---
tags: leetcode
---

# [1644. Lowest Common Ancestor of a Binary Tree II](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree-ii/)
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# My Solution
## The Key Idea for Solving This Coding Question
## C++ Code

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */

class Solution {
public:
    TreeNode *lowestCommonAncestor(TreeNode *root, TreeNode *p, TreeNode *q) {
        lca = nullptr;

        dfs(root, p, q);
        return lca;
    }

private:
    TreeNode *lca;

    TreeNode *dfs(TreeNode *root, TreeNode *p, TreeNode *q) {
        if (root == nullptr) {
            return nullptr;
        }

        TreeNode *leftSubtree = dfs(root->left, p, q);
        TreeNode *rightSubtree = dfs(root->right, p, q);

        if (root == p || root == q) {
            // root is either p or q.

            if (leftSubtree != nullptr || rightSubtree != nullptr) {
                // Case 1: Assume root is p. q is located in one of the subtrees.
                //         root is the LCA.
                lca = root;
                return root;
            } else {
                // Case 2: Assume root is p. q is not located in both of the subtrees.
                return root;
            }
        }

        // Case 3: p is located in one of the subtrees and q is in the other.
        //         Therefore, root is the LCA.
        if (leftSubtree != nullptr && rightSubtree != nullptr) {
            lca = root;
            return root;
        }

        // Case 4: Both p and q are in one of the subtrees.
        if (leftSubtree != nullptr) {
            return leftSubtree;
        }
        if (rightSubtree != nullptr) {
            return rightSubtree;
        }

        // Case 5: Both the subtrees don't have p nor q.
        return nullptr;
    }
};

## Time complexity
$O(n)$
$n$ is the number of nodes in the binary tree referred by `root`.
## Space complexity
$O(H)$
$H$ is the height of the binary tree referred by `root`.
# Miscellane
<!--
# Test Cases

[3,5,1,6,2,0,8,null,null,7,4]
5
1

[3,5,1,6,2,0,8,null,null,7,4]
5
4

[3,5,1,6,2,0,8,null,null,7,4]
5
10

-->