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Download e-book for kindle: Algorithms and Programming: Problems and Solutions (2nd by Alexander Shen

By Alexander Shen

ISBN-10: 1441917489

ISBN-13: 9781441917485

"Algorithms and Programming" is basically meant for a primary yr undergraduate path in programming. based in a problem-solution layout, the textual content motivates the scholar to imagine during the programming strategy, hence constructing an organization realizing of the underlying idea. even if a average familiarity with programming is believed, the e-book is well used by scholars new to laptop technological know-how. The extra complex chapters make the ebook helpful for a graduate path within the research of algorithms and/or compiler construction.

New to the second one version are additional chapters on suffix bushes, video games and methods, and Huffman coding in addition to an appendix illustrating the benefit of conversion from Pascal to C. the cloth covers such themes as combinatorics, sorting, looking out, queues, grammar and parsing, chosen recognized algorithms, and lots more and plenty extra.

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Additional resources for Algorithms and Programming: Problems and Solutions (2nd Edition) (Springer Undergraduate Texts in Mathematics and Technology)

Example text

26. Our solution of the preceding problem requires mn2 operations. , not more than Cmn operations for some C). [Hint. We have to break the symmetry and choose one of the rows as a “principal” row. 27. (Binary search) An array x[1] 6 . . 6 x[n] of integers and an integer a are given. n such that x[i] = a. ) Solution. ) At each step the difference r l is halved, so we get the required bound for the number of operations. Program can be simplified using the equality l + (r-l) div 2 = (2l + (r l)) div 2 = (r + l) div 2.

Then we add the card with number 3 on it; there are three possible positions, etc. n. n; if we denote by y[i] the number of cards before the inserted card at step i, we get the one-to-one correspondence defined above. We make one more remark about this correspondence. Assume that we increase or decrease y[i] by 1 for some i (leaving y[j] unchanged for all j 6 = i). Assume also that all subsequent y[j] (for all j > i) have maximal or minimal values. In this case two adjacent numbers in our permutation are exchanged.

M] of integer the coefficients of their product. ) Solution. 16. The polynomial multiplication algorithm given above uses about n 2 operations to compute the product of two polynomials of degree n. Find an (asymptotically) more effective algorithm that uses only O(n log 4/ log 3 ) operations. [Hint. Suppose we want to multiply two polynomials of degree 2k. Represent these polynomials as A(x) x k + B(x) and C(x) x k + D(x) where A, B, C, D are polynomials of degree k. The product in question is equal to A(x)C(x) x 2k + (A(x)D(x) + B(x)C(x)) x k + B(x)D(x).

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Algorithms and Programming: Problems and Solutions (2nd Edition) (Springer Undergraduate Texts in Mathematics and Technology) by Alexander Shen

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