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.
用到二叉搜索树本问题就很好解。
二叉搜索树的特点就是root->leff < root < root->right。
如果root>p && root>q，那么LCA在左子树上；
如果root<p && root<q，那么LCA在右子树上。
递归实现。
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 || !p || !q) return NULL; 14 if(root->val>p->val && root->val>q->val) return lowestCommonAncestor(root->left,p,q); 15 if(root->val<p->val && root->val<q->val) return lowestCommonAncestor(root->right,p,q); 16 return root; 17 } 18 };
迭代实现。
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 || !p || !q) return NULL; 14 TreeNode *cur = root; 15 while(cur) 16 { 17 if(cur->val>p->val && cur->val>q->val) cur = cur->left; 18 else if(cur->val<p->val && cur->val<q->val) cur = cur->right; 19 else return cur; 20 } 21 return cur; 22 } 23 };