By Mikhail J. Atallah, Marina Blanton

ISBN-10: 1584888229

ISBN-13: 9781584888222

Algorithms and idea of Computation guide, moment version: basic suggestions and Techniques offers an up to date compendium of basic laptop technology issues and methods. It additionally illustrates how the themes and strategies come jointly to carry effective options to big functional difficulties. in addition to updating and revising some of the current chapters, this moment variation includes 4 new chapters that disguise exterior reminiscence and parameterized algorithms in addition to computational quantity thought and algorithmic coding conception.

This best-selling instruction manual keeps to aid laptop execs and engineers locate major details on a variety of algorithmic issues. The professional participants essentially outline the terminology, current simple effects and strategies, and provide a few present references to the in-depth literature. additionally they offer a glimpse of the key study matters in regards to the appropriate topics.

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Read Online or Download Algorithms and Theory of Computation Handbook, Second Edition, Volume 1: General Concepts and Techniques (Chapman & Hall CRC Applied Algorithms and Data Structures series) PDF

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Additional info for Algorithms and Theory of Computation Handbook, Second Edition, Volume 1: General Concepts and Techniques (Chapman & Hall CRC Applied Algorithms and Data Structures series)

Example text

Element uniqueness problem: The problem of determining if there are duplicates in a set of numbers. Greedy heuristic: A paradigm of algorithm design in which an optimization problem is solved by making locally optimum decisions. ” Information theoretic bounds: Lower bounds based on the rate at which information can be accumulated. −c(i) ≤ 1, where the sum is taken over the N leaves of Kraft’s inequality: The statement that N i=1 2 a binary tree and c(i) is the depth of leaf i. Lower bound: A function (or growth rate) below which solving a problem is impossible.

We will use the letter U to denote the cost ∗ We will not consider in detail the case of nondistinct keys. Most of the algorithms work in that case too, or can be extended without much effort, but the performance may not be the same, especially in degenerate cases. 2-1 2-2 General Concepts and Techniques of an unsuccessful search and S to denote the cost of a successful search. ” Unless otherwise noted, we assume that the elements to be accessed are chosen with uniform probability. The notations Cn and Cn have been used in the literature to denote the expected values of Un and Sn , respectively [Knu75].

For example, each call W(i,j) uses time Θ(j − i) and such calls are made repeatedly for the same values of i and j. We can make the process more efficient by caching the values of W(i,j) in an array as they are computed and using the cached values when possible: 1 2 3 4 5 6 7 8 9 10 11 12 13 int w[n][n]; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) w[i][j] = MAXINT; int W (int i, int j) { if (w[i][j] == MAXINT) if (i == j) w[i][j] = alpha[j]; else w[i][j] = W(i,j-1) + beta[j] + alpha[j]; return w[i][j]; } In the same way, we should cache the values of C(i,j) in an array as they are computed: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 int c[n][n]; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) c[i][j] = MAXINT; int C (int i, int j) { if (c[i][j] == MAXINT) if (i == j) c[i][j] = 0; else { int minCost = MAXINT; int cost; for (int k = i+1; k <= j; k++) { cost = C(i,k-1) + C(k,j) + W(i,j); if (cost < minCost) minCost = cost; } c[i][j] = minCost; } return c[i][j]; } 1-17 Algorithm Design and Analysis Techniques The idea of caching the solutions to subproblems is crucial in making the algorithm efficient.

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Algorithms and Theory of Computation Handbook, Second Edition, Volume 1: General Concepts and Techniques (Chapman & Hall CRC Applied Algorithms and Data Structures series) by Mikhail J. Atallah, Marina Blanton


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