Lowest Common Ancestor of a Binary Search Tree

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.

说明：若指针tmp所指向结点为最小祖先，则(tmp->val - p->val) * (tmp->val - q->val) <= 0。其中，小于0表示指针p,q所指结点在tmp所指结点的左右子树上；等于0表示tmp == p || tmp == q成立。

/**
* 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) {
struct TreeNode *tmp = root;
if((p->val - root->val) * (q->val - root->val) <= 0)
return root;
else if(p->val < root->val)
tmp = tmp->left;
else
tmp = tmp->right;

while(NULL != tmp->left || NULL != tmp->right)
{
if(NULL == tmp->left)
tmp = tmp->right;
else if(NULL == tmp->right)
tmp = tmp->left;

if((p->val - tmp->val) * (q->val - tmp->val) <= 0)
return tmp;
else if(p->val < tmp->val)
tmp = tmp->left;
else
tmp = tmp->right;
}
return NULL;
}