[Stanford Algorithms: Design and Analysis, Part 2] c17-21 greedy algorithm | prim MST

Specific topics in Part 2 include: greedy algorithms (scheduling, minimum spanning trees, clustering, Huffman codes), dynamic programming (knapsack, sequence alignment, optimal search trees, shortest paths), NP-completeness and what it means for the algorithm designer, analysis of heuristics, local search.

Resources

 

  1. INTRODUCTION [Chapter 17]

    1. Overview, Resources, and Policies
       
    2. Pre-Course Survey
       
    3. All Lecture slides
       

  2. TWO MOTIVATING APPLICATIONS [Chapter 18]

    1. Overview
       
    2. Application: Internet Routing (10 min)
       
    3. Application: Sequence Alignment (8 min)
       

  3. INTRODUCTION TO GREEDY ALGORITHMS [Chapter 19]

    1. Introduction to Greedy Algorithms (12 min)
       
    2. Application: Optimal Caching (10 min)
       

  4. A SCHEDULING APPLICATION  [Chapter 20]

    1. Problem Definition (5 min)
       
    2. A Greedy Algorithm (12 min)
       
    3. Correctness Proof - Part I (6 min)
       
    4. Correctness Proof - Part II (4 min)
       
    5. Handling Ties [Advanced - Optional] (7 min)
       

  5. PRIM'S MINIMUM SPANNING TREE ALGORITHM [Chapter 21]

    1. MST Problem Definition (11 min)
       
    2. Prim's MST Algorithm (7 min)
       
    3. Correctness Proof I (15 min)
       
    4. Correctness Proof II (8 min)
       
    5. Proof of Cut Property [Advanced - Optional] (11 min)
       
    6. Fast Implementation I (14 min)
       
    7. Fast Implementation II (9 min)
       

  6. Homework 1

    1. Problem Set 1
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    2. Optional Theory Problems
       
    3. Programming Assignment 1
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  7. KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM [Chapter 22]

    1. Overview
       
    2. Kruskal's MST Algorithm (7 min)
       
    3. Correctness of Kruskal's Algorithm (9 min)
       
    4. Implementing Kruskal's Algorithm via Union-Find I (9 min)
       
    5. Implementing Kruskal's Algorithm via Union-Find II (13 min)
       
    6. MSTs: State-of-the-Art and Open Questions [Advanced - Optional] (9 min)
       

  8. CLUSTERING [Chapter 23]

    1. Application to Clustering (11 min)
       
    2. Correctness of Clustering Algorithm (9 min)
       

  9. ADVANCED UNION-FIND [Chapter 24]

    1. Lazy Unions [Advanced - Optional] (10 min)
       
    2. Union-by-Rank [Advanced - Optional] (12 min)
       
    3. Analysis of Union-by-Rank [Advanced - Optional] (14 min)
       
    4. Path Compression [Advanced - Optional] (14 min)
       
    5. Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional] (9 min)
       
    6. Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional] (11 min)
       
    7. The Ackermann Function [Advanced - Optional] (16 min)
       
    8. Path Compression: Tarjan's Analysis I [Advanced - Optional] (14 min)
       
    9. Path Compression: Tarjan's Analysis II [Advanced - Optional] (13 min)
       

  10. HUFFMAN CODES [Chapter 25]

    1. Introduction and Motivation (9 min)
       
    2. Problem Definition (10 min)
       
    3. A Greedy Algorithm (16 min)
       
    4. A More Complex Example (4 min)
       
    5. Correctness Proof I (10 min)
       
    6. Correctness Proof II (12 min)
       

  11. Homework 2

    1. Problem Set 2
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    2. Optional Theory Problems
       
    3. Programming Assignment 2
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  12. INTRODUCTION TO DYNAMIC PROGRAMMING [Chapter 26]

    1. Overview
       
    2. Introduction: Weighted Independent Sets in Path Graphs (7 min)
       
    3. WIS in Path Graphs: Optimal Substructure (9 min)
       
    4. WIS in Path Graphs: A Linear-Time Algorithm (9 min)
       
    5. WIS in Path Graphs: A Reconstruction Algorithm (6 min)
       
    6. Principles of Dynamic Programming (7 min)
       

  13. THE KNAPSACK PROBLEM [Chapter 27]

    1. The Knapsack Problem (9 min)
       
    2. A Dynamic Programming Algorithm (9 min)
       
    3. Example [Review - Optional] (12 min)
       

  14. SEQUENCE ALIGNMENT [Chapter 28]

    1. Optimal Substructure (13 min)
       
    2. A Dynamic Programming Algorithm (12 min)
       

  15. OPTIMAL BINARY SEARCH TREES [Chapter 29]

    1. Problem Definition (12 min)
       
    2. Optimal Substructure (9 min)
       
    3. Proof of Optimal Substructure (6 min)
       
    4. A Dynamic Programming Algorithm I (9 min)
       
    5. A Dynamic Programming Algorithm II (9 min)
       

  16. Homework 3

    1. Problem Set 3
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    2. Optional Theory Problems
       
    3. Programming Assignment 3
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  17. THE BELLMAN-FORD ALGORITHM: [Chapter 30]

    1. Overview
       
    2. Single-Source Shortest Paths, Revisited (10 min)
       
    3. Optimal Substructure (10 min)
       
    4. The Basic Algorithm I (8 min)
       
    5. The Basic Algorithm II (10 min)
       
    6. Detecting Negative Cycles (9 min)
       
    7. A Space Optimization (12 min)
       
    8. Internet Routing I [Optional] (11 min)
       
    9. Internet Routing II [Optional] (6 min)
       

  18. ALL-PAIRS SHORTEST PATHS [Chapter 31]

    1. Problem Definition (7 min)
       
    2. Optimal Substructure (12 min)
       
    3. The Floyd-Warshall Algorithm (13 min)
       
    4. A Reweighting Technique (14 min)
       
    5. Johnson's Algorithm I (11 min)
       
    6. Johnson's Algorithm II (11 min)
       

  19. Homework 4

    1. Problem Set 4
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    2. Optional Theory Problems
       
    3. Programming Assignment 4
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  20. NP-COMPLETE PROBLEMS [Chapter 32]

    1. Overview
       
    2. Polynomial-Time Solvable Problems (14 min)
       
    3. Reductions and Completeness (13 min)
       
    4. Definition and Interpretation of NP-Completeness I (10 min)
       
    5. Definition and Interpretation of NP-Completeness II (7 min)
       
    6. The P vs. NP Question (9 min)
       
    7. Algorithmic Approaches to NP-Complete Problems (12 min)
       

  21. FASTER EXACT ALGORITHMS FOR NP-COMPLETE PROBLEMS [Chapter 33]

    1. The Vertex Cover Problem (8 min)
       
    2. Smarter Search for Vertex Cover I (9 min)
       
    3. Smarter Search for Vertex Cover II (7 min)
       
    4. The Traveling Salesman Problem (14 min)
       
    5. A Dynamic Programming Algorithm for TSP (12 min)
       

  22. Homework 5

    1. Problem Set 5
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    2. Optional Theory Problems
       
    3. Programming Assignment 5
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  23. APPROXIMATION ALGORITHMS FOR NP-COMPLETE PROBLEMS [Chapter 34]

    1. Overview
       
    2. A Greedy Knapsack Heuristic (14 min)
       
    3. Analysis of a Greedy Knapsack Heuristic I (7 min)
       
    4. Analysis of a Greedy Knapsack Heuristic II (9 min)
       
    5. A Dynamic Programming Heuristic for Knapsack (11 min)
       
    6. Knapsack via Dynamic Programming, Revisited (10 min)
       
    7. Analysis of Dynamic Programming Heuristic (15 min)
       

  24. LOCAL SEARCH ALGORITHMS [Chapter 35]

    1. The Maximum Cut Problem I (8 min)
       
    2. The Maximum Cut Problem II (9 min)
       
    3. Principles of Local Search I (8 min)
       
    4. Principles of Local Search II (10 min)
       
    5. The 2-SAT Problem (14 min)
       
    6. Random Walks on a Line (16 min)
       
    7. Analysis of Papadimitriou's Algorithm (14 min)
       

  25. THE WIDER WORLD OF ALGORITHMS [Chapter 36]

    1. Stable Matching [Optional] (15 min)
       
    2. Matchings, Flows, and Braess's Paradox [Optional] (13 min)
       
    3. Linear Programming and Beyond [Optional] (11 min)
       
    4. Epilogue (1 min)
       

  26. Homework 6

    1. Problem Set 6
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    2. Optional Theory Problems
       
    3. Programming Assignment 6
      Programming Assignment This content is graded

  27. Final Exam

    1. Final Exam
      Final Exam This content is graded

  28. Finishing Up

    1. Post-Course Survey
       
    2. Generate Your Statement of Accomplishment
       

Course Tools

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Today is Mar 14, 2019 18:26 EDT

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https://github.com/SSQ/Coursera-Stanford-Algorithms-Specialization

 

 

 

03/14/2019 Last few days:

https://www.youtube.com/playlist?list=PLXFMmlk03Dt5EMI2s2WQBsLsZl7A5HEK6

 

 

 

 

 

 

 

 

 

 

Minimum spanning tree:

https://www.cnblogs.com/infroad/p/9245794.html

 

 

 

posted @ 2019-03-15 06:31  ecoflex  阅读(443)  评论(0)  编辑  收藏  举报