This module introduces the Chinese Remainder Theorem, covering its principles and applications in solving systems of congruences.
This module covers the foundational concepts of graph theory, including definitions, properties, and basic terminologies used in graph algorithms.
This module explores the Breadth-First Search (BFS) algorithm, its implementation, and applications in finding shortest paths and traversing graphs.
Focuses on Dijkstra's algorithm, detailing its mechanism for finding the shortest path in weighted graphs and its practical applications.
This module examines algorithms for finding the shortest paths between all pairs of nodes in a graph, including Floyd-Warshall.
Introduces matroids, their properties, and their significance in optimization and graph theory, setting the stage for subsequent optimization techniques.
This module covers techniques to find minimum spanning trees, including algorithms like Prim's and Kruskal's with real-world applications.
Explores Edmonds' matching algorithms, detailing their principles and applications in finding maximum matchings in bipartite graphs.
This module continues the exploration of Edmonds' algorithms, focusing on more advanced techniques and their applications in optimization problems.
This module covers flow networks, emphasizing concepts of flow and capacity, and the application of flow network theory in solving real-world problems.
Focuses on the Ford-Fulkerson method for computing maximum flow in a flow network, illustrating key concepts and practical applications.
This module introduces the Edmond-Karp algorithm, a specific implementation of the Ford-Fulkerson method utilizing BFS to find maximum flows.
Teaches matrix inversion techniques, detailing methods to compute the inverse of matrices and their applications in solving linear systems.
This module covers matrix decomposition methods such as LU decomposition, discussing their significance in numerical analysis and solving equations.
This module introduces the Knuth-Morris-Pratt algorithm for string matching, explaining its efficiency and applications in searching patterns.
Covers the Rabin-Karp algorithm, focusing on its probabilistic approach to string matching and its practical implementations.
This module explores NFA simulation techniques and their application in pattern matching and automata theory.
Focuses on integer polynomial operations, including multiplication and division techniques, with applications in computational mathematics.
This module continues integer polynomial operations, delving into advanced techniques and their computational implications.
Completes the discussion on integer polynomial operations, focusing on applications in number theory and algorithm design.
This module introduces the Chinese Remainder Theorem, covering its principles and applications in solving systems of congruences.
Continues the exploration of the Chinese Remainder Theorem, discussing more complex applications in algorithmic contexts.
This module completes the study of the Chinese Remainder Theorem, emphasizing its significance in computational techniques.
Introduces Discrete Fourier Transform (DFT) concepts, detailing its mathematical foundation and applications in signal processing and data analysis.
This module continues with DFT, exploring its computational techniques and the Fast Fourier Transform (FFT) approach.
Completes the study of DFT by discussing advanced applications in engineering and computer science.
This module covers the Schonhage-Strassen algorithm for fast multiplication of large integers, emphasizing its significance in computational efficiency.
Introduces linear programming concepts, including formulations, the simplex method, and applications in optimization problems.
This module continues linear programming with advanced techniques and duality theory, exploring their implications in practical scenarios.
Explores geometric algorithms, focusing on computational geometry concepts such as triangulation, area computation, and other spatial problems.
This module continues geometric algorithms, discussing intersection problems and convex hulls, and their importance in various fields.
This module completes the study of geometric algorithms by discussing advanced spatial data structures and their applications.
This module introduces approximation algorithms, discussing their role in providing near-optimal solutions for NP-hard problems.
Continues with approximation algorithms, focusing on specific techniques and case studies demonstrating their effectiveness.
This module completes the exploration of approximation algorithms by discussing their limits and theoretical foundations.
This module introduces dynamic programming concepts, outlining its principles and applications in solving complex problems.