Download e-book for iPad: Algorithmic Puzzles by Anany Levitin, Maria Levitin

By Anany Levitin, Maria Levitin

ISBN-10: 0199740445

ISBN-13: 9780199740444

Whereas many ponder algorithms as particular to desktop technology, at its middle algorithmic pondering is outlined by means of analytical good judgment to unravel difficulties. This common sense extends a long way past the area of laptop technological know-how and into the broad and interesting global of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many vintage brainteasers in addition to more recent examples from task interviews with significant firms to teach readers how you can observe analytical pondering to unravel puzzles requiring well-defined procedures.

The book's certain number of puzzles is supplemented with rigorously built tutorials on set of rules layout options and research concepts meant to stroll the reader step by step throughout the a variety of techniques to algorithmic challenge fixing. Mastery of those strategies--exhaustive seek, backtracking, and divide-and-conquer, between others--will relief the reader in fixing not just the puzzles contained during this publication, but in addition others encountered in interviews, puzzle collections, and all through lifestyle. all the one hundred fifty puzzles includes tricks and ideas, in addition to remark at the puzzle's origins and answer equipment.

The in basic terms publication of its variety, Algorithmic Puzzles homes puzzles for all ability degrees. Readers with basically heart university arithmetic will enhance their algorithmic problem-solving talents via puzzles on the user-friendly point, whereas professional puzzle solvers will benefit from the problem of considering via tougher puzzles.

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Example text

2 If the answer is “no,” the selected number is among the integers 1 to n/2 ; if the answer is “yes,” the selected number is among the integers n/2 + 1 to n. In either case, the algorithm reduced the problem of size n to an instance of the same problem of about half the size of the original instance. Repeating this step until the instance size is reduced to 1 solves the problem. Since this algorithm reduces the size of an instance (the range of the numbers that still can contain the selected number) by about half on each iteration, it works amazingly fast.

It also leads to several other useful formulas. For example, for the sum of the first n positive even numbers, we obtain 2 + 4 + · · · + 2n = 2(1 + 2 + · · · + n) = n(n + 1), and for the sum of the first n positive odd numbers, we get 1 + 3 + · · · + (2n − 1) = (1 + 2 + 3 + 4 + · · · + (2n − 1) + 2n) − (2 + 4 + · · · + 2n) = 2n(2n + 1) − n(n + 1) = n2 . 2 Another very important formula is the sum of consecutive powers of 2, which we already used in the first tutorial: 1 + 2 + 22 + · · · + 2n = 2n+1 − 1.

For n > 1, 27 Tutorials condition for the number of moves made by the recursive algorithm for the Tower of Hanoi puzzle with n disks: Algorithmic Puzzles 28 Invariants We conclude this tutorial with a brief discussion of the idea of an invariant. For our purposes, an invariant is a property that is preserved by any algorithm that solves the problem. For puzzle-like questions, an invariant is often used to show that the problem has no solution because the invariant property holds for the initial state of the puzzle but fails for the required final state.

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Algorithmic Puzzles by Anany Levitin, Maria Levitin

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