# Lowest Common Ancestor of a Binary Tree

{% embed url="<https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree>" %}

### Problem

> 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](https://en.wikipedia.org/wiki/Lowest_common_ancestor): “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**).”
>
> &#x20;
>
> **Example 1:**
>
> ![](https://assets.leetcode.com/uploads/2018/12/14/binarytree.png)
>
> <pre><code>Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
> <strong>Output: 3
> </strong><strong>Explanation: The LCA of nodes 5 and 1 is 3.
> </strong></code></pre>
>
> **Example 2:**
>
> ![](https://assets.leetcode.com/uploads/2018/12/14/binarytree.png)
>
> <pre data-overflow="wrap"><code>Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
> <strong>Output: 5
> </strong><strong>Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
> </strong></code></pre>
>
> **Example 3:**
>
> <pre><code>Input: root = [1,2], p = 1, q = 2
> <strong>Output: 1
> </strong></code></pre>

### Pseudocode

```
-dfs to traverse BT, bfs not suitable here
    - set up conditions to return LCA node
```

### Solution

```javascript
var lowestCommonAncestor = function (root, p, q) {
  function walk(node) {
    // base condition
    if (!node) {
      return null;
    }

    if (node === p || node === q) {
      return node;
    }

    // pre
    // recurse
    const walkLeft = walk(node.left);
    const walkRight = walk(node.right);
    // post

    if (walkLeft && walkRight) {
      return node;
    } else {
      return walkLeft || walkRight;
    }
  }

  return walk(root);
};

```

### Time and Space Complexity

#### Time

* What did the code do
* Total -

#### Space

* What did the code do
* Total -