GATE CS 2015 Set 1 — Question 64
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Algorithms → Asymptotic Analysis → Best, Worst, Average Case
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Question
Consider the following C function.Which one of the following most closely approximates the return value of the function
int fun1(int n){
int i,j,k,p,q=0;
for (i=1; i<n; ++i) {
p=0;
for (j=n; j>1; j=j/2)
++p;
for (k=1; k<p; k=k*2)
++q;
}
return q;
}
fun1?Correct answer
(D) n log (log n)
Solution
Let's analyze the loops:
1.The outer loop runs for to , i.e., iterations.
2.Inside the outer loop, the first inner loop
for (j=n; j>1; j=j/2) divides by 2 repeatedly. The number of iterations is . Thus, after this loop, .3.The second inner loop
for (k=1; k<p; k=k*2) multiplies by 2 repeatedly until . The number of iterations is . Since , this loop runs times.4.The variable is incremented in the innermost loop. So for each iteration of the outer loop, increases by .
Total value of .Complexity: .Continue learning with Success Tracker
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