Fundamental Algorithms Lecture Notes

G22.1170.001 Spring 2003

Lecture 1: Introduction to Algorithmics
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READING GUIDE:
• Read Section 1 (General Intro)
• Read Section 7 (Asymptotic Notations), up to page 13 only.
• The rest can be read in order, at your leisure.
• Use the Appendix for general reference.
Lecture 2: Recurrences
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READING GUIDE:
• Skim Section 1.
• Read Sections 2, 3, 4.
• Section 5: Know the arithmetic, geometric and harmonic series.
• Section 6: Standard form, polynomial-type and exponential-type sum.
• Section 9.2: Know the Master Theorem and how to apply it.
Lecture 3: Balanced Search Trees
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READING GUIDE:
• Skim Sections 1, 2, 3. Be familiar with the definitions of Dictionary and Priority Queues (p. 4).
• Read Sections 3: this section is essential, but it is mostly a review of basic Binary Search Trees (BST).
• Read Section 4: AVL Trees. In page 12, you see \mu(h). In our lecture on Monday, we used i instead of h, and wrote "s(T_i)" or "s_i" instead of \mu(i).
• Read Section 5: (a,b)-Trees.
Lecture 4: Pure Graph Algorithms
ERRATA
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READING GUIDE:
• Read all Sections (1-5).
Lecture 5: Greedy Method
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READING GUIDE:
• Read Sections 1,2,5. NOTE: At the beginning of Section 5, there is some reference to the matroid material in Section 4. Just ignore these.
Lecture 6: Amortization Method
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READING GUIDE:
• Read Sections 1-4 and 9. For Section 9, you just need to know the amortized complexity bounds when Fibonacci heaps are used to implement "mergeable queues" (Intro. to Section 5, p.16)
Lecture 7: Dynamic Programming
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READING GUIDE:
• Read Sections 1, 2 and 4. We recommend reading section 3 if you can.
Lecture 8: Randomized Algorithms:
Choose a Format: QuickSort.pdf and Lecture 8 (pdf)   |   QuickSort.ps and Lecture 8 (ps)
READING GUIDE:
• Read all of the notes on Quicksort. But for Lecture VIII, you are only responsible for Section 4 (random number generator).
Lecture 9: Hashing:
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READING GUIDE:
• Read the first five sections, including universal hashing.
Lecture 10: NP Completeness:
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READING GUIDE:
• Read all. But you must understand the concept of reduction to do some simple problems.