PAT/html/a1143.html

<!DOCTYPE html>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<h1>1143. Lowest Common Ancestor (30)</h1>
<div id="problemContent">
<p>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.
</p>
<p>A binary search tree (BST) is recursively defined as a binary tree which has the following properties:</p>
<ul>
<li>The left subtree of a node contains only nodes with keys less than the node's key.
<li>The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
<li>Both the left and right subtrees must also be binary search trees. 
</li></li></li></ul>
<p>
Given any two nodes in a BST, you are supposed to find their LCA.
</p>
<p><b>
Input Specification:
</b></p>
<p>Each input file contains one test case.  For each case, the first line gives two positive integers: M (&lt;= 1000), the number of pairs of nodes to be tested; and N (&lt;= 10000), 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 <b>int</b>.
</p>
<p><b>
Output Specification:
</b></p>
<p>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.".</p>
<b>Sample Input:</b><pre>
6 8
6 3 1 2 5 4 8 7
2 5
8 7
1 9
12 -3
0 8
99 99
</pre>
<b>Sample Output:</b><pre>
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.
</pre>
</div>