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Chennai Mathematical Institute
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.
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