Algorithms And Data Structures

By Robert Sedgewick

ISBN-10: 0201066726

ISBN-13: 9780201066722

This e-book is meant to survey an important algorithms in use on desktops this day and educate the basic thoughts to the growing to be inhabitants drawn to changing into severe desktop clients.

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Example text

6. Write a Pascal procedure that sets the value of the element in the ith row and jth column of a sparse matrix to v, assuming that the matrix is represented using a linked list representation with no nodes for 0 entries. 7. What is the running time of matrix multiplication in terms of the number of data items? 8. Does the running time of the polynornial addition programs for nonsparse input depend on the value of any of the coefficients? 9. Run an experiment to determine which of the polynomial addition pro grams runs fastest on your computer system, for relatively large N.

For example, it uses twice as much space, since a link must be stored along with each coefficient. However, as suggested by the example above, we can take advantage of the possibility that many of the coefficients may be zero. We can have list nodes represent only the nonzero terms of the polynomial by also including the degree of the term represented within the list node, so that each list node contains values of c and j to represent cxj. j:=j; listadd:=t; end ; The listadd function creates a new node, gives it the specified fields, and links it into a list after node t.

In the example, the last two terms are 0 when z = 1, the first and last terms are 0 when x = 2, and the first two terms are 0 when x = 3. To convert a polynomial from the form described by Lagrange’s formula to our standard coefficient representation is not at all straightforward. At least N2 operations seem to be required, since there are N terms in the sum, each consisting of a product with N factors. Actually, it takes some cleverness to achieve a quadratic algorithm, since the factors are not just numbers, but polynomials of degree N.