Có 20+ tài liệu thuộc chủ đề "sorting"
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Many of the problems are flat-out fun. This lays the foundation for the more algorithmic sections in the second part of the book. Help for Students at All Levels — The challenges included in this book have been selected to span a wide range of difficulty. 10.5.2 The Necklace. 10.5.7 The Grand Dinner. 10.5.8 The Problem With the Problem Setter....
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Huffman’s algorithm (for file compression . Indexed sequential access, 226- 228.. Indirect binary search trees, 184- 185.. Insertion sort insertion . spline quadrature, 85.. horizontal and vertical lines . Jensen, K., 19.. Kahn, D., 304.. searching, 171.. Knuth-Morris-Pratt string search- ing, 244-249.. Kruskal’s algorithm (minimum spanning tree kruskal), 417.. Lagrange’s interpolation formula, 47, 472.. Linear congruential generator random).. Linear running...
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This book is in the. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written per- mission of the publisher. Printed in the United States of America.. This book is intended to survey the most important algorithms in use...
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The objective of this book is to study a broad variety of important and useful algorithms: methods for solving problems which are suited for computer implementation. We’ll deal with many different areas of applica- tion, always trying to concentrate on “fundamental” algorithms which are important to know and interesting to stu.dy. Because of the large number of areas and algorithms...
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Many of the algorithms in this book are very well understood, to the point that accurate mathematical formulas are known for the average- and worst- case running time. Such formulas are developed first by carefully studying the program, to find the running time in terms of fundamental mathematical quantities and then doing a mathematical analysis of the quantities involved.. For...
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very long history, dating back to the origins of algorithm studies in the work of the Arabic mathematician al-Khowdrizmi, with roots going even further back to the Greeks and the Babylonians.. for example, Pascal allows numbers to be of type integer or re;d, with all of the normal arithmetic operations defined on both types. In this section, we’ll look at...
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Random Numbers. Our next set of algorithms will bie methods for using a computer to generate random numbers. We will find many uses for random numbers later on. By contrast, a random number is a precisely defined mathematical concept:. A random number will satisfy someone who needs an arbitrary number, but not the other way around.. For “every number to...
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Why wouldn’t the “or” or “and” function (instead of the “exclusive or”. Why would it be unwise to use, for example, b=3 and c=6 in the additive congruential generator?. What is the value of the x2 statistic for a degenerate generator which always returns the same number?. The methods for doing arithmetic operations given in Chapter 2 are simple and...
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Our purpo,se in this discussion is to gain some intuitive feeling for how divide-and-conquer algorithms achieve efficiency, not to do detailed analysis of the algorithms. Indeed, the particular recurrences that we’ve just solved are sufficient to describe the performance of most of the algorithms that we’ll be studying, and we’ll simply be referring back to them.. Matrix Multiplication. The most...
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by adding the appropriate multiple of a[N, N], then do the same for the next- to-last column, etc. That is, we do “partial pivoting” again, but on the other. As mentioned above, we should be wary of situations when the mag- nitudes of the coefficients vastly differ. Using the largest available element in the column for partial pivoting ensures that...
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the same steps of determining the coefficients for each of the spline pieces by solving the system of linear equations derived from imposing constraints on how they are joined.. Method of Least Squares. A very common experimental situation is that, while the data values that we have are not exact, we do have some idea of the form of the...
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(Recall that the area of a trapezoid is one-half the product of the height and the sum of the lengths of the two bases.) The error for this method can be derived in a similar way as for the rectangle method. Thus the rectangle method is twice as accurate as the trapezoid method.. The following procedure implements the trapezoid method...
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It is easy to take stability for granted: people often react to the unpleasant effects of instability with disbelief. The following program, for sorting three records, is intended to illustrate the general conventions that we’ll be using. (In particular, the main program is a peculiar way to exercise a program that is known to work only for N = 3:...
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The desirable features of the Quicksort algorithm are that it is in-place (uses only a small auxiliary stack), requires only about NlogN operations on the average to sort N items, and has an extremely short inner loop.. The drawbacks of the algorithm are that it is recursive (implementation is complicated if recursion is not available), has a worst case where...
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In order for the sort to take N2 time, two out of the three elements examined must be among the largest or among the smallest elements in the file, and this must happen consistently through most of the partitions. Third, it actually reduces the total running time of the algorithm by about 5%.. The combination of a nonrecursive implementation of...
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have straight radix sort, the rightrto-left l&by-bit radix sort described in the example above.. loop could be eliminated if desired by making two copies of the distribution counting code, one to sort from a into t, the other to sort from t into a.. The straight radix sort implementation given in the previous section makes b/m passes through the file....
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The process continues until the heap condition is no longer violated at the node occupied by C. In the example, C makes it all the way to the bottom of the heap, leaving:. Since the heap will be one element smaller after the operation, it is necessary to decrement iV, leaving no place for the element that was stored in...
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Selection and Merging. Selection and merging are intimately related to sorting, as we’ll see, and they have wide applicability in their own right.. Selection and merging are complementary operations in the sense that selection splits a file into two independent files and merging joins two inde- pendent files to make one file. The file can either be rearranged so that...
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Describe how you would rearrange an array of 4N elements so that the N smallest keys fall in the first N Isositions, the next N keys fall in the next N positions, the next N in the next N positions, and the N largest in the last N positions.. Show the recursive calls made when select is used to find...
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exactly after the sort phase is completed ) The best choice between these two alternatives of the lowest reasonable value of P and the highest reasonable value of P is obviously very dependent on many systems parameters: both alternatives (and some in between) should be considered.. One problem with balanced multiway merging for tape sorting is that it requires either...