1143 Lowest Common Ancestor（30 分）

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本文介绍了一种在二叉搜索树中查找两个节点的最低公共祖先的方法，利用了二叉搜索树的特性及前序遍历的顺序。通过输入节点对，程序能够有效地找到或报告未找到的节点。

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The lowest common ancestor (LCA) of two nodes U and V in a tree is the deepest node that has both U and V as descendants.

A binary search tree (BST) is recursively defined as a binary tree which has the following properties:

The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
Both the left and right subtrees must also be binary search trees.

Given any two nodes in a BST, you are supposed to find their LCA.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 1,000), the number of pairs of nodes to be tested; and N (≤ 10,000), the number of keys in the BST, respectively. In the second line, N distinct integers are given as the preorder traversal sequence of the BST. Then M lines follow, each contains a pair of integer keys U and V. All the keys are in the range of int.

Output Specification:

For each given pair of U and V, print in a line LCA of U and V is A. if the LCA is found and A is the key. But if A is one of U and V, print X is an ancestor of Y. where X is A and Y is the other node. If U or V is not found in the BST, print in a line ERROR: U is not found. or ERROR: V is not found. or ERROR: U and V are not found..

Sample Input:

6 8
6 3 1 2 5 4 8 7
2 5
8 7
1 9
12 -3
0 8
99 99

Sample Output:

LCA of 2 and 5 is 3.
8 is an ancestor of 7.
ERROR: 9 is not found.
ERROR: 12 and -3 are not found.
ERROR: 0 is not found.
ERROR: 99 and 99 are not found.

思路：

给出一棵二叉搜索树的前序遍历，问结点u和v的共同最低祖先是谁，利用先序遍历特点。

C++

#include "iostream"
#include "map"
#include "vector"
using namespace std;
map<int,bool> mp;
int main(){
	int m,n,u,v,a;
	cin>>m>>n;
	vector<int> pre(n);
	for (int i=0;i<n;i++){
		cin>>pre[i];
		mp[pre[i]]=true;
	}
	for (int i=0;i<m;i++)
	{
		cin>>u>>v;
		for (int j=0;j<n;j++)
		{
			a=pre[j];
			if ((a>u&&a<v)||(a>v&&a<u)||(a==u)||(a==v))break;
		}
		if (mp[u]==false&&mp[v]==false)
			printf("ERROR: %d and %d are not found.\n",u,v);
		else if (mp[u] == false || mp[v] == false)
			printf("ERROR: %d is not found.\n", mp[u] == false ? u : v);
		else if (a == u || a == v)
			printf("%d is an ancestor of %d.\n", a, a == u ? v : u);
		else
			printf("LCA of %d and %d is %d.\n", u, v, a);
	}
	return 0;
}