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LowestCommonAncestorOfABinarySearchTree235.java
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LowestCommonAncestorOfABinarySearchTree235.java
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/**
* Given a binary search tree (BST), find the lowest common ancestor (LCA) of
* two given nodes in the BST.
*
* According to the definition of LCA on Wikipedia: “The lowest common ancestor
* is defined between two nodes p and q as the lowest node in T that has both p
* and q as descendants (where we allow a node to be a descendant of itself).”
*
* Given binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]
*
* _______6______
* / \
* ___2__ ___8__
* / \ / \
* 0 _4 7 9
* / \
* 3 5
*
* Example 1:
* Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
* Output: 6
* Explanation: The LCA of nodes 2 and 8 is 6.
*
* Example 2:
* Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
* Output: 2
* Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant
* of itself according to the LCA definition.
*
* Note:
* All of the nodes' values will be unique.
* p and q are different and both values will exist in the BST.
*/
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
public class LowestCommonAncestorOfABinarySearchTree235 {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if (root == null) return root;
if (p.val > root.val && q.val > root.val) {
return lowestCommonAncestor(root.right, p, q);
} else if (p.val < root.val && q.val < root.val) {
return lowestCommonAncestor(root.left, p, q);
} else {
return root;
}
}
public TreeNode lowestCommonAncestor2(TreeNode root, TreeNode p, TreeNode q) {
while ((root.val - p.val) * (root.val - q.val) > 0)
root = p.val < root.val ? root.left : root.right;
return root;
}
public TreeNode lowestCommonAncestor3(TreeNode root, TreeNode p, TreeNode q) {
return (root.val - p.val) * (root.val - q.val) < 1 ? root :
lowestCommonAncestor(p.val < root.val ? root.left : root.right, p, q);
}
// in case the node p or q is not in the BST
public TreeNode lowestCommonAncestor4(TreeNode root, TreeNode p, TreeNode q) {
if (root == null || p == null || q == null) return null;
if (root.val > p.val && root.val > q.val) {
return lowestCommonAncestor(root.left, p, q);
} else if (root.val < p.val && root.val < q.val) {
return lowestCommonAncestor(root.right, p, q);
} else if (find(root, p) && find(root, q)) {
return root;
} else {
return null;
}
}
private boolean find(TreeNode root, TreeNode n) {
if (root == null || n == null) return false;
if (root.val == n.val) {
return true;
} else if (root.val > n.val) {
return find(root.left, n);
} else {
return find(root.right, n);
}
}
}