<p>Given the <code>root</code> of a binary tree, the value of a target node <code>target</code>, and an integer <code>k</code>, return <em>an array of the values of all nodes that have a distance </em><code>k</code><em> from the target node.</em></p>

<p>You can return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/28/sketch0.png" style="width: 500px; height: 429px;" />
<pre>
<strong>Input:</strong> root = [3,5,1,6,2,0,8,null,null,7,4], target = 5, k = 2
<strong>Output:</strong> [7,4,1]
Explanation: The nodes that are a distance 2 from the target node (with value 5) have values 7, 4, and 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> root = [1], target = 1, k = 3
<strong>Output:</strong> []
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 500</code></li>
	<li>All the values <code>Node.val</code> are <strong>unique</strong>.</li>
	<li><code>target</code> is the value of one of the nodes in the tree.</li>
	<li><code>0 &lt;= k &lt;= 1000</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */

class Solution {
public:
    // Function to find all nodes at distance `k` in the subtree rooted at `node`.
    void findSubtreeNodes(TreeNode* node, int k, vector<int>& result) {
        if (node == NULL || k < 0) return;
        if (k == 0) {
            result.push_back(node->val);
            return;
        }
        findSubtreeNodes(node->left, k - 1, result);
        findSubtreeNodes(node->right, k - 1, result);
    }

    // Function to find all nodes at distance `k` from the target node.
    int findNodes(TreeNode* root, TreeNode* target, int k, vector<int>& result) {
        if (root == NULL) return -1;
        
        if (root == target) {
            // When the target node is found, search for nodes at distance `k` in its subtree.
            findSubtreeNodes(root, k, result);
            return 0;
        }
        
        // Search the left subtree for the target node.
        int leftDist = findNodes(root->left, target, k, result);
        if (leftDist != -1) {
            if (leftDist + 1 == k) {
                result.push_back(root->val);
            } else {
                findSubtreeNodes(root->right, k - leftDist - 2, result);
            }
            return leftDist + 1;
        }
        
        // Search the right subtree for the target node.
        int rightDist = findNodes(root->right, target, k, result);
        if (rightDist != -1) {
            if (rightDist + 1 == k) {
                result.push_back(root->val);
            } else {
                findSubtreeNodes(root->left, k - rightDist - 2, result);
            }
            return rightDist + 1;
        }
        
        return -1;
    }
    
    // Main function to find nodes at distance `k` from the target node.
    vector<int> distanceK(TreeNode* root, TreeNode* target, int k) {
        vector<int> result;
        findNodes(root, target, k, result);
        return result;
    }
};

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