GATE CS 2017 Set 2 — Question 38
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Algorithms → Asymptotic Analysis → Asymptotic Notations
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Question
Consider the following C function.Time complexity of fun in terms of notation is
int fun(int n) {
int i, j;
for(i = 1; i <= n; i++) {
for(j = 1; j < n; j += i) {
printf(" %d %d", i, j);
}
}
}
Correct answer
(C) Θ(n log n)
Solution
The outer loop runs times ().
For a fixed , the inner loop runs for as long as . The number of iterations is approximately .
Total number of iterations .
The sum is the -th Harmonic number , which is .
Therefore, .
For a fixed , the inner loop runs for as long as . The number of iterations is approximately .
Total number of iterations .
The sum is the -th Harmonic number , which is .
Therefore, .
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