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NPTEL

Design and analysis of algorithms

NPTEL and Chennai Mathematical Institute via YouTube

Overview

COURSE OUTLINE: This course will cover basic concepts in the design and analysis of algorithms.Asymptotic complexity, O() notation Sorting and search.Algorithms on graphs: exploration, connectivity, shortest paths, directed acyclic graphs, spanning trees. Design techniques: divide and conquer, greedy, dynamic programming. Data structures: heaps, union of disjoint sets, search trees Intractability.

Syllabus

Course Outline.
Example: Air Travel.
Example: Xerox shop.
Example: Document similarity.
Introduction and motivation.
Input size, worst case, average case.
Quantifying efficiency: O( ), Omega( ), Theta( ).
Examples: Analysis of iterative and recursive algorithms.
Arrays and lists.
Searching in an array.
Selection Sort.
Insertion sort.
Merge sort.
Merge sort - analysis.
Quicksort.
Quicksort - analysis.
Sorting - Concluding remarks.
Introduction to graphs.
Representing graphs.
Breadth first search (BFS).
Depth first search (DFS).
Applications of BFS and DFS.
Directed acylic graphs: topological sort.
Directed acylic graphs: longest paths.
Dijkstras algorithm: analysis.
Negative edge weights: Bellman-Ford algorithm.
All pairs shortest paths.
Minimum Cost Spanning Trees.
Prims Algorithm.
Kruskals algorithm.
Union-Find using arrays.
Union-Find using pointers.
Priority queues.
Heaps.
Heaps: Updating values, sorting.
Counting inversions.
Closest pair of points.
Binary Search Trees.
Balanced search trees.
Interval scheduling.
Scheduling with deadlines: minimizing lateness.
Huffman codes.
Introduction to dynamic programming.
Memoization.
Grid paths.
Common subwords and subsequences.
Edit distance.
Matrix multiplication.
Linear Programming.
LP modelling: Production Planning.
LP modelling: Bandwidth allocation.
Network Flows.
Reductions.
Checking Algorithms.
P and NP.
Single source shortest paths: Dijkstras algorithm.

Taught by

NPTEL-NOC IITM

Reviews

5.0 rating, based on 1 Class Central review

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  • Jnanesh Rm
    Design and analysis of algorithms. Its really helped me to again my extra knowledge. I came to know that how to design algorithms.finally tq u for this online cousres

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