Complexity T(n)
Write a linear-time algorithm that sorts n distinct
integers, each of which is between 1 and 500.
Hint: Use a 500-element array. (Linear-time means your
algorithm runs in time c*n + b, where c and b are any
constants that do not depend on n.
For example, your algorithm can run in time n, or time 2n +
1, or time 5n + 10, or time 100n + 6, but not time c*n*n =
c*n?.)
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Complexity T(n) What is the time complexity T(n) of the following portions of code? For simplicity, you may assume that n is a power of 2. That is, n = 2k for some positive integer k. a) ? for (i = 1; i <= n; i++) { j = n; cout << i << ? ? j << ? ? << endl; } b) ? for (i = 0; i <= n; i += 2) { j = n; cout << i << ? ? j << ? ? << endl; } c) ? for (i = n; i >= 1; i = i/2) { j = n; cout << i << ? ? j << ? ? << endl; } d) for (i = 1; i <= n; i++) { j = n; while (j >= 0) { cout << i << ? ? j << ? ? << endl; j = j - 2; } }
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