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Lowest Common Ancestor of a Binary Search Tree

时间:2016-03-16 20:54:07      阅读:192      评论:0      收藏:0      [点我收藏+]

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.
  
思路,先判断入口是否有非法输入。
 
1 如果某一个root==p || root == q,那么LCA肯定是root(因为是top down,LCA肯定在root所囊括的树上,而root又是p q其中一个节点了,那么另外一个节点肯定在root之下,那么root就是LCA),那么返回root
 
2 如果root<min(p, q),那么LCA肯定在右子树上,那么递归
 
3 如果max(p, q)<root,那么LCA肯定在左子树上,那么递归
 
4 如果p<root<q,那么root肯定为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. TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
  13. if(root==p||root==q)
  14. return root;
  15. if(p->val>q->val)
  16. swap(p,q);
  17. if(root->val > p->val && root->val < q->val)
  18. return root;
  19. TreeNode *node;
  20. if(root->val > max(p->val,q->val))
  21. node=lowestCommonAncestor(root->left,p,q);
  22. if(root->val < min(p->val,q->val))
  23. node=lowestCommonAncestor(root->right,p,q);
  24. return node;
  25. }
  26. };








Lowest Common Ancestor of a Binary Search Tree

原文:http://www.cnblogs.com/zhxshseu/p/5284969.html

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