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I. INTRODUCTION (Week 1)
(collapsed, click to expand)- Completed
Introduction : Why Study Algorithms ? (19 min)
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- Completed About the Course (17 min)
- Completed
Merge Sort: Motivation and Example (9 min)
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- Completed Merge Sort: Pseudocode (13 min)
- Completed Merge Sort: Analysis (9 min)
- Completed
Guiding Principles for Analysis of Algorithms (15 min)
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II. ASYMPTOTIC ANALYSIS (Week 1)
(collapsed, click to expand)- Completed Big-Oh Notation (4 min)
- Completed Basic Examples (7 min)
- Completed Big Omega and Theta (7 min)
- Completed
Additional Examples [Review - Optional] (8 min)
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III. DIVIDE & CONQUER ALGORITHMS (Week 1)
(collapsed, click to expand)- Completed
O(n log n) Algorithm for Counting Inversions I (13 min)
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- Completed
O(n log n) Algorithm for Counting Inversions II (17 min)
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- Completed
Strassen's Subcubic Matrix Multiplication Algorithm (22 min)
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- Completed
O(n log n) Algorithm for Closest Pair I [Advanced - Optional] (32 min)
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- Completed
O(n log n) Algorithm for Closest Pair II [Advanced - Optional] (19 min)
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IV. THE MASTER METHOD (Week 2)
(collapsed, click to expand)- Completed Motivation (8 min)
- Completed Formal Statement (10 min)
- Completed Examples (13 min)
- Completed Proof I (10 min)
- Completed
Interpretation of the 3 Cases (11 min)
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- Completed Proof II (16 min)
V. QUICKSORT - ALGORITHM (Week 2)
(collapsed, click to expand)- Completed Quicksort: Overview (12 min)
- Completed
Partitioning Around a Pivot (25 min)
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- Completed
Correctness of Quicksort [Review - Optional] (11 min)
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- Completed Choosing a Good Pivot (22min)
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Analysis I: A Decomposition Principle [Advanced - Optional] (22 min)
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Analysis II: The Key Insight [Advanced - Optional] (12min)
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Analysis III: Final Calculations [Advanced - Optional] (9min)
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VII. PROBABILITY REVIEW (Weeks 2-3)
(collapsed, click to expand)- Completed Part I [Review - Optional] (25 min)
- Completed
Part II [Review - Optional] (17 min)
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- Completed
Randomized Selection - Algorithm (22 min)
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- Completed
Randomized Selection - Analysis (21 min)
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Deterministic Selection - Algorithm [Advanced - Optional] (17 min)
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Deterministic Selection - Analysis I [Advanced - Optional] (22 min)
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Deterministic Selection - Analysis II [Advanced - Optional] (13 min)
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Omega(n log n) Lower Bound for Comparison-Based Sorting [Advanced - Optional] (13 min)
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IX. GRAPHS AND THE CONTRACTION ALGORITHM (Week 3)
(collapsed, click to expand)- Completed Graphs and Minimum Cuts (16 min)
- Completed Graph Representations (14 min)
- Completed
Random Contraction Algorithm (9 min)
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- Completed
Analysis of Contraction Algorithm (30 min)
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- Completed Counting Minimum Cuts (7 min)
- Completed Graph Search - Overview (23 min)
- Completed
Breadth-First Search (BFS): The Basics (14 min)
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- Completed BFS and Shortest Paths (8 min)
- Completed
BFS and Undirected Connectivity (13 min)
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- Completed
Depth-First Search (DFS): The Basics (7 min)
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- Completed Topological Sort (22 min)
- Completed
Computing Strong Components: The Algorithm (29 min)
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- Completed
Computing Strong Components: The Analysis (26 min)
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Structure of the Web [Optional] (19 min)
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- Completed
Dijkstra's Shortest-Path Algorithm (21 min)
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- Completed
Dijkstra's Algorithm: Examples (13 min)
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Correctness of Dijkstra's Algorithm [Advanced - Optional] (19 min)
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- Completed
Dijkstra's Algorithm: Implementation and Running Time (26 min)
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XII. HEAPS (Week 5)
(collapsed, click to expand)- Completed Data Structures: Overview (5 min)
- Completed
Heaps: Operations and Applications (18 min)
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- Completed
Heaps: Implementation Details [Advanced - Optional] (21 min)
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XIII. HASHING: THE BASICS (Week 5)
(collapsed, click to expand)- Completed
Hash Tables: Operations and Applications (19 min)
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- Completed
Hash Tables: Implementation Details, Part I (19 min)
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- Completed
Hash Tables: Implementation Details, Part II (22 min)
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- Completed
Pathological Data Sets and Universal Hashing Motivation (22 min)
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Universal Hashing: Definition and Example [Advanced - Optional] (26 min)
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Universal Hashing: Analysis of Chaining [Advanced - Optional] (19 min)
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Hash Table Performance with Open Addressing [Advanced - Optional] (16 min)
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XV. BLOOM FILTERS (Week 6)
(collapsed, click to expand)- Completed Bloom Filters: The Basics (16 min)
- Completed
Bloom Filters: Heuristic Analysis (13 min)
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XVI. BALANCED BINARY SEARCH TREES (Week 6)
(collapsed, click to expand)- Completed
Balanced Search Trees: Operations and Applications (11 min)
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- Completed
Binary Search Tree Basics, Part I (13 min)
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- Completed
Binary Search Tree Basics, Part II (30 min)
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- Completed Red-Black Trees (21 min)