LeetCode 236 - Lowest Common Ancestor of a Binary Tree

Table of Contents

• Problem Statement
• Using Tree DFS (Depth First Search)
• Conclusion

Problem Statement

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

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).”

Using Tree DFS

Explanation

We use Tree DFS to efficiently traverse a tree.

1. Base Case:

   • If the current node is nullptr, that means we’ve reached the end of a branch.

   • If the current node matches p or q, we’ve found one of the nodes.

2. Recursive Search:

   • Traverse both left and right subtrees to search for p and q.
     
     

3. Combine Results:

   • If one node is found in the left subtree and the other in the right subtree, the current node is their LCA.

   • If both are in the same subtree, propagate the result up the tree.

/**
 * 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) {
        if (!root || root == p || root == q) {
                return root;
            }
            
            TreeNode* left = lowestCommonAncestor(root->left, p, q);
            TreeNode* right = lowestCommonAncestor(root->right, p, q);

            if (left && right) {
                return root;
            }
            
            return left ? left : right;
    }
};

Conclusion

• Time Complexity: 𝑂(𝑛) - Where 𝑛 is the number of nodes in the binary tree.

• Space Complexity: 𝑂(ℎ) - Where ℎ is the height of the binary tree, due to the recursion stack.

Source:

236. Lowest Common Ancestor of a Binary Tree