PPT-CS 312 - Divide and Conquer/Recurrence Relations

Author : lindy-dunigan | Published Date : 2017-10-29

1 Recurrence Relations Time complexity for Recursive Algorithms Can be more difficult to solve than for standard algorithms because we need to know complexity for

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CS 312 - Divide and Conquer/Recurrence Relations: Transcript

1 Recurrence Relations Time complexity for Recursive Algorithms Can be more difficult to solve than for standard algorithms because we need to know complexity for the subrecursions of decreasing size. The structure of a divideandconquer algorithm applied to a given problem has the following form Base Case When the instance of the problem is suf64257ciently small return the answer directly or resort to a different usually simpler algorithm that is CS 46101 Section 600. CS 56101 Section 002. . Dr. Angela Guercio. Spring 2010. Analyzing Divide-and-Conquer Algorithms. Use a recurrence to characterize the running time of a divide-and-conquer algorithm.. CIS 606. Spring 2010. Analyzing Divide-and-Conquer Algorithms. Use a recurrence to characterize the running time of a divide-and-conquer algorithm.. Solving the recurrence gives us the asymptotic running time. n where Observe, that the number of subproblems is not necessarily equal to . The total numberof steps is obtained by all steps needed to solve smaller subproblems plus thenumber needed to combi . Recursion & Merge Sort. CSE 680. Prof. Roger Crawfis. Motivation. For insertion sort (and other problems) as . n. doubles in size, the quadratic quadruples!. Can we decrease . n. ?. What if we . Peeking into Computer Science. 1. Reading Assignment. Mandatory: Chapter 1. Optional: None. 2. Problems & Solutions. Computer Science perspective. 3. Objectives. At the end of this section, you will be able to:. A. Fiat and T. Tassa, “. Dynamic Traitor . Tracing. ”, . J. . Cryptology. , vol. 14, no. . 3, 2001.. T. Laarhoven et al., “. Dynamic Tardos Traitor Tracing . Schemes. ”, . submitted for publication. . Answers to your questions. Divide and Conquer. Closest . Points. Convex Hull intro. Exercise from . last time. Which permutation follows each of these in lexicographic order?. 183647520 471638520. Advanced Counting. Spring 2015. Sukumar Ghosh. Compound Interest. A person deposits $10,000 in a savings account that yields . 10% interest annually. How much will be there in the account . after 30 years?. Some of these recurrence relations can be solved using iteration or some other ad hoc technique. . However, one important class of recurrence relations can be explicitly solved in a systematic way. These are recurrence relations that express the terms of a sequence as linear combinations of previous terms.. Vostinar. Grinnell College. Many slides borrowed lovingly from . Skiena. Outline. Homework . reqs. Divide and Conquer. Find the median. Implementation on . HackerRank. No office hours today. Homework requirements. Advanced Counting. Fall 2018. Sukumar Ghosh. Compound Interest. A person deposits $10,000 in a savings account that yields . 10% interest annually. How much will be there in the account . after 30 years?. Assorted Minutiae. HW6 out tonight. . – Due next Tuesday at midnight. Assorted Minutiae. HW6 out tonight. . – Due next Tuesday at midnight. Extra assignment – Due next Friday, last day of class. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Application: Maxima Sets. We can visualize the various trade-offs for optimizing two-dimensional data, such as points representing hotels according to their pool size and restaurant quality, by plotting each as a two-dimensional point, (x, y), where x is the pool size and y is the restaurant quality score. .

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