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

By Alexander Shen

"Algorithms and Programming" is basically meant for a primary yr undergraduate direction in programming. based in a problem-solution structure, the textual content motivates the coed to imagine throughout the programming strategy, hence constructing a company realizing of the underlying conception. even if a reasonable familiarity with programming is thought, the ebook is well used by scholars new to machine technological know-how. The extra complicated chapters make the publication worthwhile for a graduate path within the research of algorithms and/or compiler construction.

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

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

Example text

In this case two adjacent numbers in our permutation are exchanged. Namely, an increase in y[i] means that i is exchanged with its right neighbor, while a decrease means that i is exchanged with its left neighbor. k in such a way that each sequence differs from the preceding sequence in one and only one place by using n ⇥ k rectangle. Now replace it by a board that resembles a staircase (the i-th column is a rectangle of width 1 and height i). 5 Gray codes and similar problems 43 the property mentioned above (i-th term changes only if all subsequent terms are maximal or minimal) holds.

This is possible only if the robot goes down at each step, but this is a contradiction. 2. Prove that the following program also processes all the leaves of a tree (once each): var state: (LP, LAP); state := LP; while is_down or (state <> LAP) do begin if (state = LP) and is_up then begin up_left; end else if (state = LP) and not is_up then begin process; state := LAP; end else if (state = LAP) and is_right then begin right; state := LP; end else begin {state = LAP, not is_right, is_down} down; end; end; Solution.

N} having k elements. Solution. Each subset may be represented by a bit string of length n that contains exactly k 1s. ) We generate these bit strings in lexicographic order. There is a natural way to do this: Generate all bit strings and select those that contain exactly k 1s. However, this solution is considered inefficient, because bit strings with k 1s form a tiny fraction of all bit strings of length n. In the program below the generation of each subsequent string requires not more than C · n operations (for some constant C).

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