00:01
Next question, suppose you have a computer that in one second it can perform 10 to the power of 10 operations.
00:09
And we want to find the largest input of size n that will be able to give us a result within an hour for a, b, c, d all the way to f.
00:22
So in one hour we know there are 3600 seconds.
00:26
So number of operations will be 3600 times 10 to the power of 10.
00:30
And this would be 3 .6 times 10 to the power of 13.
00:38
Now for part a, we have n square.
00:41
So i'm going to set n square to less than or equal to 3 .6 times 10 to the power of 13 operations in an hour.
00:49
So since we know this n square is positive and over here is positive, we can take square root on both sides and the inequality will not change.
00:59
We have n less than equals to 6 million.
01:07
So the largest n will be 6 million.
01:17
B, where n cubed, just set it less than equals to this figure here.
01:23
Now, taking cube root, n is less than equals to this number.
01:38
So the largest n is 33019.
01:45
C, 100 n square less than equals to 3 .6 times 10 to the power 13.
01:54
Divide by 100 and since 100 is positive, inequality sign will not change.
01:58
So i will get 3 .6 times 10 to the power 11.
02:03
Again taking square roots, n is less than equals to 600 ,000.
02:12
So the the largest n will be 600 ,000.
02:19
Now, d is interesting.
02:22
N log n less than equals to 3 .6 times 10 to the power 13...