Thursday Code Puzzler: Lowest Common Ancestor
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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).
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Comments
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{ public: 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); else 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 else 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 xThe 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.