time complexity

Question

2. What is asymptotical complexity of the following program:
```
n= readInt()
n = readInt()
t = m
s = 4
for (int 1 = 0;1 for (Int j = 0; j< n/ 10000; J++)
while ( }n>0
5 += =
m/= 2
n=t
writeInt(s)
```
$O\left(n^{2} \times \log _{2}(m)\right)$
$O\left(n^{2}\right)$
$O\left(n \times \log _{2}(m)\right)$
$O(n \times m)$

Answer 1

The inner most loop will run for O(log(m)) as m is getting halved in every iteration of the while loop. Now, the loop with iterator j runs for n/1000 which is independent of the value of i. So, j runs for O(n) every time and then the outermost loop with iterator as i runs for O(n) time.

Therefore, total complexity = $O(n^{2}log(m))$ . So, (a) should be the correct answer.