Simple Explanation of Big O Part II

So if you want to find a name in a phone book of a million names you can actually find any name by doing this at most 20 times. In comparing search algorithms we decide that this comparison is our 'n'. For a phone book of 3 names it takes 2 comparisons (at most).For 7 it takes at most 3.For 15 it takes 4....For 1,000,000 it takes 20. That is staggeringly good isn't it? In Big-O terms this is O(log n) or logarithmic complexity. Now the logarithm in question could be ln (base e), log10, l...