Introduction to Algorithm and Properties | GATECSE | DAA

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"Welcome to our video on Introduction to Algorithms! In this video, we will discuss the basics of algorithms and their importance in computer science. You will learn about the different types of algorithms and how they are used to solve problems in a systematic way. You will also learn about the key features that define an algorithm, such as being well-defined, having a clear set of inputs and outputs, and being effective and efficient. We will also cover the concept of determinism and how algorithms can be either deterministic or non-deterministic. Additionally, we will discuss the importance of step-by-step instructions and their role in ensuring the algorithm can be implemented and executed correctly. Whether you're a computer science student or just curious about algorithms, this video will provide a comprehensive overview of the key characteristics of algorithms."

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The word Algorithm means “a process or set of rules to be followed in calculations or other problem-solving operations”. Therefore Algorithm refers to a set of rules/instructions that step-by-step define how a work is to be executed upon in order to get the expected results.
Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output.
Characteristics of an Algorithm:
1. Input: An algorithm has some input values. We can pass 0 or more input value to an algorithm.
2. Output: We will get 1 or more output at the end of an algorithm.
3. Definiteness: An algorithm should be unambiguous which means that the instructions in an algorithm should be clear and simple.
4. Finiteness: An algorithm should have finiteness. Here, finiteness means that the algorithm should contain a limited number of instructions, i.e., the instructions should be countable.
5. Effectiveness: An algorithm should be effective as each instruction in an algorithm affects the overall process.
Advantages of Algorithms:
It is easy to understand.
Algorithm is a step-wise representation of a solution to a given problem.
In Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.
Disadvantages of Algorithms:
Writing an algorithm takes a long time so it is time-consuming.
Branching and Looping statements are difficult to show in Algorithms.

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[phunsukhwangdu]

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This is our Syllabus.

Units and Unit Content
1. Foundation of Algorithm Analysis
teaching hours: 4 hrs
1.1. Algorithm and its properties, RAM model, Time and Space Complexity, detailed analysis

of algorithms (Like factorial algorithm), Concept of Aggregate Analysis

1.2. Asymptotic Notations: Big-O, Big-Ω and Big-Ө Notations their Geometrical Interpretation

and Examples.

1.3. Recurrences: Recursive Algorithms and Recurrence Relations, Solving Recurrences

(Recursion Tree Method, Substitution Method, Application of Masters Theorem)




2. Iterative Algorithms
teaching hours: 4 hrs
2.1. Basic Algorithms: Algorithm for GCD, Fibonacci Number and analysis of their time and

space complexity

2.2. Searching Algorithms: Sequential Search and its analysis

2.3. Sorting Algorithms: Bubble, Selection, and Insertion Sort and their Analysis




3. Divide and Conquer Algorithms
teaching hours: 8 hrs
3.1. Searching Algorithms: Binary Search, Min-Max Finding and their Analysis

3.2. Sorting Algorithms: Merge Sort and Analysis, Quick Sort and Analysis (Best Case, Worst

Case and Average Case), Heap Sort (Heapify, Build Heap and Heap Sort Algorithms and

their Analysis), Randomized Quick sort and its Analysis

3.3. Order Statistics: Selection in Expected Linear Time, Selection in Worst Case Linear Time

and their Analysis.




4. Greedy Algorithms
teaching hours: 6 hrs
4.1. Optimization Problems and Optimal Solution, Introduction of Greedy Algorithms,

Elements of Greedy Strategy.

4.2. Greedy Algorithms: Fractional Knapsack, Job sequencing with Deadlines, Kruskal’s

Algorithm, Prims Algorithm, Dijkstra’s Algorithm and their Analysis

4.3. Huffman Coding: Purpose of Huffman Coding, Prefix Codes, Huffman Coding

Algorithm and its Analysis





5. Dynamic Programming
teaching hours: 8 hrs
5.1. Greedy Algorithms vs Dynamic Programming, Recursion vs Dynamic Programming,

Elements of DP Strategy

5.2. DP Algorithms: Matrix Chain Multiplication, String Editing, Zero-One Knapsack

Problem, Floyd Warshwall Algorithm, Travelling Salesman Problem and their

Analysis.

5.3. Memoization Strategy, Dynamic Programming vs Memoization





6. Backtracking
teaching hours: 5 hrs
6.1. Concept of Backtracking, Recursion vs Backtracking

6.2. Backtracking Algorithms: Subset-sum Problem, Zero-one Knapsack Problem, N-queen

Problem and their Analysis.


7. Number Theoretic Algorithms
teaching hours: 5 hrs
7.1. Number Theoretic Notations, Euclid’s and Extended Euclid’s Algorithms and their

Analysis.

7.2. Solving Modular Linear Equations, Chinese Remainder Theorem, Primility Testing: Miller-

Rabin Randomized Primility Test and their Analysis





8. NP Completeness
teaching hours: 5 hrs
8.1. Tractable and Intractable Problems, Concept of Polynomial Time and Super Polynomial

Time Complexity

8.2. Complexity Classes: P, NP, NP-Hard and NP-Complete

8.3. NP Complete Problems, NP Completeness and Reducibility, Cooks Theorem, Proofs of NP

Completeness (CNF-SAT, Vertex Cover and Subset Sum)

8.4. Approximation Algorithms: Concept, Vertex Cover Problem, Subset Sum Problem

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