哈希函数何时相互正交？

能否提供Java中两个相互正交的哈希函数的示例？

解决方法:

从(a Google search result paper)

(正交哈希函数)两个哈希函数h1和h2是正交的,
    如果对于所有状态s,s’∈S且h1(s)= h1(s’)和h2(s)= h2(s’)
    s = s’.

S. Edelkamp,GPU上用于状态空间探索的完美哈希.

用英语来说,如果传递给两个不同的正交哈希函数的任何两个给定值导致相同的输出,则这些输入必须具有相同的值.

例：

Let h and g be hash functions.
Let b be a currently unknown value.
h(0) = h(b) = 5
g(0) = g(b) = 4
if h and g are orthogonal, b MUST equal 0.

Thus for any values given to h that result in a unique result,
If those same values are given to g, they must also result in a unique result,
  IF they are orthogonal hash functions.

伪代码：

// Assume no wraparound will ever occur due to overflow.
HashFunc h = x -> x + 1;
HashFunc g = y -> y + 2;
h(0) = 1 // No other input value results in --> 1
g(0) = 2 // No other input value results in --> 2
// These must have been orthogonal hash functions.

// Now for some non-orthogonal hash functions:
// Let the domain be integers only.
HashFunc j = x -> ceil(abs(x / 2));
HashFunc k = x -> ceil(sqrt(x));
j(0) = 0 // Unique result
k(0) = 0 // Unique result
j(1) = j(2) = 1
k(1) = 1 != k(2) = 2 
// k(1) results in a unique value, but it isn't unique for j.
// These cannot be orthogonal hash functions.