Sunday, January 31, 2021

235. Lowest Common Ancestor of a Binary Search Tree

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).”

 

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.

Example 3:

Input: root = [2,1], p = 2, q = 1
Output: 2

 

Constraints:

  • The number of nodes in the tree is in the range [2, 105].
  • -109 <= Node.val <= 109
  • All Node.val are unique.
  • p != q
  • p and q will exist in the BST.


My answer: it is one important constraints that both p and q must exits. My answer works for any binary tree, even not BST

Better solution given BST: find the 1st node whose value is between p and q, starting from top-down direction. It is put after below answer.

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/**
 * 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) {
        if (root == null || root == p || root == q) {
            return root;
        }
        TreeNode leftResult = lowestCommonAncestor(root.left, p, q);
        TreeNode rightResult = lowestCommonAncestor(root.right, p, q);

        if (leftResult == null && rightResult == null) {
            return null;
        } else if (leftResult == null) {
            return rightResult;
        } else if (rightResult == null) {
            return leftResult;
        } else {
            return root;
        }
    }
}

Solution for BST

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/**
 * 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) {
//         if (root == null || root == p || root == q) {
//             return root;
//         }
//         TreeNode leftResult = lowestCommonAncestor(root.left, p, q);
//         TreeNode rightResult = lowestCommonAncestor(root.right, p, q);

//         if (leftResult == null && rightResult == null) {
//             return null;
//         } else if (leftResult == null) {
//             return rightResult;
//         } else if (rightResult == null) {
//             return leftResult;
//         } else {
//             return root;
//         }
        if (p.val > q.val) {
            TreeNode temp = null;
            temp = p;
            p = q;
            q = temp;
        }
        if (root == null || (root.val >= p.val && root.val <= q.val)) {
            return root;
        }
        if (root.val >= q.val) {
            return lowestCommonAncestor(root.left, p, q);
        }
        if (root.val <= p.val) {
            return lowestCommonAncestor(root.right, p, q);
        }
        return null;
    }
}

 

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