07/16/2016 Tree

## Question

Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “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).”

_______6______
/              \
___2__          ___8__
/      \        /      \
0      _4       7       9
/  \
3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

## Solution

Result: Accepted Time: 24 ms

Here should be some explanations.

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     struct TreeNode *left;
*     struct TreeNode *right;
* };
*/
struct TreeNode* lowestCommonAncestor(struct TreeNode* root, struct TreeNode* p, struct TreeNode* q) {
if(p->val > root-> val && q->val > root->val)
return lowestCommonAncestor(root->right,p,q);
if(p->val < root-> val && q->val < root->val)
return lowestCommonAncestor(root->left,p,q);
return root;
}

Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$