for (int p = t; p > 0; p >>= 1) {
for (int i = 0; i < n - p; ++i) {
if ((i & p) != 0) {
sort2(a, i, i+p);
}
}
for(int q = t; q > p; q >>= 1) {
for(int i = 0; i < n- q; ++i) {
if ((i & p) != 0) {
sort2(a, i+p, i+q);
}
}
}
}
Here n
is some positive integer and t
is greater than n/2
, but not equal to n
.
As per my understanding, the inner for loop runs for (np)
times but I could not figure out the outer for loop.
I tried finding it as below:
If t=64
and n=100
, it takes the binary value of p
which is equal to 64
and so p=1000000
base 2 .
I understand that every time it reduces by one digit and it executes a total of 7 times in this case. I somehow couldn't figure out general time.
Also, my understanding is that the 3rd for loop ie
for(int q = t; q > p; q >>= 1)
doesn't execute at all because the condition q>p
doesn't satisfy as p=q=t
.
Is this correct? I am just starting out with algorithms.
For this: Complexity would be BigO( log(t)(nt)log(t) )
Excluding the sort2
function complexity inside the for
loop.
Explaination:
log(p)+1
[Each time it is right shifting the bit by 1 and going for greater than 0
], so for t = 64, the loop will go as [64, 32, 16, 8, 4, 2, 1]. greater of ( O(np), O((nt)log(t)) )
Execution
for the second inner loop having nested for loop with the most outer loop:
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