# Algorithms in a Nutshell: A Practical Guide # Algorithms in a Nutshell: A Practical Guide

Language: English

Pages: 390

ISBN: 1491948922

Format: PDF / Kindle (mobi) / ePub

Creating robust software requires the use of efficient algorithms, but programmers seldom think about them until a problem occurs. This updated edition of Algorithms in a Nutshell describes a large number of existing algorithms for solving a variety of problems, and helps you select and implement the right algorithm for your needs—with just enough math to let you understand and analyze algorithm performance.

With its focus on application, rather than theory, this book provides efficient code solutions in several programming languages that you can easily adapt to a specific project. Each major algorithm is presented in the style of a design pattern that includes information to help you understand why and when the algorithm is appropriate.

With this book, you will:

• Solve a particular coding problem or improve on the performance of an existing solution
• Quickly locate algorithms that relate to the problems you want to solve, and determine why a particular algorithm is the right one to use
• Get algorithmic solutions in C, C++, Java, and Ruby with implementation tips
• Learn the expected performance of an algorithm, and the conditions it needs to perform at its best
• Discover the impact that similar design decisions have on different algorithms
• Learn advanced data structures to improve the efficiency of algorithms

Problem Instancepointer-based information, Overviewpreprocessing, OverviewPrim's Algorithm, Minimum Spanning Tree Algorithms, Minimum Spanning Tree Algorithmsimplementation, Minimum Spanning Tree Algorithms- (private), Empirical Evaluation Formatprobing, Hash-based Searchproblem instance, Size of a Problem Instanceproblem reduction, Principle: If No Solution Is Evident, Construct a Searchproblems, classifying, Overviewprogramming and problem solving, Patterns: A Communication Languageprogramming

numerous enhancements and optimizations researched for Quicksort that have wrought the most efficiency out of any sorting algorithm. The various options are discussed in detail later, in the upcoming "Variations" section. Analysis In the ideal case, partition divides the original array in half; if this behavior is consistent for each recursion, then the resulting behavior produces the same results as Median Sort without incurring an additional performance penalty. Let's define t(n) to be the

to update all shortest paths while (true) { // find shortest distance so far in unvisited vertices int u = −1; int sd = numeric_limits::max( ); // assume not reachable for (int i = 0; i < n; i++) if (!visited[i] && dist[i] < sd) { sd = dist[i]; u = i; } } if (u == −1) { break; } // no more progress to be made // For neighbors of u, see if length of best path from s->u + weight // of edge u->v is better than best path from s->v. visited[u] = true; for (VertexList::const_iterator ci =

graph, compute MST starting from a randomly * selected vertex. Encoding of MST is done using 'pred' entries. */ void mst_prim (Graph const &graph, vector &pred) { // initialize pred[] and key[] arrays. Start with arbitrary // vertex s=0. Priority Queue PQ contains all v in G. const int n = graph.numVertices( ); pred.assign(n, −1); vector key(n, numeric_limits::max( )); key = 0;BinaryHeap pq(n); vector inQueue(n, true); for (int v = 0; v < n; v++) { pq.insert(v, key[v]); }

rapidly become overwhelmed by the sheer number of game states generated during the recursive search. In chess, where the average number of moves on a board is often considered to be 30 (Laramée, 2000), to look ahead only five moves (i.e., b=30, d=5) requires evaluating up to 25,137,931 board positions. This value is determined by the expression: Minimax can take advantage of symmetries in the game state (such as rotations of the board or reflections) by caching past states viewed (and their