Yair saphira mathematical objects in c++

Đây là quyển sách tiếng anh về lĩnh vực công nghệ thông tin cho sinh viên và những ai có đam mê. Quyển sách này trình về lý thuyết ,phương pháp lập trình cho ngôn ngữ C và C++.

[...]... two ordered linked lists into one ordered linked list The items in the top linked list (the current object) are scanned by the pointer ”runner” in the outer loop The items in the bottom linked list ’L’ (the argument) are scanned by the pointer ”Lrunner” in the inner loop, and inserted into the right places 17.4 The ordering algorithm: the original list is split into two sublists, which are first ordered... transfer the top n−1 rings from the initial column to column ”empty” (By the induction hypothesis, this is done in the correct order.) Then, the move in the head is printed to move the bottom ring from the initial column to the destination column Finally, the moves in the right subtree are printed in the correct order required to transfer the n − 1 rings from column ”empty” to the destination column ... set is obtained from the closed unit interval by dropping from it the open subinterval (1/3, 2/3), then dropping the open subintervals (1/9, 2/9) and (7/9, 8/9) from the remaining closed subintervals [0, 1/3] and [2/3, 1], and so on 8.4 9.1 9.2 9.3 9.4 The vector (x, y) starts at the origin (0, 0) and points to the point (x, y) in the Cartesian plane Adding the vectors... 19.3 A node indexing in an oriented graph The six nodes are numbered 1, 2, 3, 4, 5, 6 19.4 A 5 × 5 sparse matrix, implemented as a list of five row objects Each row object is a linked list of row-element objects Each row-element object contains an integer field to indicate the column in which it is placed in the matrix 19.5 Node indexing in an nonoriented... stand for pointers that point to the bullets, which stand for objects of type ’T’ (to be specified later in compilation time) 17.2 A linked list: each item (denoted by a bullet) contains a pointer (denoted by an arrow) to point to the next item [except of the last item, which contains the null (or zero) pointer] 17.3 Merging two ordered linked lists into one... problems in the fine (low) level are solved by climbing up the tree to form the general problem (induction), solving it optimally by introducing general concepts, terminology, and theory, and then going back to the original problem (deduction) 10.2 The V-cycle: the concrete problem is solved by forming the general problem (induction) in the left leg of the ’V’, solving it optimally... background, including preliminary definitions, algorithms, and simple results Part IV teaches C from a mathematical point of view, with an emphasis on recursion Part V teaches C++ from a mathematical point of view, using templates to implement vectors and linked lists Part VI implements more complex objects such as trees, graphs, and triangulations Finally, Part VII implements yet more advanced objects, ... numbers in the parentheses in the right-hand side are easily produced by the original mathematical induction But what happens when m is very large? Who could guarantee that n + m can always be calculated and produce a legitimate natural number? Fortunately, mathematical induction can help not only in the original definition of mathematical objects but also in arithmetic operations between them Indeed,... field, it can serve as a text book in courses in discrete mathematics, computational physics, numerical methods for PDEs, introduction to C for mathematicians and engineers, introduction to C++ for mathematicians and engineers, and data structures Parts I–II introduce elementary mathematical objects, such as numbers and geometrical objects These parts are aimed at beginners, and can be skipped by more... optimally by introducing general concepts, terminology, and theory, and then going back to the original problem (deduction) in the right leg of the ’V’ 10.3 Mathematical induction as a multilevel process In the first level at the top, it is known that the property holds for 1 For n = 2, 3, 4, , the induction hypothesis assumes that the property holds for n − 1 In the induction . without intent to infringe. Library of Congress Cataloging in Publication Data Shapira, Yair, 196 0- Mathematical objects in C++ : computational tools in a. references and index. ISBN-13: 97 8-1 -4 39 8-1 14 7-4 (alk. paper) ISBN-10: 1-4 39 8-1 14 7-4 (alk. paper) 1. Numerical analysis Data processing. 2. C++ (Computer