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Thursday Code Puzzler: Lowest Common Ancestor

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Thursday is code puzzler day here at DZone. The idea is simple: solve the coding problem as efficiently as you can, in any language or framework that you find suitable.

Note: Even though there really is nothing stopping you from finding a solution to this on the internet, try to keep honest, and come up with your own answer.  It's all about the participation!

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Find the Lowest Common Ancestor in a Binary Search Tree

Given a binary search tree, find the lowest common ancestor of two nodes on the tree. Wikipedia defines  the lowest common ancestor as follows: 

The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).

Catch up on all our previous puzzlers here.



Michael Gomez replied on Thu, 2013/03/07 - 4:33pm

Basically mutated the standard binary search algorithm to find the node which is greater than the low input and smaller than the big input.  BNode::hasChild only exists to double check that both inputs actually exist at all.

class BNode{
  int self_val;
  BNode *left;
  BNode *right;
  bool hasChild(int val)
    //standard binary search
    if (self_val < val)
      return left->hasChild(val);
    else if (self_val > val)
      return right->hasChild(val);
      return self_val == val;

BNode* findMinRoot(BNode *root, int low, int high)
  //find which half of the tree we can eliminate
  if (root->self_val > high)
    return findMinRoot(root->left, low, high);
  else if (root->self_val < low)
    return findMinRoot(root->right, low, high);
  //only return a value iff low and high actually exist
    return (root->hasChild(low) && root->hasChild(high)) ? root:NULL;

Régis Décamps replied on Fri, 2013/03/08 - 7:36am

Going bottom-up from v, this is simply the first anchestor of v whose parent is greater than w (assuming v<w and the Node tructure provides parent).

def lowest_common_anchestror(v, w):
    if v > w:
        v, w = w, v
    x = v
    while x is not None and x.parent < w:
        x = x.parent
    return x

The complexity will be the height between the common ancestror and v.


Michael Gomez replied on Fri, 2013/03/08 - 11:06am in response to: Régis Décamps

 I never thought of adding a parent reference to each node.... that does make it a lot faster.

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