[LeetCode] 235. Lowest Common Ancestor of a Binary Search Tree

轉自LeetCode

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 v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

<Solution>

考慮兩種情況

• 如果是 v 和 w 剛好是一左一右的子節點，那麼 (root.val - v.val) * (root.val - w.val) 一定會小於 0

• 如果 v 和 w 其中一個剛好是要找的 LCA，那麼 (root.val - v.val) * (root.val - w.val) = 0

code 如下

Java

	/**
	* Definition for a binary tree node.
	* public class TreeNode {
	* int val;
	* TreeNode left;
	* TreeNode right;
	* TreeNode(int x) { val = x; }
	* }
	*/
	class Solution {
	public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
	//>> (root.val - (long)p.val ) * (root.val - (long)q.val) to avoid overflow
	while((root.val - p.val ) * (root.val - q.val) > 0) {
	root = p.val < root.val ? root.left : root.right;
	}
	return root;
	}
	}

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