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Learn comprehensive algorithm design and analysis techniques through this extensive course covering fundamental concepts essential for technical interviews and competitive programming. Master time complexity analysis including Big O, Omega, and Theta notations, asymptotic behavior, and growth rates with step-by-step examples and calculations. Explore divide and conquer strategies through practical implementations of binary search, merge sort, quick sort, and Strassen's matrix multiplication algorithm. Dive deep into greedy algorithms by solving job sequencing, minimum spanning trees using Kruskal's and Prim's algorithms, Dijkstra's shortest path, and fractional knapsack problems. Understand dynamic programming principles and applications through detailed solutions to 0/1 knapsack, traveling salesman problem, longest common subsequence, multistage graphs, optimal binary search trees, and Floyd-Warshall all-pairs shortest path algorithm. Study graph theory fundamentals, terminology, and traversal methods including depth-first search (DFS) and breadth-first search (BFS). Master backtracking techniques by solving N-Queens, sum of subsets, Hamiltonian cycle, and graph coloring problems with complete state space tree analysis. Learn branch and bound methodology through traveling salesman and knapsack problem solutions using least cost and FIFO approaches. Explore advanced data structures including disjoint sets with union-find operations, weighted union, and collapsing find optimizations. Compare algorithmic paradigms including divide and conquer versus dynamic programming, and dynamic programming versus greedy methods with practical examples and key differences highlighted throughout the comprehensive curriculum.
