Shaitan00

How can it be easy to order exponential growth seeing as it depends on time (t). For example - if you have 3^t and 4^(t/2+1) then it completly depends on (t), sometimes the first is smaller and other times the second is smaller, all depending on values of (t). So how can you determine an order?

I was given the following problem description for a depth-determination problem, however I am completly unable to figure out how this "pseudo-distance" feature works, if anyone has any clues and can provide a uber-simple example it would be much appreciated - I just can't see how it works/applies. [Problem] In the depth-determination problem, we maintain a forest F = {Ti} of rooted trees. We use the disjoint-set forest S=Si, where each set Si (which is itself a tree) corresponds to a tree Ti in the forest F. The tree structure within a set Si, however, does not necessarily correspond to that of Ti. In fact, the implementation of Si does not record the exact parent-child relationships but nevertheless allows us to determine any node’s depth in Ti. The key idea is to maintain each node v a ”pseudo-distance” d[v], which is defined so that the sum of the pseudo-distances along the path from v to the root of its set Si equals the depth of v in Ti. That is, if the path from v to its root in v0 , v1 , . . . , vk , where v0 = v and vk is Si’s root, then the depth of v in Ti is the sum of d[vj] where j=0 to j=k.

Your friends are starting a security company that needs to obtain licenses for n different pieces of cryptographic software. Due to regulations, they can only obtain these licenses at the rate of at most one per month. Each license is currently selling for a price of $100. However, they are all becoming more expensive according to exponential growth curves: in particular, the cost of license j increases by a factor of rj > 1 each month, where rj is a given parameter. This means that if license j is purchased t months from now, it will cost 100×rtj . We will assume that all the price growth rates are distinct. The question is: Given that the company can only buy at most one license a month, in which order should it buy the licenses so that the total amount of money it spends is as small as possible?