O(1) algorithm to determine if node is descendant of another node in a multiway tree?

Question

Imagine the following tree:

    A
   / \\
  B   C
 / \\   \\
D   E   F

I\'m looking for a way to query if for example F is a descendant of A (n

Answer 1

For a M-way tree, instead of your bit array, why not just store the binary "trie id" (using M bits per level) with each node? For your example (assuming M==2) : A=0b01, B=0b0101, C=0b1001, ...

Then you can do the test in O(1):

bool IsParent(node* child, node* parent)
{ 
   return ((child->id & parent->id) == parent->id)
}

You could compress the storage to ceil(lg2(M)) bits per level if you have a fast FindMSB() function which returns the position of the most significant bit set:

mask = (1<<( FindMSB(parent->id)+1) ) -1;
retunr (child->id&mask == parent->id);