Lowest Common Ancestor of a Binary Tree

Posted 2020-06-16

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 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).”

        _______3______
       /                  ___5__          ___1__
   /      \        /         6      _2       0       8
         /           7   4

For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

 

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