Lowest Common Ancestor of a Binary Tree

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

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).”

        _______3______

       /              \

    ___5__          ___1__

   /      \        /      \

   6      _2       0       8

         /  \

         7   4

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

 1 /**

 2  * Definition for a binary tree node.

 3  * struct TreeNode {

 4  *     int val;

 5  *     TreeNode *left;

 6  *     TreeNode *right;

 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}

 8  * };

 9  */

10 class Solution {

11 public:

12     TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {

13         if(root==NULL||p==NULL||q==NULL)

14           return NULL;

15         return FindLCA(root,p,q);

16     }

17 

18 private:

19     TreeNode* FindLCA(TreeNode* root, TreeNode* p, TreeNode* q){

20         if(root==NULL)

21             return NULL;

22         if(root==p||root==q)

23           return root;

24         TreeNode* left;

25         TreeNode* right;

26         left=FindLCA(root->left,p,q);

27         right=FindLCA(root->right,p,q);

28         if(left&&right)

29           return root;

30         return left?left:right;

31         }  

32     

33 };