int sum = 0;
for (int n = N; n > 0; n /= 2)
for (int i = 0; i < n; i++)
sum++;
I was pretty sure it grows in nlogn but was told it’s linear… Why is it linear and not linearithmic?
int sum = 0; for (int n = N; n > 0; n /=
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int sum = 0;
for (int n = N; n > 0; n /= 2)
for (int i = 0; i < n; i++)
sum++;
I was pretty sure it grows in nlogn but was told it’s linear… Why is it linear and not linearithmic?
It is linear. Imagine for a second
nis 64. The inner loop runs 64 times, then 32 times, then 16 times, then 8 times, then 4 times, then 2 times, then 1 time. 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127.So it requires
2n-1total operations (for a power of 2, but that doesn’t change the analysis), assuming the inner loop is not optimized away. That’s clearlyO(n)— linear.If the inner for loop is optimized away (to
sum += n;), it’s logarithmic.