Introduction to Algorithms

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Introduction – Analysis of Algorithms, Insertion Sort, Merge sort – Asymptotic Notation | Recurrences | Substitution, Master Method – Divide-and-Conquer: Strassen, Fibonacci, Polynomial Multiplication- Quick sort, Randomized Algorithms- Linear-time Sorting: Lower Bounds, Counting Sort, Radix Sort – Order Statistics, Median-Hashing, Hash Functions-Universal Hashing, Perfect Hashing-Relation of BSTs to Quick sort | Analysis of Random BST – Red-black Trees, Rotations, Insertions, Deletions – Augmenting Data Structures, Dynamic Order Statistics, Interval Trees-Skip Lists – Amortized Algorithms, Table Doubling, Potential Method – Competitive Analysis: Self-organizing Lists-Dynamic Programming, Longest Common Subsequence – Greedy Algorithms, Minimum Spanning Trees – Shortest Paths I: Properties, Dijkstra,Bellman-Ford, Linear Programming, Difference Constraints,ll-pairs Shortest Paths, Matrix Multiplication, Floyd-Warshall, Johnson-Advanced Topics

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