# Lowest Common Ancestor of a Binary Tree

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 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 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.

### Definition for a binary tree node

```
/**
* Definition for a binary tree node.
*/
function TreeNode(val) {
this.val = val;
this.left = this.right = null;
}
```

### Solution

```
/**
* @param {TreeNode} root
* @param {TreeNode} p
* @param {TreeNode} q
* @return {TreeNode}
* @time complexity: O(n) where n is the number of nodes
* @space complexity: O(n) utilized by recursion stack
*/
var lowestCommonAncestor = function(root, p, q) {
if (!root || root.val === p.val || root.val === q.val) {
return root;
}
const left = lowestCommonAncestor(root.left, p, q);
const right = lowestCommonAncestor(root.right, p, q);
if (!left) {
return right;
}
if (!right) {
return left;
}
return root;
};
```

### Test Case

```
const assert = require('chai').assert;
describe('Lowest Common Ancestor of a Binary Tree', () => {
let tree;
before(() => {
tree = arrayToTree([3,5,1,6,2,0,8,null,null,7,4]);
function arrayToTree(arr, root = null, index = 0) {
if (index < arr.length) {
root = new TreeNode(arr[index]);
root.left = arrayToTree(arr, root.left, 2 * index + 1);
root.right = arrayToTree(arr, root.right, 2 * index + 2);
}
return root;
}
});
it('should return node with value of 3', () => {
const result = lowestCommonAncestor(tree, new TreeNode(5), new TreeNode(1));
assert.strictEqual(result.val, 3);
});
it('should return node with value of 5', () => {
const result = lowestCommonAncestor(tree, new TreeNode(5), new TreeNode(4));
assert.strictEqual(result.val, 5);
});
});
```

```
Lowest Common Ancestor of a Binary Tree
✓ should return node with value of 3
✓ should return node with value of 5
2 passing (12ms)
```