Hi, I am trying to learn myself from algorithms (Sedgewick) and I have encountered the following problem:

```
3.1.15: Assume that searches are 1,000 times more frequent
than insertions for a BinarySearchST client. Estimate the
percentage of the total time that is devoted to insertions,
when the number of searches is 10^3, 10^6, and 10^9.
```

As stated in the problem Searches (S) = 1000 * Inserts (I)

- $ S = 10 ^ 3 to I = 1 $
- $ S = 10 ^ 6 to I = 10 ^ 3 $
- $ S = 10 ^ 9 to I = 10 ^ 6 $

At this stage of the book, we use simple tables and linked lists to save the symbol table (inefficient hash maps, trees, etc.). This would mean that the searches take ~ log2 (N) times and the insertions take ~ N / 2 times (assuming a uniform distribution on which the inserts are placed).

Am I right to calculate the percentage of insertion into the search time would be approximately:

$ frac {Inserts times N / 2} {Searches times log_2 (N)} $

Using $ Searches = 10 ^ 3 times inserts $ this reduces to

$ frac {N / 2} {(10 ^ 3 times log_2 (N)} $

This would mean that the percentage strongly depends on the initial size of the symbol table and that it is not a constant percentage that we can use to answer the question.

Any suggestions on what I'm saying, should I assume the initial size of the table?