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I. TWO MOTIVATING APPLICATIONS (Week 1)
(collapsed, click to expand)- Completed Application: Internet Routing (11 min)
- Completed Application: Sequence Alignment (9 min)
II. SELECTED REVIEW FROM PART I (Week 1)
(collapsed, click to expand)- Completed About the Course [Part I Review - Optional] (17 min)
- Completed
Why Study Algorithms? [Part I Review - Optional] (19 min)
Slides (PDF) for Why Study Algorithms? [Part I Review - Optional] (19 min)Subtitles (text) for Why Study Algorithms? [Part I Review - Optional] (19 min)Subtitles (srt) for Why Study Algorithms? [Part I Review - Optional] (19 min)Video (MP4) for Why Study Algorithms? [Part I Review - Optional] (19 min)
- Completed
Guiding Principles for Analysis of Algorithms [Part I Review - Optional] (15 min)
Slides (PDF) for Guiding Principles for Analysis of Algorithms [Part I Review - Optional] (15 min)Subtitles (text) for Guiding Principles for Analysis of Algorithms [Part I Review - Optional] (15 min)Subtitles (srt) for Guiding Principles for Analysis of Algorithms [Part I Review - Optional] (15 min)Video (MP4) for Guiding Principles for Analysis of Algorithms [Part I Review - Optional] (15 min)
- Completed Big-Oh Notation [Part I Review - Optional] (4 min)
- Completed
Graph Representations [Part I Review - Optional] (14 min)
Slides (PDF) for Graph Representations [Part I Review - Optional] (14 min)Subtitles (text) for Graph Representations [Part I Review - Optional] (14 min)Subtitles (srt) for Graph Representations [Part I Review - Optional] (14 min)Video (MP4) for Graph Representations [Part I Review - Optional] (14 min)
- Completed
Graph Search - Overview [Part I Review - Optional] (23 min)
Slides (PDF) for Graph Search - Overview [Part I Review - Optional] (23 min)Subtitles (text) for Graph Search - Overview [Part I Review - Optional] (23 min)Subtitles (srt) for Graph Search - Overview [Part I Review - Optional] (23 min)Video (MP4) for Graph Search - Overview [Part I Review - Optional] (23 min)
- Completed
Dijkstra's Shortest-Path Algorithm [Part I Review - Optional] (21 min)
Slides (PDF) for Dijkstra's Shortest-Path Algorithm [Part I Review - Optional] (21 min)Subtitles (text) for Dijkstra's Shortest-Path Algorithm [Part I Review - Optional] (21 min)Subtitles (srt) for Dijkstra's Shortest-Path Algorithm [Part I Review - Optional] (21 min)Video (MP4) for Dijkstra's Shortest-Path Algorithm [Part I Review - Optional] (21 min)
- Completed
Data Structures: Overview [Part I Review - Optional] (5)
Slides (PDF) for Data Structures: Overview [Part I Review - Optional] (5)Subtitles (text) for Data Structures: Overview [Part I Review - Optional] (5)Subtitles (srt) for Data Structures: Overview [Part I Review - Optional] (5)Video (MP4) for Data Structures: Overview [Part I Review - Optional] (5)
- Completed
Heaps: Operations and Applications [Part I Review - Optional] (18)
Slides (PDF) for Heaps: Operations and Applications [Part I Review - Optional] (18)Subtitles (text) for Heaps: Operations and Applications [Part I Review - Optional] (18)Subtitles (srt) for Heaps: Operations and Applications [Part I Review - Optional] (18)Video (MP4) for Heaps: Operations and Applications [Part I Review - Optional] (18)
III. INTRODUCTION TO GREEDY ALGORITHMS (Week 1)
(collapsed, click to expand)- Completed Introduction to Greedy Algorithms (13 min)
- Completed Application: Optimal Caching (11 min)
IV. A SCHEDULING APPLICATION (Week 1)
(collapsed, click to expand)- Completed Problem Definition (6 min)
- Completed A Greedy Algorithm (13 min)
- Completed Correctness Proof - Part I (7 min)
- Completed Correctness Proof - Part II (5 min)
- Completed Handling Ties [Advanced - Optional] (7 min)
V. PRIM'S MINIMUM SPANNING TREE ALGORITHM (Week 1)
(collapsed, click to expand)- Completed MST Problem Definition (11 min)
- Completed Prim's MST Algorithm (8 min)
- Completed Correctness Proof I (16 min)
- Completed Correctness Proof II (8 min)
- Completed Proof of Cut Property [Advanced - Optional] (12 min)
- Completed Fast Implementation I (15 min)
- Completed Fast Implementation II (10 min)
VI. KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM (Week 2)
(collapsed, click to expand)- Completed Kruskal's MST Algorithm (8 min)
- Completed Correctness of Kruskal's Algorithm (9 min)
- Completed
Implementing Kruskal's Algorithm via Union-Find I (9 min)
Slides (PDF) for Implementing Kruskal's Algorithm via Union-Find I (9 min)Subtitles (text) for Implementing Kruskal's Algorithm via Union-Find I (9 min)Subtitles (srt) for Implementing Kruskal's Algorithm via Union-Find I (9 min)Video (MP4) for Implementing Kruskal's Algorithm via Union-Find I (9 min)
- Completed
Implementing Kruskal's Algorithm via Union-Find II (14 min)
Slides (PDF) for Implementing Kruskal's Algorithm via Union-Find II (14 min)Subtitles (text) for Implementing Kruskal's Algorithm via Union-Find II (14 min)Subtitles (srt) for Implementing Kruskal's Algorithm via Union-Find II (14 min)Video (MP4) for Implementing Kruskal's Algorithm via Union-Find II (14 min)
- Completed
MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)
Slides (PDF) for MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)Subtitles (text) for MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)Subtitles (srt) for MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)Video (MP4) for MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)
VII. CLUSTERING (Week 2)
(collapsed, click to expand)- Completed Application to Clustering (12 min)
- Completed Correctness of Clustering Algorithm (10 min)
VIII. ADVANCED UNION-FIND (Week 2)
(collapsed, click to expand)- Completed Lazy Unions [Advanced - Optional] (10 min)
- Completed Union-by-Rank [Advanced - Optional] (12 min)
- Completed Analysis of Union-by-Rank [Advanced - Optional](15)
- Completed Path Compression [Advanced - Optional] (15)
- Completed
Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]
Slides (PDF) for Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]Subtitles (text) for Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]Subtitles (srt) for Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]Video (MP4) for Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]
- Completed
Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]
Slides (PDF) for Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]Subtitles (text) for Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]Subtitles (srt) for Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]Video (MP4) for Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]
- Completed The Ackermann Function [Advanced - Optional](17 min)
- Completed
Path Compression: Tarjan's Analysis I [Advanced - Optional]
Slides (PDF) for Path Compression: Tarjan's Analysis I [Advanced - Optional]Subtitles (text) for Path Compression: Tarjan's Analysis I [Advanced - Optional]Subtitles (srt) for Path Compression: Tarjan's Analysis I [Advanced - Optional]Video (MP4) for Path Compression: Tarjan's Analysis I [Advanced - Optional]
- Completed
Path Compression: Tarjan's Analysis II [Advanced - Optional]
Slides (PDF) for Path Compression: Tarjan's Analysis II [Advanced - Optional]Subtitles (text) for Path Compression: Tarjan's Analysis II [Advanced - Optional]Subtitles (srt) for Path Compression: Tarjan's Analysis II [Advanced - Optional]Video (MP4) for Path Compression: Tarjan's Analysis II [Advanced - Optional]
IX. HUFFMAN CODES (Week 2)
(collapsed, click to expand)- Completed Introduction and Motivation (9 min)
- Completed Problem Definition (10 min)
- Completed A Greedy Algorithm (17 min)
- Completed Correctness Proof I (10 min)
- Completed Correctness Proof II (13 min)
X. INTRODUCTION TO DYNAMIC PROGRAMMING (Week 3)
(collapsed, click to expand)- Completed
Introduction: Weighted Independent Sets in Path Graphs (8 min)
Slides (PDF) for Introduction: Weighted Independent Sets in Path Graphs (8 min)Subtitles (text) for Introduction: Weighted Independent Sets in Path Graphs (8 min)Subtitles (srt) for Introduction: Weighted Independent Sets in Path Graphs (8 min)Video (MP4) for Introduction: Weighted Independent Sets in Path Graphs (8 min)
- Completed WIS in Path Graphs: Optimal Substructure (9 min)
- Completed WIS in Path Graphs: A Linear-Time Algorithm (10 min)
- Completed WIS in Path Graphs: A Reconstruction Algorithm (7 min)
- Completed Principles of Dynamic Programming (8 min)
XI. THE KNAPSACK PROBLEM (Week 3)
(collapsed, click to expand)- Completed The Knapsack Problem (10 min)
- Completed A Dynamic Programming Algorithm (10 min)
XII. SEQUENCE ALIGNMENT (Week 3)
(collapsed, click to expand)- Completed Optimal Substructure (14 min)
- Completed A Dynamic Programming Algorithm (12 min)
XIII. OPTIMAL BINARY SEARCH TREES (Week 3)
(collapsed, click to expand)- Completed Problem Definition (12 min)
- Completed Optimal Substructure (9 min)
- Completed Proof of Optimal Substructure (7 min)
- Completed A Dynamic Programming Algorithm I (10 min)
- Completed A Dynamic Programming Algorithm II (9 min)
XIV. THE BELLMAN-FORD ALGORITHM (Week 4)
(collapsed, click to expand)- Completed Single-Source Shortest Paths, Revisted (11 min)
- Completed Optimal Substructure (11 min)
- Completed The Basic Algorithm I (9 min)
- Completed The Basic Algorithm II (11 min)
- Completed Detecting Negative Cycles (9 min)
- Completed A Space Optimization (12 min)
- Completed Internet Routing I [Optional] (11 min)
- Completed Internet Routing II [Optional] (7 min)
XV. ALL-PAIRS SHORTEST PATHS (Week 4)
(collapsed, click to expand)- Completed Problem Definition (7 min)
- Completed Optimal Substructure (12 min)
- Completed The Floyd-Warshall Algorithm (13 min)
- Completed A Reweighting Technique (14 min)
- Completed Johnson's Algorithm I (11 min)
- Completed Johnson's Algorithm II (11 min)
XVI. NP-COMPLETE PROBLEMS (Week 5)
(collapsed, click to expand)- Completed Polynomial-Time Solvable Problems (14 min)
- Completed Reductions and Completeness (14 min)
- Completed
Definition and Interpretation of NP-Completeness I (11 min)
Slides (PDF) for Definition and Interpretation of NP-Completeness I (11 min)Subtitles (text) for Definition and Interpretation of NP-Completeness I (11 min)Subtitles (srt) for Definition and Interpretation of NP-Completeness I (11 min)Video (MP4) for Definition and Interpretation of NP-Completeness I (11 min)
- Completed
Definition and Interpretation of NP-Completeness II (8 min)
Slides (PDF) for Definition and Interpretation of NP-Completeness II (8 min)Subtitles (text) for Definition and Interpretation of NP-Completeness II (8 min)Subtitles (srt) for Definition and Interpretation of NP-Completeness II (8 min)Video (MP4) for Definition and Interpretation of NP-Completeness II (8 min)
- Completed The P vs. NP Question (9 min)
- Completed Algorithmic Approaches to NP-Complete Problems (13 min)
XVII. FASTER EXACT ALGORITHMS FOR NP-COMPLETE PROBLEMS (Week 5)
(collapsed, click to expand)- Completed The Vertex Cover Problem (9 min)
- Completed Smarter Search for Vertex Cover I (10 min)
- Completed Smarter Search for Vertex Cover II (8 min)
- Completed The Traveling Salesman Problem (15 min)
- Completed A Dynamic Programming Algorithm for TSP (12 min)
XVIII. APPROXIMATION ALGORITHMS FOR NP-COMPLETE PROBLEMS (Week 6)
(collapsed, click to expand)- Completed A Greedy Knapsack Heuristic (14 min)
- Completed Analysis of a Greedy Knapsack Heuristic I (7 min)
- Completed Analysis of a Greedy Knapsack Heuristic II (10 min)
- Completed A Dynamic Programming Heuristic for Knapsack (12 min)
- Completed Knapsack via Dynamic Programming, Revisited (10 min)
- Completed Ananysis of Dynamic Programming Heuristic (15 min)
XIX. LOCAL SEARCH ALGORITHMS (Week 6)
(collapsed, click to expand)- Completed The Maximum Cut Problem I (9 min)
- Completed The Maximum Cut Problem II (9 min)
- Completed Principles of Local Search I (9 min)
- Completed Principles of Local Search II (10 min)
- Completed The 2-SAT Problem (15 min)
- Completed Random Walks on a Line (16 min)
- Completed Analysis of Papadimitriou's Algorithm (15 min)
XX. THE WIDER WORLD OF ALGORITHMS (Week 6)
(collapsed, click to expand)- Completed Stable Matching [Optional] (15 min)
- Completed
Matchings, Flows, and Braess's Paradox [Optional] (14 min)
Slides (PDF) for Matchings, Flows, and Braess's Paradox [Optional] (14 min)Subtitles (text) for Matchings, Flows, and Braess's Paradox [Optional] (14 min)Subtitles (srt) for Matchings, Flows, and Braess's Paradox [Optional] (14 min)Video (MP4) for Matchings, Flows, and Braess's Paradox [Optional] (14 min)
- Completed Linear Programming and Beyond [Optional] (11 min)
- Completed Epilogue (1 min)