00:01
Okay, so we just have to figure out what's the highest orders.
00:05
So let's write out f of n.
00:08
So the first thing to note is what is the order of 2 to the n plus n to the end? well, it should be sort of obvious because n is increasing, is that this should be like order of n to the end, because it's always better to have an increasing base and increasing exponent rather than just a constant base and increasing exponent.
00:40
So this will be order of n to the n.
00:43
So f of n, okay, so i should, okay, so i should write it like this.
00:50
So f of n is something order of n to the n times n cubed plus n log of n.
01:06
N to the n so what we can do is that this is well this is saying this is order of well n to the n plus n cubed is n plus 3 plus uh well log of n to the n is actually just n squared n squared log n so this will be order of n to the uh n plus 2 log n okay but it's always better to have an extra n than to have an extra than to replace the extra n with a log n because this is n to the n plus 2 times n right and this is n plus 2 times log in so this is order of n to the n plus 3 so i guess it depends if you want to really type bound this is the bound you want but as n goes to infinity the additional 3 sort of doesn't matter so this actually is just order of n to the n because the additional three really doesn't matter if n is going to infinity.
02:29
So you can write this as order of n to the n.
02:34
Okay, so let's, i'll do h of n next because that's easier before we go to g of n.
02:41
So h of n will do something similar.
02:44
Well, you have n to the n plus n squared.
02:49
So that's order of n to the n.
02:53
And then you're multiplying by again, n to the n plus n, n, which again, is order of n to the n...
