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).”
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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.
经典问题！
方法一：找到两个节点的路径，然后根据路径找LCA。
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 void getPath(TreeNode *root, TreeNode *p, vector<TreeNode*> &path) { 13 TreeNode *tmp = root; 14 while (tmp != p) { 15 path.push_back(tmp); 16 if (tmp->val > p->val) tmp = tmp->left; 17 else tmp = tmp->right; 18 } 19 path.push_back(p); 20 } 21 TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) { 22 vector<TreeNode*> path1, path2; 23 getPath(root, p, path1); 24 getPath(root, q, path2); 25 TreeNode *res = root; 26 int idx = 0; 27 while (idx < path1.size() && idx < path2.size()) { 28 if (path1[idx] != path2[idx]) break; 29 else res = path1[idx++]; 30 } 31 return res; 32 } 33 };
方法二：根据BST的性质，两个节点a，b的公共袓先c一定满足a <= c <= b 或者 a >= c >= b。
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 TreeNode *cur = root; 14 while (cur != NULL) { 15 if (cur->val > p->val && cur->val > q->val) cur = cur->left; 16 else if (cur->val < p->val && cur->val < q->val) cur = cur->right; 17 else return cur; 18 } 19 return cur; 20 } 21 };