Deep dive into algorithm analysis, design techniques, and optimization strategies for complex computational problems. This advanced course focuses on mathematical foundations, algorithm design paradigms, and performance analysis essential for solving challenging computational problems efficiently.
Divide & conquer, greedy, dynamic programming
Time complexity, space optimization
Performance tuning and efficiency
Network flows and approximation algorithms
Asymptotic notation, mathematical induction, and algorithm analysis basics
Divide and conquer paradigm, merge sort, and binary search analysis
Strassen's algorithm, closest pair problem, and master theorem
Greedy choice property, activity selection, and fractional knapsack
Huffman coding, minimum spanning trees (Kruskal and Prim)
Optimal substructure, overlapping subproblems, and memoization
Longest common subsequence, 0/1 knapsack, and matrix chain multiplication
Graph representations, BFS, DFS, and topological sorting
Shortest path algorithms: Dijkstra and Bellman-Ford
All-pairs shortest paths: Floyd-Warshall and Johnson's algorithm
Maximum flow problem, Ford-Fulkerson method, and applications
Disjoint sets, Fibonacci heaps, and advanced tree structures
Pattern matching, KMP algorithm, and suffix trees
P vs NP, NP-completeness, and reduction techniques
Approximation ratios, vertex cover, and traveling salesman problem
Randomized algorithms, linear programming, and final project presentations
This advanced course is currently being developed. Mathematical proofs, algorithm implementations, and challenging problem sets will be added progressively.