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An Introduction to Algorithms and Analysis

An Introduction to Algorithms and Analysis. Instructor: Prof. Sourav Mukhopadhyay, Department of Mathematics, IIT Kharagpur. This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. (from nptel.ac.in)

Lecture 01 - Insertion Sort

Problem of Sorting, Pseudo code, Insertion sort, Loop Invariant, Runtime, parameterise the runtime by size of the input.

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Lecture 01 - Insertion Sort

Lecture 02 - Analysis of Insertion Sort

Lecture 03 - Asymptotic Notation

Lecture 04 - Recurrence for Merge Sort

Lecture 05 - Substitution Method for Solving Recurrence

Lecture 06 - The Master Method

Lecture 07 - Divide and Conquer

Lecture 08 - Divide and Conquer (cont.)

Lecture 09 - Strassen's Algorithm

Lecture 10 - Quicksort

Lecture 11 - Analysis of Quicksort

Lecture 12 - Randomized Quicksort

Lecture 13 - Heap

Lecture 14 - Heap Sort

Lecture 15 - Decision Tree

Lecture 16 - Linear Time Sorting

Lecture 17 - Radix Sort and Bucket Sort

Lecture 18 - Order Statistics

Lecture 19 - Randomized Order Statistics

Lecture 20 - Worst Case Linear Time Order

Lecture 21 - Hash Function

Lecture 22 - Open Addressing

Lecture 23 - Universal Hashing

Lecture 24 - Perfect Hashing

Lecture 25 - Binary Search Tree (BST) Sort

Lecture 26 - Randomly Built BST

Lecture 27 - Red Black Tree

Lecture 28 - Red Black Tree (cont.)

Lecture 29 - Augmentation of Data Structure

Lecture 30 - Interval Trees

Lecture 31 - Fixed Universe Successor

Lecture 32 - Van Emde Boas Data Structure

Lecture 33 - Amortized Analysis

Lecture 34 - Computational Geometry

Lecture 35 - Computational Geometry (cont.)

Lecture 36 - Dynamic Programming

Lecture 37 - Longest Common Subsequence

Lecture 38 - Graphs

Lecture 39 - Prim's Algorithm

Lecture 40 - Graph Search

Lecture 41 - Breadth-First Search and Depth-First Search

Lecture 42 - Shortest Path Problem

Lecture 43 - Dijkstra's Algorithm

Lecture 44 - Example of Dijkstra's Algorithm

Lecture 45 - Bellman-Ford Algorithm

Lecture 46 - Correctness of Bellman-Ford Algorithm

Lecture 47 - Application of Bellman-Ford Algorithm

Lecture 48 - All Pairs of Shortest Path

Lecture 49 - Floyd-Warshall Algorithm

Lecture 50 - Johnson Algorithm

Lecture 51 - Disjoint Set Data Structure

Lecture 52 - Union-Find

Lecture 53 - Augmented Disjoint Set Data Structure

Lecture 54 - Network Flow

Lecture 55 - Network Flow (cont.)

Lecture 56 - Network Flow (cont.)

Lecture 57 - More On Dynamic Programming

Lecture 58 - More On Dynamic Programming (cont.)

Lecture 59 - Computational Complexity

Lecture 60 - Computational Complexity (cont.)