In this article Introduction to Algorithms explains what an algorithm is, how it works, types like searching, sorting, divide and conquer, greedy and dynamic programming, along with real examples and benefits.
Introduction to Algorithms
What is an Algorithm?
An algorithm is a sequence of ordered, finite, definite, and effective steps designed to solve a problem.
It is the most basic and important concept in computer science.
Examples of algorithms:
- Adding two numbers
- Finding the largest number in a list
- Sorting student marks
- Checking whether a password is valid
All these tasks can be solved using specific algorithms.
Characteristics of a Good Algorithm
1) Input
An algorithm may receive one or more inputs.
Example: If 5 numbers are given, the algorithm uses them to calculate the sum.
2) Output
An algorithm must produce at least one output.
Example: Sum = 65
3) Definiteness
Every step must be clear, definite, and unambiguous.
4) Finiteness
An algorithm must complete in a finite number of steps.
If it contains an infinite loop, it is not an algorithm.
5) Effectiveness
Each step should be simple, practical, and easy to implement.
Why Algorithms Are Important
- They tell the computer exactly what to do.
- They make problem-solving systematic and clear.
- They help choose the best method to save time and memory.
- A single algorithm can be implemented in any language (C, Python, Java).
- They allow fast and efficient processing of large datasets.
Structure of an Algorithm
A typical algorithm includes:
- Input
- Processing Steps
- Output
- Conditions (Decision-making)
- Loops (Repetitions)
- Termination (End of the process)
Types of Algorithms
1) Simple Recursive Algorithms
Examples:
- Factorial
- Fibonacci Series
2) Divide and Conquer Algorithms
Examples:
- Merge Sort
- Quick Sort
3) Greedy Algorithms
Examples:
- Kruskal’s Algorithm
- Prim’s Algorithm
4) Dynamic Programming Algorithms
Example:
- Knapsack Problem
5) Backtracking Algorithms
Example:
- N-Queen Problem
6) Searching Algorithms
- Linear Search
- Binary Search
7) Sorting Algorithms
- Bubble Sort
- Selection Sort
- Insertion Sort
Points to Consider While Designing an Algorithm
- Understand the problem clearly
- Identify input and output
- Keep steps simple and clear
- Analyze time and space complexity
- Use loops and recursion appropriately
- Optimize the algorithm wherever possible
Examples of Algorithms
Example 1: Find the Largest of Three Numbers
Step 1: Read a, b, c
2: If a > b and a > c → Largest = a
3: Else if b > a and b > c → Largest = b
4: Else → Largest = c
5: Print Largest
Example 2: Sum of Numbers from 1 to N
Step 1: Read N
2: Set Sum = 0
3: Repeat from i = 1 to N:
Sum = Sum + i
4: Print Sum
Algorithm vs Program
| Algorithm | Program |
| A set of logical steps to solve a problem | A set of instructions written in a programming language |
| Language-independent | Language-dependent |
| Focuses on the logic | Focuses on implementation |
Benefits of Algorithms
- Improves program performance
- Helps select better alternatives
- Makes code easier to write
- Reduces errors
- Enhances speed in searching and data processing
Conclusion
Algorithms are the foundation of computer science.
Without algorithms, programming, software development, data science, and machine learning would not be possible.
A well-designed algorithm helps a program run faster, use less memory, and work more reliably.