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1. CONTENTS
• Introduction
• Relation of algorithm with Data Structures
• Multiplication of numbers
• Multiplication Problem with Iterative and
Recusrive Algorithm
• Karatsuba Integer Multiplication

2. INTRODUCTION TO DATA STRUCTURE
• Introduction
• Types of Data Structure
1. Primitive data structure
2. Non-primitive data structure
3. Static Data structure
4. Dynamic Data Structure
• Need for Data Structure

3. INTRODUCTION TO ALGORITHMS
• Introduction
• Types of Algorithms
1. Recursive Algorithm:
2. Randomized Algorithm:
3. Sorting Algorithm:
4. Searching Algorithm:
• Advantages of Algorithms:
• Disadvantages of Algorithms:
• Properties of algorithms:

4. RELATION OF ALGORITHM WITH DATA
STRUCTURES

5. Algorithm to find multiplication of numbers
• Start
Step 1: Int i;
Step 2: Int j ;
Step 3: Mul = i*j;
Step 4: print mul
Explanation:
• First we initialize the i variable .
• Initialize j variable.
• Declare variable mul which multiply i and j

6. Multiplication problem with iterative Method
Start
Step 1: int n;
Step 2: int factorial;
Step 3: for(int i ; i<=n ; i++)
factorial* = i;
Step 4: print factorial

7. Recursive Algorithm
Recursion is a method of solving a computational problem
where the solution depends on solutions to smaller instances
of the same problem. Recursion solves such recursive
problems by using functions that call themselves from within
their own code.

8. Recursive Algorithm
1. Read n
2. result = fact(n)
3. int fact (int n) { //function
if (n==0 || n==1)
return 1;
} else {
return n*fact(n-1);
}
}
4. print result;

9. Factorial program using recursive method
• import java.util.Scanner;
• public class FactorialCalculator3 {
• public static void main(String[] args) {
• Scanner scanner = new Scanner(System.in);
• System.out.print("Enter a number (n): ");
• int n = scanner.nextInt();
• int result = fact(n);
• System.out.println("The factorial of " + n + " is: " + result);
• scanner.close();
• }
• public static int fact(int n) {
• if (n == 0 || n == 1) {
• return 1; // Base case: factorial of 0 and 1 is 1
• } else {
• return n * fact(n - 1);
• }
• }
• }

10. Karatsuba algorithm
• The Karatsuba algorithm is a fast multiplication algorithm that
was introduced by Anatolii Alexeevitch Karatsuba in 1960. Its
primary advantage is that it reduces the number of recursive
multiplications involved in the process, making it more efficient
than traditional multiplication algorithms, especially for large
numbers.