Lowest Common Ancestor of a Binary Search Tree.md

#Lowest Common Ancestor of a Binary Search Tree ##Problem: 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. ##Idea: When p and q are not in the same subtree.

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        TreeNode* current=root;
        while((p->val<current->val&&q->val<current->val)||(p->val>current->val&&q->val>current->val))
        {
            if(p->val<current->val)
            {
                current=current->left;
            }
            else
            {
                current=current->right;
            }
        }
        return current;
    }
};