Lowest Common Ancestor of a Binary Search Tree、Lowest Common Ancestor of a Binary Search Tree
1、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.
/**
* 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(root->val >= min(p->val,q->val) && root->val <= max(p->val,q->val)) return root;
if(root->val >=max(p->val,q->val)) return lowestCommonAncestor(root->left,p,q) ;
else return lowestCommonAncestor(root->right,p,q);
}
};
2、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.
方法1.
/**
* 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(root == p || root == q || root == NULL) {
return root;
} TreeNode* left = lowestCommonAncestor(root->left ,p,q);
TreeNode* right = lowestCommonAncestor(root->right,p,q); if(left==NULL && right==NULL){
return NULL;
} if(left!=NULL && right==NULL){
return left;
} if(right!=NULL && left == NULL){
return right;
} return root;
}
};
方法2.
/**
* 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 {
private:
bool getPath(TreeNode* root,TreeNode* node,list<TreeNode*>& list_path){
if(root==NULL){
return false;
} list_path.push_back(root); if(root == node) {
return true;
} bool in_left = getPath(root->left,node,list_path);
if(in_left){
return true;
} bool in_right = getPath(root->right,node,list_path); if(!in_right){
list_path.pop_back();
} return in_right;
}
public:
TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
list<TreeNode*> list_path_p,list_path_q; bool list_path_p_exist = getPath(root,p,list_path_p);
bool list_path_q_exist = getPath(root,q,list_path_q); if(!list_path_p_exist && !list_path_q_exist){
return NULL;
} TreeNode* res = NULL;
while(list_path_p.front() == list_path_q.front()){
res = list_path_p.front();
list_path_p.pop_front();
list_path_q.pop_front();
} return res;
}
};
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