leetcode235
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- 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(4的左右)
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.
二叉搜索树的特点:小的值在左边,大的值在右边。
所以可以利用这一特性,如果两个值一左一右,那最小公共祖先就是root,若都在左边(即两个val都小于root->val),就root变root->left,都在右边,就root变root->right(递归实现)。
/** * 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(p->val<root->val&&q->val<root->val) return lowestCommonAncestor(root->left,p,q); if(p->val>root->val&&q->val>root->val) return lowestCommonAncestor(root->right,p,q); return root; }};
1、这样的结构有一个好处是很容易获得最大值(Maximum)、最小值(minimum)、某元素的前驱(Precursor)、某元素的后继(Successor)。
最大值:树的最右节点。
最小值:树的最左节点。
某元素前驱(小于它的最大):左子树的最右。
某元素的后继(大于它的最小):右子树的最左。
2、二叉平衡树
平衡二叉树(Balanced Binary Tree)又被称为AVL树(有别于AVL算法),且具有以下性质:它是一 棵空树或它的左右两个子树的高度差的绝对值不超过1,并且左右两个子树都是一棵平衡二叉树。
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