Algorithms and Programming: Problems and Solutions (2nd by Alexander Shen

By Alexander Shen

"Algorithms and Programming" is essentially meant for a primary yr undergraduate direction in programming. dependent in a problem-solution structure, the textual content motivates the scholar to imagine during the programming method, hence constructing an organization knowing of the underlying idea. even though a average familiarity with programming is thought, the booklet is well used by scholars new to machine technological know-how. The extra complicated chapters make the e-book necessary for a graduate path within the research of algorithms and/or compiler construction.

New to the second one variation are further chapters on suffix bushes, video games and techniques, and Huffman coding in addition to an appendix illustrating the benefit of conversion from Pascal to C. the cloth covers such issues as combinatorics, sorting, looking, queues, grammar and parsing, chosen recognized algorithms, and masses extra.

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

Sample text

If the sequence is no longer non-decreasing, we combine two terms into one. 4. Partitions are represented as non-decreasing sequences. Generate them in reversed alphabetic order. 5 Gray codes and similar problems 39 [Hint. The element x[s] can be decreased only if s=1 or x[s-1]

These subsets are in one-to-one correspondence with all sequences of 0s and 1s of length k. 4. Print all sequences of length k of positive integers such that the i-th term does not exceed i for all i. 1. , all sequences of length n that contain all the numbers 1 . . n). Solution. x[n]. Permutations are printed in lexicographic order. ni. 2 1i. How do we find the next permutation in the lexicographic order? When is it possible to increase k-th term in a permutation without changing all preceding terms?

6 y[q], z[1] 6 . . 6 z[r]. Find this number (or one of them, if there is more than one). The number of operations should be of order p + q + r. Solution. 24. Repeat the previous problem assuming that we do not know in advance if such a common element exist. Determine whether or not it exists and locate it if it does. 25. m] of integer; a[1][1] 6 . . 6 a[1][m], . . , a[n][1] 6 . . 6 a[n][m]. m such that a[i][j] = x). Find such a number x. Solution. b[n] whose elements mark the start of the “non-scanned” portions of arrays a[1], .

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