Hash attack: find strings of length 2^N with same hashCode()

John :

Reading algorithms fourth edition by Robert Sedgewick and Kevin Wayne I found the following question:

Hash attack: find 2^N strings, each of length 2^N, that have the same hashCode() value, supposing that the hashCode() implementation for String is the following:

public int hashCode() {
   int hash = 0;
   for (int i = 0; i < length(); i++)
      hash = (hash * 31) + charAt(i);
   return hash;
}

Strong hint: Aa and BB have the same value.

What comes on my mind is generating all possible strings of length 2^N and compare their hashCodes. This, however, is very expensive for large N and I doubt it's the correct solution. Can you give me hints what I miss in the whole picture?

ruakh :

Andreas' and Glains' answers are both correct, but they aren't quite what you need if your goal is to produce 2^N distinct strings of length 2N.

Rather, a simpler approach is to build strings consisting solely of concatenated sequences of Aa and BB. For length 2×1 you have { Aa, BB }; for length 2×2 you have { AaAa, AaBB, BBAa, BBBB }, for length 2×3 you have { AaAaAa, AAaaBB, AaBBAa, AaBBBB, BBAaAa, BBAaBB, BBBBAa, BBBBBB }; and so on.

(Note: you've quoted the text as saying the strings should have length 2^N. I'm guessing that you misquoted, and it's actually asking for length 2N; but if it is indeed asking for length 2^N, then you can simply drop elements as you proceed.)