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

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

    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
        Problem Set This content is graded
      2. Optional Theory Problems
         
      3. Programming Assignment 4
        Programming Assignment This content is graded

    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
        Problem Set This content is graded
      2. Optional Theory Problems
         
      3. Programming Assignment 5
        Programming Assignment This content is graded

    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
        Problem Set This content is graded
      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

    Important Course Dates

    Today is Mar 14, 2019 18:26 EDT

    Course Handouts

     
    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
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  • 原文地址：https://www.cnblogs.com/ecoflex/p/10534706.html
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