Question

What is the performance of these?

BigInteger -> toString() // what is the runtime?

String -> toCharArray()  // what is the runtime?

Thanks.

Answer 1

Conversion of BigInteger to string is O(N^2), where N is the number of digits in the result, when the base of the internal representation does not divide the target base; when the target base is divisible by the storage base, conversion takes O(N).

Consider conversion to base 10 when the internal representation is base-256. A division by ten has to happen N times; each time, all elements of the BigInteger representation get modified. The number of elements in the representation is proportional to the number of digits in the printout, so the overall conversion takes O(N^2).

On the other hand, converting to hex of a big int in base-256 internal representation takes O(N), because division is not necessary in this case. Each subelement can be converted in isolation from the remaining ones, and the number of sub-elements is proportional to the number of digits in the printout.

As far as String.toCharArray() goes, it’s O(N), where N is the number of characters in the string, because each character must be copied into the output.