1650. Lowest Common Ancestor of a Binary Tree III

Description

Given two nodes of a binary tree p and q, return their lowest common ancestor (LCA).

Each node will have a reference to its parent node. The definition for Node is below:

class Node {
    public int val;
    public Node left;
    public Node right;
    public Node parent;
}

According to the definition of LCA on Wikipedia: "The lowest common ancestor of two nodes p and q in a tree T is the lowest node that has both p and q as descendants (where we allow a node to be a descendant of itself)."

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 exist in the tree.

Approach

Links

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

Examples

Example 1

Input: root = [3, 5, 1, 6, 2, 0, 8, null, null, 7, 4], p = 5, q = 1

Output: 3

Explanation: The LCA of nodes 5 and 1 is 3.

Example 2

Input: root = [3, 5, 1, 6, 2, 0, 8, null, null, 7, 4], p = 5, q = 4

Output: 5

Explanation: The LCA of nodes 5 and 4 is 5 since a node can be a descendant of itself according to the LCA definition.

Example 3

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

Output: 1

Solutions

Node

// Definition for a Node.
class Node {
    public int val;
    public Node left;
    public Node right;
    public Node parent;
};

Solution 1

/**
 * Time complexity : O(N)
 * Space complexity : O(N)
 */

class Solution {
    public Node lowestCommonAncestor(Node p, Node q) {
        Set<Node> ancestors = new HashSet();
        while(p != null) {
            ancestors.add(p);
            p = p.parent;
        }
        while(q != null && !ancestors.contains(q)) {
            q = q.parent;
        }
        return q;
    }
}

Follow up