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# Blog

## Lowest Common Ancestor of a Binary Tree

Posted by in LeetCode on

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).”

Given the following binary search tree:  root = [3,5,1,6,2,0,8,null,null,7,4]

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

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 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.```

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the binary tree.

Solution 1:
1. Find the path to specific node p, and q.
2. Compare the path array from beginning, if same, move to next path node, until they didn’t match
3. return the last match node.

Solution 2:

The idea is to traverse the tree starting from root. If any of the given keys (n1 and n2) matches with root, then root is LCA (assuming that both keys are present). If root doesn’t match with any of the keys, we recur for left and right subtree. The node which has one key present in its left subtree and the other key present in right subtree is the LCA. If both keys lie in left subtree, then left subtree has LCA also, otherwise LCA lies in right subtree.