Question

While preparing an answer to Secret Santa – Generating 'valid' permutations I came across the need to check if a list contains zero. I am wondering what the fastest way to do this in Mathematica 7 is, with emphasis on a short list of non-negative integers.

Using Min[list] === 0 is the fastest I have found, faster than MemberQ or FreeQ, but I am hoping there is a faster way, on par with the BitXor operation below:

r = Range@9;
p = Permutations@r;

BitXor[r, #] & /@ p; // Timing
0 === Min[BitXor[r, #]] & /@ p; // Timing

{0.062, Null}

{0.452, Null}

Answer 1

It appears that part of the slowdown with 0 === Min as used in the question is interference with the autocompile of Map. Separating these steps provides nearly a twofold improvement:

r = Range@9;
p = Permutations@r;

Min@# === 0 & /@ (BitXor[r, #] & /@ p); // Timing

{0.296, Null}

---

If I accept a result as (0|1) and if I process the list as one then I can use this:

Unitize[Times @@ BitXor[r, #] & /@ p]; // Timing

{0.156, Null}