1143 Lowest Common Ancestor (30 point(s))

1143 Lowest Common Ancestor (30 point(s))

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.

类似1151。根据BST前序重建树、

只需要注意：

1. BST的中序遍历是非递减的。

2. 结点的静态存储是基于前序或者后序的。

#include<iostream>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
int M,N;
const int MAX = 1e4+7;
struct Node{
	int data;int level;int father;
	Node(int d=0,int l=0,int f=-1):data(d),level(l),father(f){}
};
Node pre[MAX];
int in[MAX];
void createTree(int root,int left,int right,int father,int level){
	if(left>right) return;
	pre[root] =  Node(pre[root].data,level,father);
	int index = left;
	while(pre[root].data!=in[index]) index++;
	createTree(root+1,left,index-1,root,level+1);
	createTree(root+1+index-left,index+1,right,root,level+1);
}
int main(void){
	cin>>M>>N;
	for(int i=0;i<N;i++) cin>>in[i];
	for(int i=0;i<N;i++) cin>>pre[i].data;
	createTree(0,0,N-1,-1,0);
	int a,b;
	for(int i=0;i<M;i++){
		cin>>a>>b;
		int ai=N;int bi=N;
		for(int i=0;i<N;i++){
			if(a==pre[i].data) ai = i;
			if(b==pre[i].data) bi = i;
		}
		if(ai==N&&bi==N) printf("ERROR: %d and %d are not found.\n",a,b);
		else if(ai==N&&bi!=N) printf("ERROR: %d is not found.\n",a);
		else if(ai!=N&&bi==N) printf("ERROR: %d is not found.\n",b);
		else{
			bool deeper = true;//Node a is deeper;
			if(pre[ai].level<pre[bi].level){
				deeper = false;
				swap(ai,bi);
			}
			while(pre[ai].level!=pre[bi].level) ai = pre[ai].father;
			if(ai==bi){
				printf("%d is an ancestor of %d.\n",(deeper?b:a),(deeper?a:b));
			}
			else{
				while(ai!=bi){
					ai = pre[ai].father;
					bi = pre[bi].father;
				}
				printf("LCA of %d and %d is %d.\n",a,b,pre[ai].data);
			}
		}
	}
	return 0;
}