235. 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.
尋找給定兩個節點最近的共同父節點。
利用二叉查找樹的性質，從根節點開始二分查找：
如果兩個節點其中有一個節點與根節點相等，則根節點即爲最低父節點；
如果兩個節點都大於根節點，則兩個節點肯定在根節點的右邊，選擇右半部分子樹重複過程；
如果兩個節點都小於根節點，則兩個節點肯定在根節點的左半部分，選擇左子樹進行重複過程即可；
如果兩個節點一個大於根節點一個小於根節點，則根節點即使最低父節點。
*/


/**
 * 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) {
        if(q->val > p->val) return lowestCommonAncestor(root,q,p); 
        if(root->val == p->val || root->val==q->val) return root;
        if(root->val >p->val)
            return lowestCommonAncestor(root->left,p,q);
        else if(root->val < q->val)
            return lowestCommonAncestor(root->right,p,q);
        else
            return root;
    }
};