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  1. M

    Random sequence - full alphabet run length

    Hi, Suppose we're looking at a random sequence of digits from 0 to 9. We start off reading the digits until every digit from 0 to 9 has been seen at least once and we mark the count of digits read up to that point (run length). We then reset the run length and continue until the whole random...
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    Hard Interview Problems

    Over the years I've heard gruesome stories about engineering/science/tech interviews - questions that they expect you to get on the spot (or nearly so) but which would require me to spend a good day thinking. I've already read Poundstone's books but I have to say there are very few good ones...
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    TAOCP Exercise 5.1.1-6

    Hi, Knuth's TAOCP exercise 5.1.1-6 asks to construct an n-log-n algorithm which would generate an inversion table corresponding to a particular permutation. My algorithm constructs inversion table for a random permutation of 1..N numbers (Knuth, Volume 3, exercise 5.1.1-6) using binary...
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    Memory Investigation

    Hi guys, I've been given the code below and asked to explain the data shown in the attached chart. Any ideas? The data shows periodicity, what could explain it? I know it has to do with memory. ------------------------------------------------------- #include <iostream> #include...
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    Sorting Algorithm Performance - Interview-Based Problem

    Hi guys, My professor recently asked a challenging question - he says it's been asked on an interview and he wanted to pose it as a homework. Attached is the graph of sorting algorithm performance. The interviewer asks: "Tell me everything you can about this algorithm just by looking at...
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    Random Sampling: Set Inclusion

    Hello, I don't really know if this is considered a challenging problem but this is not for homework: You're given a set of numbers S of size n. From S, you draw a random sample A, |A| < n. From S, you draw a random sample B, |B| < n. Sampling doesn't remove items from S. What is the...
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    Numerical Methods vs Differential Equations

    Hi guys, I'm currently in computer science program and I have an urgent feeling that I need better exposure to math. I have taken Discrete Math, Calculus i, ii, iii and I've independently studied linear algebra. I guess my concern is lack of differential equations and numerical methods. In...
  8. M

    Random walk question

    Hello Everyone, The following is a subproblem of research project I'm working on, i.e. not a homework. Let's suppose you have a bounded 2d plane and n distinct probes that do random-walk in that plane. The world is closed in a sense that a probe going outside the border ends up being on the...
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    Master of Arts vs. Master of Science: Pros and Cons

    I have a rather general question, but I think it's one that many find thinking about. If you believe this topic has been covered before extensively, please point me to the URLs. I noticed there is a bunch of schools out there offering Master of Art degrees in scientific disciplines as...
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    Outlook in parallel computing

    Hi, I'm curious what is a general view on parallel computing? Is it something that's important only for science and computer graphics professionals or does it also have applications in business, etc. Are there any particular skills in parallel computing that employers are looking for, any...
  11. M

    Color convergence

    Hello, I'm pondering over this research question. Let's suppose you've got a bunch of units which can be colored black or white. They're roaming around 2d grid in random walk. Any time a unit meets with another unit, it has an option to change color. It doesn't have to though, depending...
  12. M

    Difficult random walk modeling

    Hi guys, I'm doing some thinking about random walk. Imagine there is a bounded 2D plane and a single spawn point. The spawn produces units which must bring in minerals scattered around the spawn. The locations of minerals are not known, so the units diffuse randomly away from the spawn...
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    Masters in Computer Science - Potential

    Hi guys, I'd like to know your opinion about a potential of masters degree in Computer Science for an individual's career in U.S. industry - along the track of data analysis, IT project management etc. Does it make a difference if it is a M.S. or M.A.? What about threat of outsourcing? What...
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    Vector Spaces: Cartesian vs Tensor products

    Hi, I have a problem understanding the difference between Cartesian product of vector spaces and tensor product. Let V1 and V2 be vector spaces. V1 x V2 is Cartesian product and V1 xc V2 is tensor product (xc for x circled). How many dimensions are in V1 x V2 vs V1 xc V2? Thanks, Monte
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    Digraph automorphisms

    Hello, I have the following abstract algebra problem. It has to do with digraph automorphisms. You're given a digraph G with vertices V(G) = {x, y, z, w} and edges E(G) = { (x, y), (x, z), (x, w) }. How many essentially different ways are there to color the edges of G using the following...
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    Speed of thinking

    Since I don't have have a formal math background, I'm always under impression that academically trained mathematicians/physicists/computer scientists have superb arithmetic abilities. For example, they can add large numbers on a fly. Say a physics Ph.D. just got job in a bank. He is a quant...
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    Data crunching opportunities

    I've been visiting this section of the forum for some time and I'm curious about the opportunities in sciences for data-crunchers. I imagine many of the visitors here are also participating in other Internet forums and I'm eager to learn opinions about future of science employment in general...
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    Want to get into computer science Ph.D

    Hello, World! I'm taking computer science courses at undergrad level and want to get into computer science Ph.D. program. I have M.A. in biology, so I'm curious if anybody has good ideas on how to bridge the fields. How much do admission committees care about GRE? What courses in comp sci I...
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