</>DevThesis
HomeCurriculumAlgorithms

Algorithms

Asymptotic complexity analysis, divide-and-conquer strategies, dynamic programming recurrence relations, and graph traversal paradigms.

1Asymptotic Complexity & Divide-and-Conquer Analysis

Master Theorem recurrence solving, Quicksort median-of-three partitioning, and Mergesort cache efficiency.

Asymptotic Complexity & Divide-and-Conquer Analysis

Master Theorem recurrence solving, Quicksort median-of-three partitioning, and Mergesort cache efficiency.

Asymptotic Complexity & Divide-and-Conquer Analysis

Master Theorem recurrence solving, Quicksort median-of-three partitioning, and Mergesort cache efficiency.

2Dynamic Programming Paradigms & DAG Shortest Paths

Optimal substructure, overlapping subproblems, memoization vs tabulation, state compression, and bitmask dynamic programming.

Optimal Substructure, Overlapping Subproblems & State Space Compression

Bellman's principle of optimality, bottom-up tabulation, 1D rolling array compression, and bitmask state spaces.

Memoization, Tabulation, 0/1 Knapsack & State Space Bitmask Optimization

Master Bellman's principle of optimality, overlapping subproblems, top-down memoization versus bottom-up tabulation, 1D array space compression in 0/1 knapsack, and bitmask dynamic programming for subset state spaces.

3Graph Search Paradigms, Shortest Paths & Heuristic Navigation

Breadth-First Search (BFS), Depth-First Search (DFS), Dijkstra's algorithm, Bellman-Ford, and A* heuristic navigation.

Dijkstra Non-Negative Paths, Bellman-Ford Negative Cycles & A* Admissibility

Priority queue relaxation, negative-weight edge cycles, and heuristic search admissibility and consistency.

Dijkstra Heap Optimization, Bellman-Ford Negative Cycles & Admissible A* Search

Master single-source shortest path theory, Dijkstra's algorithm with min-heap relaxation, Bellman-Ford dynamic edge relaxation and negative cycle detection, and the A* search algorithm with admissible and consistent heuristics.

4Greedy Strategies, Flow Networks & NP-Completeness

Huffman coding, Prim/Kruskal MST, Ford-Fulkerson max flow, Edmonds-Karp, and NP-completeness reductions.

Ford-Fulkerson Augmenting Paths, Edmonds-Karp & Polynomial Reductions

Residual flow networks, augmenting paths, Max-Flow Min-Cut duality, and Cook-Levin polynomial reductions.

Edmonds-Karp Max-Flow, Min-Cut Duality Theorem & NP-Complete Reductions

Master flow network mechanics, residual capacities and back-edges, the Edmonds-Karp algorithm BFS path selection, the Max-Flow Min-Cut duality theorem, complexity classes P and NP, and polynomial-time Cook-Levin reductions.