This section contains lecture videos and notes. http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos 2013-01-22T12:37:12+05:00 MIT OpenCourseWare http://ocw.mit.edu en-US Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> Overview of course content, including an motivating problem for each of the modules. The lecture then covers 1-D and 2-D peak finding, using this problem to point out some issues involved in designing efficient algorithms.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: algorithm analysis, scalability, peak finding, divide and conquer, recurrence relation, complexity, asymptotic complexity, greedy ascent<br><br>Thumbnail - <a href= http://img.youtube.com/vi/HtSuA80QTyo/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec01_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-1-algorithmic-thinking/id585700718?i=126126063>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/HtSuA80QTyo>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-1-algorithmic-thinking-peak-finding Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US algorithm analysis scalability peak finding divide and conquer recurrence relation complexity asymptotic complexity greedy ascent MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Descirption:</strong> This lecture describes an algorithm as a computational procedure to solve a problem, covers the random access machine and pointer models of computation, and introduces the document distance problem.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: model of computation, Python cost model, document distance, random access machine, RAM, pointer machine, vector, history of algorithms<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Zc54gFhdpLA/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec02_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-2-models-computation/id585700718?i=126127756>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Zc54gFhdpLA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-2-models-of-computation-document-distance Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US model of computation Python cost model document distance random access machine RAM pointer machine vector history of algorithms MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> Sorting is introduced, and motivated by problems that become easier once the inputs are sorted. The lecture covers insertion sort, then discusses merge sort and analyzes its running time using a recursion tree.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: sorting, insertion sort, merge sort, divide and conquer, recurrence<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Kg4bqzAqRBM/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec03_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-3-insertion-sort-merge/id585700718?i=126127754>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Kg4bqzAqRBM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-3-insertion-sort-merge-sort Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US sorting insertion sort merge sort divide and conquer recurrence MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> Priority queues are introduced as a motivation for heaps. The lecture then covers heap operations and concludes with a discussion of heapsort.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: heap, heapsort, priority queue, max heap, min heap, data structure, operations<br><br>Thumbnail - <a href= http://img.youtube.com/vi/B7hVxCmfPtM/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec04_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-4-heaps-and-heap-sort/id585700718?i=126127727>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/B7hVxCmfPtM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-4-heaps-and-heap-sort Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US heap heapsort priority queue max heap min heap data structure operations MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, binary search trees are introduced, and several operations are covered: insertion, finding a value, finding the minimum element.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Thumbnail - <a href= http://img.youtube.com/vi/9Jry5-82I68/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec05_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-5-binary-search-trees/id585700718?i=126127763>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/9Jry5-82I68>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-5-binary-search-trees-bst-sort Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture covers AVL trees, including how to insert elements and rebalance the tree, and then discusses the difference between abstract data types and data structures.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: AVL tree, rotation, insert, abstract data type, data structure, balanced binary search tree, balanced BST<br><br>Thumbnail - <a href= http://img.youtube.com/vi/FNeL18KsWPc/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec06_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-6-avl-trees-avl-sort/id585700718?i=126127751>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/FNeL18KsWPc>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-6-avl-trees-avl-sort Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US AVL tree rotation insert abstract data type data structure balanced binary search tree balanced BST MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture starts by using the comparison model to prove lower bounds for searching and sorting, and then discusses counting sort and radix sort, which run in linear time.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: comparison model, decision tree, counting sort, radix sort, linear time sorting<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Nz1KZXbghj8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec07_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-7-counting-sort-radix/id585700718?i=126127758>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Nz1KZXbghj8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-7-counting-sort-radix-sort-lower-bounds-for-sorting Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US comparison model decision tree counting sort radix sort linear time sorting MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture starts with dictionaries in Python, considers the problems with using a direct-access table, and introduces hashing. The lecture discusses hashing with chaining, which is one way of dealing with collisions.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: dictionary, hashing, hash functions, chaining, linked list, collisions, simple uniform hashing, universal hashing<br><br>Thumbnail - <a href= http://img.youtube.com/vi/0M_kIqhwbFo/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec08_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-8-hashing-chaining/id585700718?i=126127729>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/0M_kIqhwbFo>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-8-hashing-with-chaining Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US dictionary hashing hash functions chaining linked list collisions simple uniform hashing universal hashing MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture covers table resizing, amortized analysis, string matching with the Karp-Rabin algorithm, and rolling hashes.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: hashing, chaining, amortized analysis, string matching, Karp-Rabin, rolling hash<br><br>Thumbnail - <a href= http://img.youtube.com/vi/BRO7mVIFt08/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec09_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-9-table-doubling-karp/id585700718?i=126127761>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/BRO7mVIFt08>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-9-table-doubling-karp-rabin Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US hashing chaining amortized analysis string matching Karp-Rabin rolling hash MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture covers open addressing, which is another approach to dealing with collisions (hashing with chaining was covered in Lecture 8). Cryptographic hashing is also introduced.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: hashing, open addressing, array, linear probing, double hashing, uniform hashing, cryptographic hashing, hash functions<br><br>Thumbnail - <a href= http://img.youtube.com/vi/rvdJDijO2Ro/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec10_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-10-open-addressing/id585700718?i=126127764>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/rvdJDijO2Ro>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-10-open-addressing-cryptographic-hashing Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US hashing open addressing array linear probing double hashing uniform hashing cryptographic hashing hash functions MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This is the first of two lectures on numerics, covering irrational numbers, high-precision computation, and Karatsuba multiplication.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: numerics, irrational numbers, high precision multiplication, Karatsuba multiplication, Newton's Method, square roots, Catalan numbers<br><br>Thumbnail - <a href= http://img.youtube.com/vi/eCaXlAaN2uE/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec11_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-11-integer-arithmetic/id585700718?i=126127759>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/eCaXlAaN2uE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-11-integer-arithmetic-karatsuba-multiplication Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US numerics irrational numbers high precision multiplication Karatsuba multiplication Newton's Method square roots Catalan numbers MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture begins with error analysis of Newton's method and a comparison of multiplication algorithms. It then covers high-precision division, which is required for Newton's method, and discusses the complexity of division and computing square roots.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: numerics, Newton's method, high precision division, multiplication algorithms, square roots, termination, error analysis<br><br>Thumbnail - <a href= http://img.youtube.com/vi/2YeJ-5UAke8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec12_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-12-square-roots-newtons/id585700718?i=126127765>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/2YeJ-5UAke8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-12-square-roots-newtons-method Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US numerics Newton's method high precision division multiplication algorithms square roots termination error analysis MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture begins with a review of graphs and applications of graph search, discusses graph representations such as adjacency lists, and covers breadth-first search.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: graphs, graph search, breadth first search, BFS, Rubik's cube, graph representations, adjacency lists, shortest paths<br><br>Thumbnail - <a href= http://img.youtube.com/vi/s-CYnVz-uh4/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec13_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-13-breadth-first-search/id585700718?i=126127766>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/s-CYnVz-uh4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-13-breadth-first-search-bfs Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US graphs graph search breadth first search BFS Rubik's cube graph representations adjacency lists shortest paths MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture covers depth-first search, including edge classification, and how DFS is used for cycle detection and topological sort.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: graphs, graph search, depth first search, DFS, edge classification, cycle detection, job scheduling, topological sort<br><br>Thumbnail - <a href= http://img.youtube.com/vi/AfSk24UTFS8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec14_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-14-depth-first-search/id585700718?i=126127767>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/AfSk24UTFS8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-14-depth-first-search-dfs-topological-sort Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US graphs graph search depth first search DFS edge classification cycle detection job scheduling topological sort MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture introduces weighted graphs and considers general approaches to the shortest paths problem. The lecture discusses single source shortest paths, negative-weight edges, and optimal substructure.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: weighted graphs, negative edges, single source, shortest paths, optimal substructure<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Aa2sqUhIn-E/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec15_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-15-single-source-shortest/id585700718?i=126127753>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Aa2sqUhIn-E>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-15-single-source-shortest-paths-problem Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US weighted graphs negative edges single source shortest paths optimal substructure MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture shows how to find shortest paths in directed acyclic graphs (DAGs) using topological sort, and in graphs without negative edges using Dijkstra's algorithm.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: shortest paths, relaxation operation, directed acyclic graph, topological sort, Dijkstra, greedy algorithm, array, binary min-heap, Fibonacci heap<br><br>Thumbnail - <a href= http://img.youtube.com/vi/2E7MmKv0Y24/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec16_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-16-dijkstra/id585700718?i=126127750>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/2E7MmKv0Y24>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-16-dijkstra Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US shortest paths relaxation operation directed acyclic graph topological sort Dijkstra greedy algorithm array binary min-heap Fibonacci heap MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture reviews shortest path notation, considers a generic shortest path algorithm, and then describes and proves the Bellman-Ford algorithm, which can handle graphs with negative cycles.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: shortest paths, Bellman-Ford, negative weight, negative cycle, exponential time<br><br>Thumbnail - <a href= http://img.youtube.com/vi/ozsuci5pIso/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec17_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-17-bellman-ford/id585700718?i=126127752>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ozsuci5pIso>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-17-bellman-ford Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US shortest paths Bellman-Ford negative weight negative cycle exponential time MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture covers optimizations that can improve real-life, average case performance of shortest path algorithms. These include using Dijkstra for a single source and single target, bi-directional search, and goal-directed or A* search.</p> <p><strong>Instructor:</strong> Srini Devadas</p>Keywords: shortest paths, Dijkstra, single source, single target, bidirectional search, goal directed search, A* search<br><br>Thumbnail - <a href= http://img.youtube.com/vi/CHvQ3q_gJ7E/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec18_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-18-speeding-up-dijkstra/id585700718?i=126127768>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/CHvQ3q_gJ7E>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-18-speeding-up-dijkstra Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US shortest paths Dijkstra single source single target bidirectional search goal directed search A* search MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture introduces dynamic programming, in which careful exhaustive search can be used to design polynomial-time algorithms. The Fibonacci and shortest paths problems are used to introduce guessing, memoization, and reusing solutions to subproblems.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: dynamic programming, optimization, recursion, memoization, Fibonacci, topological sort, shortest paths, optimal substructure, subproblem<br><br>Thumbnail - <a href= http://img.youtube.com/vi/OQ5jsbhAv_M/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec19_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-19-dynamic-programming/id585700718?i=126127757>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/OQ5jsbhAv_M>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-19-dynamic-programming-i-fibonacci-shortest-paths Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US dynamic programming optimization recursion memoization Fibonacci topological sort shortest paths optimal substructure subproblem MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture starts with a five-step process for dynamic programming, and then covers text justification and perfect-information blackjack. The lecture also describes how parent pointers are used to recover the solution.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: dynamic programming, text justification, blackjack, perfect information blackjack, parent pointers, subproblems, amortized analysis<br><br>Thumbnail - <a href= http://img.youtube.com/vi/ENyox7kNKeY/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec20_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-20-dynamic-programming/id585700718?i=126127769>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ENyox7kNKeY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-20-dynamic-programming-ii-text-justification-blackjack Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US dynamic programming text justification blackjack perfect information blackjack parent pointers subproblems amortized analysis MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture starts with how to define useful subproblems for strings or sequences, and then looks at parenthesization, edit distance, and the knapsack problem. The lecture ends with a brief discussion of pseudopolynomial time.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: dynamic programming, subproblems, strings, sequences, matrix multiplication, edit distance, knapsack, pseudopolynomial time<br><br>Thumbnail - <a href= http://img.youtube.com/vi/ocZMDMZwhCY/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec21_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-21-dp-iii-parenthesization/id585700718?i=126127728>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ocZMDMZwhCY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-21-dp-iii-parenthesization-edit-distance-knapsack Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US dynamic programming subproblems strings sequences matrix multiplication edit distance knapsack pseudopolynomial time MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture introduces a second type of guessing, in which more subproblems are created so that more features of the solution can be found. This type of guessing is illustrated with piano/guitar fingering and the Tetris and Super Mario Brothers games.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: dynamic programming, subproblems, guessing, guitar fingering, tetris, super mario brothers<br><br>Thumbnail - <a href= http://img.youtube.com/vi/tp4_UXaVyx8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec22_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-22-dp-iv-guitar-fingering/id585700718?i=126127760>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/tp4_UXaVyx8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-22-dp-iv-guitar-fingering-tetris-super-mario-bros Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US dynamic programming subproblems guessing guitar fingering tetris super mario brothers MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> This lecture introduces computational complexity, including how most decision problems are uncomputable, hardness and completeness, and reductions.</p> <p><strong>Instructor:</strong> Erik Demaine</p>Keywords: computational complexity, complexity classes, reductions, computational difficulty, decision problem, NP-complete, NP-hard<br><br>Thumbnail - <a href= http://img.youtube.com/vi/moPtwq_cVH8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec23_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-23-computational-complexity/id585700718?i=126127953>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/moPtwq_cVH8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-23-computational-complexity Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US computational complexity complexity classes reductions computational difficulty decision problem NP-complete NP-hard MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Description:</strong> In this lecture, both professors present areas of current research, including parallel processor architecture and algorithms, geometric folding algorithms, data structures, and graph algorithms.</p> <p><strong>Instructor:</strong> Srini Devadas, Erik Demaine</p>Keywords: parallel processor, processor architecture, execution migration, geometric folding algorithms, data structures, planar graphs, integer data structures, cache-efficient data structures<br><br>Thumbnail - <a href= http://img.youtube.com/vi/dU40AvBURDQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MIT6.006F11/MIT6_006F11_lec24_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= https://itunes.apple.com/us/itunes-u/lecture-24-topics-in-algorithms/id585700718?i=126127952>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/dU40AvBURDQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-24-topics-in-algorithms-research Demaine, Erik Devadas, Srinivas 2013-01-14T15:18:27+05:00 en-US parallel processor processor architecture execution migration geometric folding algorithms data structures planar graphs integer data structures cache-efficient data structures MIT OpenCourseWare http://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm