Data Structures Fundamentals

1. Representation of Information

Meaning: How computers store, process, and communicate different types of data.

Bit Level: Smallest unit (0 or 1).
Byte/Word Level: Group of bits, usually 8 bits = 1 byte.
Numbers: Integers and real numbers. Example: Decimal 25 → Binary 11001.
Floating-point: Stored as mantissa and exponent.
Characters: Encoded with ASCII/Unicode. Example: ‘A’ → ASCII 65 → Binary 01000001.
Multimedia: Images = pixels; Audio/Video = sampling + compression.

Key Point: All forms of data (text, numbers, images, sound) are ultimately represented in binary (0s and 1s).

2. Characteristics of an Algorithm

Definition: A sequence of clear steps to solve a problem.

Finiteness: Must terminate after finite steps.
Clarity: Instructions must be precise.
Input: Zero or more inputs allowed.
Output: At least one result produced.
Effectiveness: Steps must be practical.
Generality: Should solve a broad set of problems.

Example: To add two numbers: 1) Input two numbers. 2) Add them. 3) Display the result.

3. Program

Definition: A program is the coded form of an algorithm written in a programming language.

Difference: Algorithm = logical plan (language independent). Program = actual implementation (C, Java, Python, etc.).

#include <stdio.h>
int main() {
    int a, b, sum;
    printf("Enter two numbers: ");
    scanf("%d %d", &a, &b);
    sum = a + b;
    printf("Sum = %d", sum);
    return 0;
}

4. Analyzing Programs

Definition: Examining a program for efficiency and correctness.

Correctness: Always gives accurate results.
Time Complexity: How fast it runs (Big-O notation).
Space Complexity: Memory required.
Readability: Is the code easy to maintain?
Scalability: Handles large inputs efficiently.

Example: Linear Search → Time Complexity: O(n) | Space Complexity: O(1).

Summary

Representation of Information → Data storage in binary.
Algorithm → Logical steps to solve a problem.
Program → Algorithm implemented in code.
Program Analysis → Measures correctness and efficiency.