New PDF release: Algorithms

By R. Sedgewick

ISBN-10: 0201066726

ISBN-13: 9780201066722

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Extra resources for Algorithms

Sample text

The interpolation problem is to find the polynomial, given a set of points and values. The evaluation problem is to find the values, given the polynomial and the points. ) The classic solution to the interpolation problem is given by Lagrange’s interpolation formula, which is often used as a proof that a polynomial of degree N - 1 is completely determined by N points: This formula seems formidable at first but is actually quite simple. s+13s5=j which simplifies to x2 +a:+ 1. For x from xl, x2, .

To be consistent with current usage, we’ll refer to numbers from random sequences as random numbers. There’s no way to produce true random numbers on a computer (or any deterministic device). Once the program is written, the numbers that it will produce can be deduced, so how could they be random? The best we can hope to do is to write programs which produce isequences of numbers having many of the same properties as random numbers. Such numbers are commonly called pseudo-random numbers: they’re not really random, but they can be useful 33 CHAF’TER 3 as approximations to random numbers, in much the same way that floatingpoint numbers are useful as approximations to real numbers.

What is wrong with the following linear feedback shift register? 4. Why wouldn’t the “or” or “and” function (instead of the “exclusive or” function) work for linear feedback shift registers? 5. Write a program to produce a randorn two dimensional image. (Example: generate random bits, write a “*” when 1 is generated, ” ” when 0 is generated. ) 6. Use an additive congruential random number generator to generate 1000 positive integers less than 1000. Design a test to determine whether or not they’re random and apply the test.

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Algorithms by R. Sedgewick


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