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.
#include<iostream>
#include<algorithm>
#include<vector>
#include<unordered_set>
using namespace std;
int main(){
int m, n;
cin >> m >> n;
vector<int> preorder(n);
unordered_set<int> un_set;
for(int i = 0; i < n; i++){
scanf("%d", &preorder[i]);
un_set.insert(preorder[i]);
}
for(int i = 0; i < m; i++){
int temp_a, temp_b;
scanf("%d %d", &temp_a, &temp_b);
int ancestor;
int count = 0;
if(un_set.find(temp_a) == un_set.end() || un_set.find(temp_b) == un_set.end()){
if(un_set.find(temp_a) == un_set.end() && un_set.find(temp_b) == un_set.end()){
printf("ERROR: %d and %d are not found.\n", temp_a, temp_b);
}else if(un_set.find(temp_a) == un_set.end() && un_set.find(temp_b) != un_set.end()){
printf("ERROR: %d is not found.\n", temp_a);
}else
{
printf("ERROR: %d is not found.\n", temp_b);
}
}else
{
for(int j = 0; j < n; j++){
if(preorder[j] == temp_a)
count++;
if(preorder[j] == temp_b)
count++;
if(count <= 2){
// if(preorder[j] >= temp_a && preorder[j] >= temp_b && preorder[j] != min(temp_a, temp_b)){
// ancestor = preorder[j];
// }
// if(preorder[j] <= temp_a && preorder[j] <= temp_b && preorder[j] != min(temp_a, temp_b)){
// ancestor = preorder[j];
// }
if((((preorder[j] < temp_a) && (preorder[j] > temp_b))) || (((preorder[j] > temp_a) && (preorder[j] < temp_b))) || preorder[j] == temp_b || preorder[j] == temp_a){
ancestor = preorder[j];
break;
}
}
}
if(ancestor == temp_b || ancestor == temp_a){
printf("%d is an ancestor of %d.\n", ancestor, ancestor == temp_a ? temp_b : temp_a);
}else
{
printf("LCA of %d and %d is %d.\n", temp_a, temp_b, ancestor);
}
}
}
return 0;
}