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Extra info for Data Structures, Algorithms, and Program Style
Example text
It must treat them as data abstractions with the operations set, insert, omit, and belongs and is to return with c2's contents identical to c1's and c1's contents unaltered. 5. Change primes so that even numbers are not considered as values for factor or nextmultiple. 6. Change your solution to Exercise 5 so that even numbers, except 2, do not appear in candidates. Use only enough storage for 2 and the odd numbers between 2 and n. 7. This is the same as Exercise 6 except that candidates must use only enough storage for 2 and the odd primes between 2 and n.
This means that factor need never take on even values, so it can be increased by 2 instead of 1 in remove and can also be initialized to 3. Delete can be changed so that nextmultiple takes on only odd multiples of factor. With a little more work, candidates can be cut to roughly half its size by eliminating even integers. 9: Case Study: Bowling Scores the for loops in create and print, but it reduces the storage needed by about one-half and the time by more than one-half. Perhaps a less obvious improvement is to modify the increase of factor in remove so that, instead of increasing by 1 (or 2), factor increases to the value of the next prime in candidates (see Exercise 8).
Thus the C declaration int a[5][3]; defines a two-dimensional array of 5 X 3 or 15 entries, each of type integer. This array a can also be viewed as a collection of 5 one-dimensional arrays, each of length 3, or 3 one-dimensional arrays, each of length 5. Again, we can think of two variables i and j of the correct index type as pointing to an entry of the array. Thus a[i][j] refers to the entry of the ith row and jth column, or to the entry of a currently pointed to by i and j. We assume that the (i,j)th entry can be accessed in constant time, no matter what the value of i or j .