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Day  1  2  3 Date Contents Slides Assignments Aug 12 Time complexities with examples - Asymptotic notations - Theta for tight bound, big-O for upper bound and big-Omega for lower bound. Analogous to =, <= and >=.  o- strictly higher upper bound and small-omega- strictly lower lower bound analogous to > and < respectively. Definitions to be learned from Cormen. Aug 13 Masters theorem with examples - finding epsilon > 0 for case 1 and case 3, c < 1 for case 3,  Going to substitution for exact solution, brute force method as a backup. Sorting algorithms and time complexities in best, worst and average cases- Insertion sort-inversion, Selection sort - swapping, Bubble sort, Merge sort - external sorting, Heap sort - build heap in O(n) - proof in Cormen, Quick sort - worst case of O(n^2) Assignment 1 Aug 14 No discussion, Assignments on sorting- time complexity Assignment 2 Aug 15 Hashing- O(1)-search-perfect hashing, hash structure-table, Direct addressing, Open addressing- linear probing-primary clustering, quadratic probing-secondary clustering, double hashing Aug 16 Algorithm design techniques- Dynamic programming, Greedy algorithms, Divide and conquer - with examples, dynamic programming- top down and bottom up approach Aug 17 Graph search- breadth first search-level order traversal in tree, depth first search- algorithm and complexity analysis, applications, Spanning tree- minimum spanning tree, Prims and Kruskal's algorithm and analysis Aug 18-Aug 22 No discussion, solve previous gate questions on algorithms Aug 23 Shortest path algorithms- Relax function, Dijkstras algorithm- single source all destination,array and min heap implementation, failure(wrong output) for negative edge cycle, Bellman Ford- single source all destination, Floyd Warshall- Dynamic programming, Jhonson's algorithm- (optimised Floyd Warshall for sparse graph)- complexity and comparisons, programming- data structures used and initialisation

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posted Sep 17 | 513 views
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