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.
#include<iostream>
#include<unordered_set>
#include<vector>
#include<stack>
#include<unordered_map>
using namespace std;
struct node_tree
{
node_tree * left_child;
node_tree * right_child;
int data;
};
node_tree *in_pre_creat_tree(vector<int> &inorder, vector<int> &preorder , int in_f, int in_e, int pre_f, int pre_e){
if(in_f > in_e || pre_f > pre_e){
return NULL;
}else
{
node_tree * root = new node_tree;
int temp_root_data = preorder[pre_f];
root -> data = temp_root_data;
int flag;
for(int i = 0; i < inorder.size(); i++){
if(temp_root_data == inorder[i]){
flag = i;
break;
}
}
root -> left_child = in_pre_creat_tree(inorder, preorder, in_f, flag - 1, pre_f + 1, pre_f + flag - in_f);
root -> right_child = in_pre_creat_tree(inorder, preorder, flag + 1, in_e, pre_e - in_e + flag + 1, pre_e);
return root;
}
}
bool path_to_root(node_tree * root, stack<int> &s, int data){
if(root == NULL)
return false;
else
{
s.push(root -> data);
if(root -> data == data){
return true;
}else
{
bool succed = false;
if(root -> left_child != NULL){
succed = path_to_root(root -> left_child, s, data);
}
if(root -> right_child != NULL && !succed){
succed = path_to_root(root -> right_child, s, data);
}
if(!succed){
// cout << s.top() << "---" << endl;
s.pop();
}
return succed;
}
}
}
bool path_to_root_set(node_tree * root, unordered_set<int> &s, int data){
if(root == NULL)
return false;
else
{
s.insert(root -> data);
// cout << root -> data << "!!!!" << endl;
if(root -> data == data){
return true;
}else
{
bool succed = false;
if(root -> left_child != NULL){
succed = path_to_root_set(root -> left_child, s, data);
}
if(root -> right_child != NULL && !succed){
succed = path_to_root_set(root -> right_child, s, data);
}
if(!succed){
// cout << s.top() << "---" << endl;
s.erase(root -> data);
}
return succed;
}
}
}
bool path_to_root_arry(node_tree * root, int s[ ], int q[ ], int data){
if(root == NULL)
return false;
else
{
if(root -> data >= 0)
s[root -> data]++;
else
{
q[abs(root -> data)]++;
}
// cout << root -> data << "!!!!" << endl;
if(root -> data == data){
return true;
}else
{
bool succed = false;
if(root -> left_child != NULL){
succed = path_to_root_arry(root -> left_child, s, q, data);
}
if(root -> right_child != NULL && !succed){
succed = path_to_root_arry(root -> right_child, s, q, data);
}
if(!succed){
// cout << s.top() << "---" << endl;
if(root -> data >= 0)
s[root -> data]--;
else
{
q[abs(root -> data)]--;
}
}
return succed;
}
}
}
bool path_to_root_map(node_tree * root, unordered_map<int, bool> &s, int data){
if(root == NULL)
return false;
else
{
s[root -> data] = true;
// cout << root -> data << "!!!!" << endl;
if(root -> data == data){
return true;
}else
{
bool succed = false;
if(root -> left_child != NULL){
succed = path_to_root_map(root -> left_child, s, data);
}
if(root -> right_child != NULL && !succed){
succed = path_to_root_map(root -> right_child, s, data);
}
if(!succed){
// cout << s.top() << "---" << endl;
s[root -> data] = false;
}
return succed;
}
}
}
int main(){
int m, n;
cin >> m >> n;
vector<int> inorder(n);
vector<int> preorder(n);
for(int i = 0; i < n; i++){
scanf("%d", &inorder[i]);
}
int temp_max = 0;
for(int i = 0; i < n; i++){
scanf("%d", &preorder[i]);
if(temp_max < preorder[i])
temp_max = preorder[i];
}
node_tree * tree;
tree = in_pre_creat_tree(inorder, preorder, 0, n - 1, 0, n - 1);
for(int i = 0; i < m; i++){
int u, v;
scanf("%d %d", &u, &v);
stack<int> s_u;
// unordered_set<int> s_v;
// int s_v_pos[99999] = {0};
// int s_v_neg[99999] = {0};
unordered_map<int, bool> s_v;
int s_v_pos[99999] = {0};
int s_v_neg[99999] = {0};
bool flag_u, flag_v;
flag_u = path_to_root(tree, s_u, u);
if(temp_max > 99998)
{
flag_v = path_to_root_map(tree, s_v, v);
}else
{
flag_v = path_to_root_arry(tree, s_v_pos, s_v_neg, v);
}
if(flag_u && flag_v){
int ancestor;
while(!s_u.empty()){
if(temp_max > 99998){
if(s_v[s_u.top()]){
ancestor = s_u.top();
break;
}
}else
{
if(s_u.top() >= 0){
if(s_v_pos[s_u.top()] > 0 ){
ancestor = s_u.top();
break;
}
}else
{
if(s_v_neg[abs(s_u.top())] > 0 ){
ancestor = s_u.top();
break;
}
}
}
s_u.pop();
}
if(ancestor == u){
printf("%d is an ancestor of %d.\n", ancestor, v);
}else if(ancestor == v){
printf("%d is an ancestor of %d.\n", ancestor, u);
}else
{
printf("LCA of %d and %d is %d.\n", u, v , ancestor);
}
}
if(flag_u && !flag_v){
printf("ERROR: %d is not found.\n", v);
}
if(!flag_u && flag_v){
printf("ERROR: %d is not found.\n", u);
}
if(!flag_u && !flag_v){
printf("ERROR: %d and %d are not found.\n", u, v);
}
}
return 0;
}