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Algorithms Design and Analysis

1 Why Study Algorithms 4 min
2 Integer Multiplication 9 min
3 Karatsuba Multiplication 13 min
4 About the Course 17 min
5 Merge Sort- Motivation and Example 9 min
6 Merge Sort- Pseudocode 13 min
7 Merge Sort- Analysis 9 min
8 Guiding Principles for Analysis of Algorithms 15 min
1 The Gist 14 min
2 Big-Oh Notation 4 min
3 Basic Examples 7 min
4 Big Omega and Theta 7 min
5 Additional Examples Review - Optional 8 min
1 On log n Algorithm for Counting Inversions I 13 min
2 On log n Algorithm for Counting Inversions II 17 min
3 Strassens Subcubic Matrix Multiplication Algorithm 22 min
4 On log n Algorithm for Closest Pair I Advanced - Optional 32 min
5 On log n Algorithm for Closest Pair II Advanced - Optional 19 min
01 Motivation 8 min
02 Formal Statement 10 min
03 Examples 13 min
04 Proof I 10 min
05 Interpretation of the 3 Cases 11 min
06 Proof II 16 min
1 Quicksort- Overview 12 min
2 Partitioning Around a Pivot 25 min
3 Correctness of Quicksort Review - Optional 11 min
4 Choosing a Good Pivot 22min
1 Analysis I- A Decomposition Principle Advanced - Optional 22 min
2 Analysis II- The Key Insight Advanced - Optional 12min
3 Analysis III- Final Calculations Advanced - Optional 9min
TY REVIEW Weeks 2-31 Part I Review - Optional 25 min
TY REVIEW Weeks 2-32 Part II Review - Optional 17 min
1 Randomized Selection - Algorithm 22 min
2 Randomized Selection - Analysis 21 min
3 Deterministic Selection - Algorithm Advanced - Optional 17 min
4 Deterministic Selection - Analysis I Advanced - Optional 22 min
5 Deterministic Selection - Analysis II Advanced - Optional 13 min
6 Omegan log n Lower Bound for Comparison-Based Sorting Advanced - Optional 13 min
1 Graphs and Minimum Cuts 16 min
2 Graph Representations 14 min
3 Random Contraction Algorithm 9 min
4 Analysis of Contraction Algorithm 30 min
5 Counting Minimum Cuts 7 min
1 Graph Search - Overview 23 min
2 Breadth-First Search BFS- The Basics 14 min
3 BFS and Shortest Paths 8 min
4 BFS and Undirected Connectivity 13 min
5 Depth-First Search DFS- The Basics 7 min
6 Topological Sort 22 min
7 Computing Strong Components- The Algorithm 29 min
8 Computing Strong Components- The Analysis 26 min
9 Structure of the Web Optional 19 min
1 Dijkstras Shortest-Path Algorithm 21 min
2 Dijkstras Algorithm- Examples 13 min
3 Correctness of Dijkstras Algorithm Advanced - Optional 19 min
4 Dijkstras Algorithm- Implementation and Running Time 26 min
1 Data Structures- Overview 5 min
2 Heaps- Operations and Applications 18 min
3 Heaps- Implementation Details Advanced - Optional 21 min
1 Balanced Search Trees- Operations and Applications 11 min
2 Binary Search Tree Basics Part I 13 min
3 Binary Search Tree Basics Part II 30 min
4 Red-Black Trees 21 min
5 Rotations Advanced - Optional 8 min
6 Insertion in a Red-Black Tree Advanced 15 min
1 Hash Tables- Operations and Applications 19 min
2 Hash Tables- Implementation Details Part I 19 min
3 Hash Tables- Implementation Details Part II 22 min
1 Pathological Data Sets and Universal Hashing Motivation 22 min
2 Universal Hashing- Definition and Example Advanced - Optional 26 min
3 Universal Hashing- Analysis of Chaining Advanced - Optional 19 min
4 Hash Table Performance with Open Addressing Advanced - Optional 16 min
1 Bloom Filters- The Basics 16 min
2 Bloom Filters- Heuristic Analysis 13 min
1 Application- Internet Routing Optional 11 min
2 Application- Sequence Alignment Optional 9 min
3 Introduction to Greedy Algorithms Optional 13 min
4 Huffman Codes- Introduction and Motivation Optional 9 min
5 Principles of Dynamic Programming Optional 8 min
6 The P vs. NP Question Optional 9 min
7 Algorithmic Approaches to NP-Complete Problems Optional 13 min
1 Application- Internet Routing 11 min
2 Application- Sequence Alignment 9 min
1 About the Course Part I Review - Optional 17 min
2 Why Study Algorithms Part I Review - Optional 19 min
3 Guiding Principles for Analysis of Algorithms Part I Review - Optional 15 min
4 Big-Oh Notation Part I Review - Optional 4 min
5 Graph Representations Part I Review - Optional 14 min
6 Graph Search - Overview Part I Review - Optional 23 min
7 Dijkstras Shortest-Path Algorithm Part I Review - Optional 21 min
8 Data Structures- Overview Part I Review - Optional 5 min
9 Heaps- Operations and Applications Part I Review - Optional 18 min
1 Introduction to Greedy Algorithms 13 min
2 Application- Optimal Caching 11 min
Problem Definition 6 min
IV. A SCHEDULING APPLICATIO2 A Greedy Algorithm 13 min
IV. A SCHEDULING APPLICATIO3 Correctness Proof - Part I 7 min
IV. A SCHEDULING APPLICATIO4 Correctness Proof - Part II 5 min
IV. A SCHEDULING APPLICATIO5 Handling Ties Advanced - Optional 7 min
1 MST Problem Definition 11 min
2 Prims MST Algorithm 8 min
3 Correctness Proof I 16 min
5 V. PRIMS MINIMUM SPANNING TREE ALGORITHM Week 1Correctness Proof II 8 min
5 Proof of Cut Property Advanced - Optional 12 min
6 Fast Implementation I 15 min
7 Fast Implementation II 10 min
Kruskals MST Algorithm 8 min
2 Correctness of Kruskals Algorithm 9 min
3 Implementing Kruskals Algorithm via Union-Find I 9 min
4 Implementing Kruskals Algorithm via Union-Find II 14 min
5 MSTs- State-of-the-Art and Open Questions Advanced - Optional 9 min
21 Application to Clustering 12 min
22 Correctness of Clustering Algorithm 10 min
21 Lazy Unions Advanced - Optional 10 min
22 Union-by-Rank Advanced - Optional 12 min
23 Analysis of Union-by-Rank Advanced - Optional 15 min
2Path Compression Advanced - Optional 15 min
25 Path Compression- The Hopcroft-Ullman Analysis I Advanced - Optional 9 min
26 Path Compression- The Hopcroft-Ullman Analysis II Advanced - Optional 12 min
27 The Ackermann Function Advanced - Optional 17 min
28 Path Compression- Tarjans Analysis I Advanced - Optional 14 min
29 Path Compression- Tarjans Analysis II Advanced - Optional 14 min
21 Introduction and Motivation 9 min
22 Problem Definition 10 min
23 A Greedy Algorithm 17 min
2A More Complex Example 4 min
25 Correctness Proof I 10 min
26 Correctness Proof II 13 min
1 Introduction- Weighted Independent Sets in Path Graphs 8 min
2 WIS in Path Graphs- Optimal Substructure 9 min
3 WIS in Path Graphs- A Linear-Time Algorithm 10 min
10 X. INTRODUCTION TO DYNAMIC PROGRAMMING Week 3WIS in Path Graphs- A Reconstruction Algorithm 7 min
5 Principles of Dynamic Programming 8 min
31 The Knapsack Problem 10 min
32 A Dynamic Programming Algorithm 10 min
33 Example Review - Optional 14 min
31 Optimal Substructure 14 min
32 A Dynamic Programming Algorithm 12 min
31 Problem Definition 12 min
32 Optimal Substructure 9 min
33 Proof of Optimal Substructure 7 min
3A Dynamic Programming Algorithm I 10 min
35 A Dynamic Programming Algorithm II 9 min
41 Single-Source Shortest Paths Revisted 11 min
42 Optimal Substructure 11 min
43 The Basic Algorithm I 9 min
4The Basic Algorithm II 11 min
45 Detecting Negative Cycles 9 min
46 A Space Optimization 12 min
47 Internet Routing I Optional 11 min
48 Internet Routing II Optional 7 min
1 Problem Definition 7 min
2 Optimal Substructure 12 min
3 The Floyd-Warshall Algorithm 13 min
15 XV. ALL-PAIRS SHORTEST PATHS Week 4A Reweighting Technique 14 min
5 Johnsons Algorithm I 11 min
6 Johnsons Algorithm II 11 min
1 Polynomial-Time Solvable Problems 14 min
2 Reductions and Completeness 14 min
3 Definition and Interpretation of NP-Completeness I 11 min
16 XVI. NP-COMPLETE PROBLEMS Week 5Definition and Interpretation of NP-Completeness II 8 min
5 The P vs. NP Question 9 min
6 Algorithmic Approaches to NP-Complete Problems 13 min
1 The Vertex Cover Problem 9 min
2 Smarter Search for Vertex Cover I 10 min
3 Smarter Search for Vertex Cover II 8 min
FASTER EXACT ALGORITHMS FOR NP-COMPLETE PROBLEMS Week 5The Traveling Salesman Problem 15 min
5 A Dynamic Programming Algorithm for TSP 12 min
1 A Greedy Knapsack Heuristic 14 min
2 Analysis of a Greedy Knapsack Heuristic I 7 min
3 Analysis of a Greedy Knapsack Heuristic II 10 min
4 A Dynamic Programming Heuristic for Knapsack 12 min
5 Knapsack via Dynamic Programming Revisited 10 min
6 Ananysis of Dynamic Programming Heuristic 15 min
1 The Maximum Cut Problem I 9 min
2 The Maximum Cut Problem II 9 min
3 Principles of Local Search I 9 min
SEARCH ALGORITHMS Week 6Principles of Local Search II 10 min
5 The 2-SAT Problem 15 min
6 Random Walks on a Line 16 min
7 Analysis of Papadimitrious Algorithm 15 min
1 Stable Matching Optional 15 min
2 Matchings F