By Robert Sedgewick

ISBN-10: 0201066726

ISBN-13: 9780201066722

This booklet is meant to survey an important algorithms in use on pcs this day and educate the elemental ideas to the turning out to be inhabitants drawn to changing into severe machine clients.

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Extra info for Algorithms (Addison-Wesley series in computer science)

Sample text

This problem could be handled in Pascal by representing the polync+ mials as linked lists, as we did in Chapter 2. This program assumes that N is a power of two, though the details for general N can be worked out easily. The main complications are to make sure that the recursion terminates properly and that the polynomials are divided properly when N is odd. The same method can be used for multiplying integers, though care must be taken to treat “carries” properly during the subtractions after the recursive calls.

For example, the call new(z) creates a new node, putting a pointer to 26 CHAPTER 2 it in a. ) The procedure to write out what’s on a list is the simplest. next end; wri teln end ; The output of this program will be indistinguishable from that of the program above which uses the simple array representation. Building a list involves first calling new to create a node, then filling in the coefficient, and then linking the node to the end of the partial list built so far. next:=z end ; The dummy node z is used here to hold the link which points to the first node on the list while the list is being constructed.

5. Write out all of the polynomial multipllications performed when the divideand-conquer polynomial multiplication method described in the text is used tosquare 1+x+~2+x3+s4+x5+x6+~7+xs. 6. The polynomial multiplication routinie mult could be made more efficient for sparse polynomials by returning 0 if all coefficients of either input are 0. About how many multiplications ((to within a constant factor) would such a program use to square 1 + xN? 7. Can x32 be computed with less than five multiplications?

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