Leetcode: Closest Leaf in a Binary Tree

Given a binary tree where every node has a unique value, and a target key k, find the value of the nearest leaf node to target k in the tree.

Here, nearest to a leaf means the least number of edges travelled on the binary tree to reach any leaf of the tree. Also, a node is called a leaf if it has no children.

In the following examples, the input tree is represented in flattened form row by row. The actual root tree given will be a TreeNode object.

Example 1:

Input:
root = [1, 3, 2], k = 1
Diagram of binary tree:
          1
         / 
        3   2

Output: 2 (or 3)

Explanation: Either 2 or 3 is the nearest leaf node to the target of 1.
Example 2:

Input:
root = [1], k = 1
Output: 1

Explanation: The nearest leaf node is the root node itself.
Example 3:

Input:
root = [1,2,3,4,null,null,null,5,null,6], k = 2
Diagram of binary tree:
             1
            / 
           2   3
          /
         4
        /
       5
      /
     6

Output: 3
Explanation: The leaf node with value 3 (and not the leaf node with value 6) is nearest to the node with value 2.
Note:
root represents a binary tree with at least 1 node and at most 1000 nodes.
Every node has a unique node.val in range [1, 1000].
There exists some node in the given binary tree for which node.val == k.

Tree -----> Graph

1. First, preform DFS on root in order to find the node whose val = k, at the meantime use HashMap to keep record of all back edges from child to parent;
2. Then perform BFS on this node to find the closest leaf node.

Note only the nodes visited in DFS are put into the backedgeMap, the others don't. This is fine, cause only from KNode to root this path, we need to check backMap.

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int findClosestLeaf(TreeNode root, int k) {
        HashMap<TreeNode, TreeNode> backMap = new HashMap<>(); // store all edges that trace node back to its parent
        HashSet<TreeNode> visited = new HashSet<>(); // visited node in BFS
        Queue<TreeNode> queue = new LinkedList<>(); // for BFS
        
        TreeNode KNode = dfs(root, k, backMap); // DFS: search for node whoes val == k
        
        queue.offer(KNode);
        visited.add(KNode);
        
        while (!queue.isEmpty()) {
            TreeNode cur = queue.poll();
            if (cur.left == null && cur.right == null) {
                return cur.val;
            }
            if (cur.left != null && visited.add(cur.left)) {
                queue.offer(cur.left);
            }
            if (cur.right != null && visited.add(cur.right)) {
                queue.offer(cur.right);
            }
            if (backMap.containsKey(cur) && visited.add(backMap.get(cur))) {
                queue.offer(backMap.get(cur));
            }
        }
        
        return -1;
    }
    
    public TreeNode dfs(TreeNode cur, int k, HashMap<TreeNode, TreeNode> backMap) {
        if (cur.val == k) {
            return cur;
        }
        if (cur.left != null) {
            TreeNode left = dfs(cur.left, k, backMap);
            backMap.put(cur.left, cur);
            if (left != null) return left;
        }
        if (cur.right != null) {
            TreeNode right = dfs(cur.right, k, backMap);
            backMap.put(cur.right, cur);
            if (right != null) return right;
        }
        return null;
    }
}