# All Nodes Distance K in Binary Tree

Given the `root`

of a binary tree, the value of a target node `target`

, and an integer `k`

, return *an array of the values of all nodes that have a distance *`k`

* from the target node.*

You can return the answer in **any order**.

**Example 1:**

**Input:** root = [3,5,1,6,2,0,8,null,null,7,4], target = 5, k = 2

**Output:** [7,4,1]

Explanation: The nodes that are a distance 2 from the target node (with value 5) have values 7, 4, and 1.

**Example 2:**

**Input:** root = [1], target = 1, k = 3

**Output:** []

**Constraints:**

- The number of nodes in the tree is in the range
`[1, 500]`

. `0 <= Node.val <= 500`

- All the values
`Node.val`

are**unique**. `target`

is the value of one of the nodes in the tree.`0 <= k <= 1000`

# Solution

We can solve this problem using a combination of DFS and BFS algorithms. First, we’ll do a DFS on the tree and store every node’s parent and children in a Dictionary. After, we do a **B**readth **F**irst **S**earch to find all nodes a distance `K`

from the `target`

.

Let’s see how we might implement this functionality:

- Initialize the Dictionary.
- Perform DFS on the root node and add every node’s parents and children to the Dictionary.
- To perform BFS take a Queue and visited hash to track the processed nodes.
- Add the target node into the queue to start BFS from the target node.
- During iteration, we will get all the parents and children nodes of the current node and mark them as visited and processed.
- When the
**k**value reach 0, you’ll have the nodes that are k distance from the target node as the result.

Let’s look at the code for the solution:

**Complexity Analysis**

- Time Complexity:
*O*(*N*), where*N*is the number of nodes in the given tree. - Space Complexity:
*O*(*N*).