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Design and Analysis of Algorithms

This course introduces basic elements of the design and analysis of computer algorithms. Topics include asymptotic notations and analysis, divide and conquer strategy, greedy methods, dynamic programming, basic graph algorithms, NP-completeness, and approximation algorithms. For each topic, beside in-depth coverage, one or more representative problems and their algorithms shall be discussed.

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Foundation of Algorithm Analysis

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. Asymp. . .

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)

23199+ Students

Questions : 10+

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Iterative Algorithms

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. . .

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

15124+ Students

Questions : 6+

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Divide and Conquer Algorithms

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. . .

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.

16701+ Students

Questions : 9+

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Greedy Algorithms

4.1. Optimization Problems and Optimal Solution, Introduction of Greedy Algorithms, Elements of Greedy Strategy. 4.2. Greedy Algorithms: Fractional Knapsack, Job sequencing . . .

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

15277+ Students

Questions : 10+

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Dynamic Programming

5.1. Greedy Algorithms vs Dynamic Programming, Recursion vs Dynamic Programming, Elements of DP Strategy 5.2. DP Algorithms: Matrix Chain Multiplication, String Editing, Zer. . .

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

15101+ Students

Questions : 9+

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Backtracking

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.

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.

11434+ Students

Questions : 5+

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Number Theoretic Algorithms

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 Te. . .

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: MillerRabin Randomized Primility Test and their Analysis

9885+ Students

Questions : 3+

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NP Completeness

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 Com. . .

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

9787+ Students

Questions : 7+

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