Lowest Common Ancestor of a Binary Tree

1. 问题
   

   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 allowa 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.

2. 解答
   

   /** * Definition for a binary tree node. * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */class Solution1 {public:    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q)     {        if(root==NULL) return NULL;        if(p==root || q==root) return root;                TreeNode *pleft=lowestCommonAncestor(root->left,p,q);        TreeNode *pright=lowestCommonAncestor(root->right,p,q);                if(pleft!=NULL && pright!=NULL) return root;        else if(pleft != NULL)              return pleft;          else if (pright != NULL)              return pright;          else               return NULL;      }};class Solution {public:    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q)     {        if(root==NULL) return NULL;        if(p==root || q==root) return root;                vector<TreeNode*> path1;        vector<TreeNode*> path2;         TreeNode *res1=NULL;       if( GetNodePath(root,p,path1) && GetNodePath(root,q,path2))        {           int m=min(path1.size(),path2.size());        for(int i=0;i<m;i++)        {            if(path1[i]==path2[i])            {                res1=path1[i];            }            else            {                break;            }        }        }        return res1;     }   public:  bool GetNodePath(TreeNode* pHead, TreeNode* pNode, std::vector<TreeNode*>& path)  {     path.push_back(pHead);    if(pHead == pNode)      return true;          bool found = false;    if(pHead->left != NULL)        found = GetNodePath(pHead->left, pNode, path);    if(!found && pHead->right)        found = GetNodePath(pHead->right, pNode, path);    if(!found)        path.pop_back();    return found;   }};