## Fundamentals of Algorithms - CS502 - VU Video Lectures

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Algorithm, Informal Definition, Algorithms, Programming, Implementation Issues, Course In Review, Analyzing Algorithms, Model Of Computation, Example: 2-Dimension Maxima, Brute-Force Algorithm, Running Time Analysis, Analysis Of The Brute-Force Maxima Algorithm, Analysis: A Harder Example, 2-Dimension Maxima Revisited, Plane-Sweep Algorithm, Analysis Of Plane-Sweep Algorithm, Comparison Of Brute-Force And Plane Sweep Algorithms.
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Asymptotic Notation.
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Divide And Conquer Strategy, Merge Sort, Analysis Of Merge Sort, The Iteration Method For Solving Recurrence Relations, Visualizing Recurrences Using The Recursion Tree, A Messier Example, Selection Problem, Sieve Technique, Applying The Sieve To Selection, Selection Algorithm, Analysis Of Selection.
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Sorting, Slow Sorting Algorithms, Sorting In O(N Log N) Time, Heaps, Heapsort Algorithm, Heapify Procedure, Analysis Of Heapify, Buildheap, Analysis Of Buildheap, Analysis Of Heapsort, Quicksort, Partition Algorithm, Quick Sort Example, Analysis Of Quicksort, Worst Case Analysis Of Quick Sort, Average-Case Analysis Of Quicksort, In-Place, Stable Sorting, Lower Bounds For Sorting.
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Linear Time Sorting, Counting Sort, Bucket Or Bin Sort, Radix Sort.
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Dynamic Programming, Fibonacci Sequence, Dynamic Programming, Edit Distance, Edit Distance: Applications, Edit Distance Algorithm, Edit Distance: Dynamic Programming Algorithm, Analysis of DP Edit Distance, Chain Matrix Multiply, Chain Matrix Multiplication-Dynamic Programming Formulation, Knapsack Problem, 0/1 Knapsack Problem: Dynamic Programming Approach.
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Greedy Algorithms,Counting Money, Making Change, Dynamic Programming Solution, Complexity of Coin Change Algorithm, Greedy Algorithm: Huffman Encoding, Huffman Encoding Algorithm, Huffman Encoding, Correctness, Activity Selection, Correctness of Greedy Activity Selection, Fractional Knapsack Problem.
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Graph Traversal, Breadth-First Search, Depth-First Search, Generic Graph Traversal Algorithm, DFS - Timestamp Structure, DFS - Cycles, Precedence Constraint Graph, Topological Sort, Strong Components, Strong Components And DFS, Minimum Spanning Trees, Computing MST, Generic Approach, Greedy MST, Kruskal’s Algorithm, Prim’s Algorithm Shortest Paths, Dijkstra’s Algorithm, Correctness Of Dijkstra’s Algorithm, Bellman-Ford Algorithm, Correctness Of Bellman-Ford, Floyd-Warshall Algorithm.
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Complexity Theory, Decision Problems, Complexity Classes, Polynomial Time Verification, The Class NP, Reductions.
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