
}
cout << endl;
}
};
void main()
{
int size, choice, val;
clrscr();
cout << "Enter queue capacity: ";
cin >> size;
CircularQueue cq(size);
do
{
cout << "\n1. Enqueue\n2. Dequeue\n3. Display\n4. Exit";
cout << "\nChoice: ";
cin >> choice;
switch (choice)
{
case 1:
cout << "Value: ";
cin >> val;
cq.enqueue(val);
break;
case 2:
cq.dequeue();
break;
case 3:
cq.display();
break;
case 4:
cout << "Exit...";
break;
default:
cout << "Invalid choice!";
}
} while (choice != 4);
getch();
}
// Practical 9: Write a program to create a Binary Search Tree (BST) to perform inorder, preorder and postorder traversal.
ReplyDelete#include iostream.h
#include conio.h
#include stdlib.h
struct Node
{
int data;
struct Node *left;
struct Node *right;
};
struct Node* createNode(int val)
{
struct Node *newNode;
newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = val;
newNode->left = NULL;
newNode->right = NULL;
return newNode;
}
struct Node* insert(struct Node* root, int val)
{
if (root == NULL)
return createNode(val);
if (val < root->data)
root->left = insert(root->left, val);
else if (val > root->data)
root->right = insert(root->right, val);
return root;
}
void inorder(struct Node* root)
{
if (root != NULL)
{
inorder(root->left);
cout << root->data << " ";
inorder(root->right);
}
}
void preorder(struct Node* root)
{
if (root != NULL)
{
cout << root->data << " ";
preorder(root->left);
preorder(root->right);
}
}
void postorder(struct Node* root)
{
if (root != NULL)
{
postorder(root->left);
postorder(root->right);
cout << root->data << " ";
}
}
void main()
{
struct Node *root = NULL;
clrscr();
root = insert(root, 50);
root = insert(root, 30);
root = insert(root, 70);
root = insert(root, 20);
root = insert(root, 40);
root = insert(root, 60);
root = insert(root, 80);
cout << "Inorder traversal of BST: ";
inorder(root);
cout << endl;
cout << "Preorder traversal of BST: ";
preorder(root);
cout << endl;
cout << "Postorder traversal of BST: ";
postorder(root);
cout << endl;
getch();
}
// Practical 10: Implement BFS for graph traversal.
ReplyDelete#include iostream.h
#include conio.h
#define MAX 4
int graph[MAX][MAX] =
{
{0, 1, 1, 0},
{1, 0, 0, 1},
{1, 0, 0, 1},
{0, 1, 1, 0}
};
int visited[MAX];
int queue[MAX];
int front = 0, rear = -1;
void enqueue(int v)
{
queue[++rear] = v;
}
int dequeue()
{
return queue[front++];
}
int isEmpty()
{
if (front > rear)
return 1;
else
return 0;
}
void bfs(int start)
{
int i, v;
enqueue(start);
visited[start] = 1;
cout << "BFS Traversal: ";
while (!isEmpty())
{
v = dequeue();
cout << v << " ";
for (i = 0; i < MAX; i++)
{
if (graph[v][i] == 1 && visited[i] == 0)
{
visited[i] = 1;
enqueue(i);
}
}
}
}
void main()
{
int i;
clrscr();
for (i = 0; i < MAX; i++)
visited[i] = 0;
bfs(0);
getch();
}
// Practical 12: Write a program to find factorial of number using recursion.
ReplyDelete#include iostream.h
#include conio.h
long factorial(int n)
{
if (n == 0 || n == 1)
return 1;
else
return n * factorial(n - 1);
}
void main()
{
int num;
clrscr();
cout << "Enter number: ";
cin >> num;
cout << "Factorial of " << num << " is " << factorial(num);
getch();
}