Given a binary tree, return all root-to-leaf paths.

Note: A leaf is a node with no children.

Example:

Input:

   1
 /   \
2     3
 \
  5

Output: ["1->2->5", "1->3"]

Explanation: All root-to-leaf paths are: 1->2->5, 1->3

Soution: DFS

1. Recursion维护2个变量：List<Integer> pathEntry：每条路径的节点值, List<String> result：结果
2. Base Case： root为空，则返回
3. 遇到leaf node，则根据pathEntry生成路径，插入result
4. pathEntry.add (root.val);
binaryTreePaths (root.left, pathEntry, result);
binaryTreePaths (root.right, pathEntry, result);
5. 要记得每次退出迭代时，清除pathEntry中子节点的状态！！！

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> result = new ArrayList<> ();
        
        List<Integer> pathEntry = new ArrayList<> ();
        binaryTreePaths (root, pathEntry, result);
        
        return result;
    }
    
    private void binaryTreePaths (TreeNode root, List<Integer> pathEntry, List<String> result) {
        if (root == null) {
            return;
        }
        
        pathEntry.add (root.val);
        
        // 注意需要清除子节点的状态
        if (root.left != null) {
            binaryTreePaths (root.left, pathEntry, result);
            pathEntry.remove (pathEntry.size () - 1);
        }
            
        if (root.right != null) {
            binaryTreePaths (root.right, pathEntry, result);
            pathEntry.remove (pathEntry.size () - 1);
        }
        
        if (root.left == null && root.right == null) {
            StringBuilder path = new StringBuilder ();
            //先让prefix为空，就可以避免到出现 ->1->2->5，多余的箭头
            String prefix = "";
            for (int num : pathEntry) {
                String numStr = Integer.toString (num);
                path.append (prefix);
                prefix = "->";
                path.append (numStr);
            }
            
            result.add (path.toString());
        }
        
    }
}