# Introduction

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: βThe 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).β

```
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.
```

# Approach

First the given nodes p and q are to be searched in a binary tree and then their lowest common ancestor is to be found. We can resort to a normal tree traversal to search for the two nodes. Once we reach the desired nodes p and q, we can backtrack and find the lowest common ancestor.

## Complexity Analysis

Time Complexity:

`O(N)`

, where `N`

is the number of nodes in the binary tree. In the worst case we might be visiting all the nodes of the binary tree.

Space Complexity:

`O(N)`

. This is because the maximum amount of space utilized by the recursion stack would be `N`

since the height of a skewed binary tree could be `N`

.