1151 LCA in a Binary Tree（30 分）

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.

Given any two nodes in a binary tree, 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 binary tree, respectively. In each of the following two lines, N distinct integers are given as the inorder and preorder traversal sequences of the binary tree, respectively. It is guaranteed that the binary tree can be uniquely determined by the input sequences. 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 binary tree, 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

7 2 3 4 6 5 1 8

5 3 7 2 6 4 8 1

2 6

8 1

7 9

12 -3

0 8

99 99

Sample Output:

LCA of 2 and 6 is 3.

8 is an ancestor of 1.

ERROR: 9 is not found.

ERROR: 12 and -3 are not found.

ERROR: 0 is not found.

ERROR: 99 and 99 are not found.

 

C++:

/*
 @Date    : 2018-09-11 09:07:02
 @Author  : 酸饺子 (changzheng300@foxmail.com)
 @Link    : https://github.com/SourDumplings
 @Version : $Id$
*/

/*
https://pintia.cn/problem-sets/994805342720868352/problems/1038430130011897856
 */

#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

struct TreeNode
{
    TreeNode *left = nullptr, *right = nullptr;
    int key;
    TreeNode *father = nullptr;
    int level;
};

int M, N;
const int MAXN = 10005;
int pre[MAXN], in[MAXN];

TreeNode* build_tree(int preB, int preE, int inB, int inE)
{
    if (preB == preE)
        return nullptr;
    TreeNode *r = new TreeNode;
    r->key = pre[preB];
    if (preB + 1 == preE)
        return r;
    int leftE;
    for (int i = inB; i != inE; ++i)
    {
        if (in[i] == pre[preB])
        {
            leftE = i;
            break;
        }
    }
    r->left = build_tree(preB + 1, preB + 1 + leftE - inB, inB, leftE);
    if (r->left)
        r->left->father = r;
    r->right = build_tree(preB + 1 + leftE - inB, preE, leftE + 1, inE);
    if (r->right)
        r->right->father = r;
    return r;
}

TreeNode* search(TreeNode *T, int c, int level)
{
    if (!T)
        return nullptr;
    if (T->key == c)
    {
        T->level = level;
        return T;
    }
    else
    {
        TreeNode *lRes = search(T->left, c, level + 1);
        if (lRes)
            return lRes;
        else
        {
            TreeNode *rRes = search(T->right, c, level + 1);
            return rRes;
        }
    }
}

int main()
{
    scanf("%d %d", &M, &N);
    for (int i = 0; i != N; ++i)
        scanf("%d", &in[i]);

    for (int i = 0; i != N; ++i)
        scanf("%d", &pre[i]);

    TreeNode *T = nullptr;
    T = build_tree(0, N, 0, N);
    while (M--)
    {
        int c1, c2;
        scanf("%d %d", &c1, &c2);
        TreeNode *r1 = search(T, c1, 1), *r2 = search(T, c2, 1);
        if (r1 && r2)
        {
            int res = -1;
            int tempC1 = c1, tempC2 = c2;
            if (r1->level < r2->level)
            {
                swap(r1, r2);
                swap(tempC1, tempC2);
            }
            int dLevel = r1->level - r2->level;
            for (int i = 0; i != dLevel; ++i)
                r1 = r1->father;
            while (r1 != r2)
            {
                r1 = r1->father;
                r2 = r2->father;
            }
            res = r1->key;
            if (res == tempC1)
                printf("%d is an ancestor of %d.\n", tempC1, tempC2);
            else if (res == tempC2)
                printf("%d is an ancestor of %d.\n", tempC2, tempC1);
            else
                printf("LCA of %d and %d is %d.\n", c1, c2, res);
        }
        else if (r2)
        {
            printf("ERROR: %d is not found.\n", c1);
        }
        else if (r1)
        {
            printf("ERROR: %d is not found.\n", c2);
        }
        else
        {
            printf("ERROR: %d and %d are not found.\n", c1, c2);
        }
    }
    return 0;
}