257. Binary Tree Paths

题目：

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

For example, given the following binary tree:

   1
 /   \
2     3
 \
  5

All root-to-leaf paths are:

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

链接： http://leetcode.com/problems/binary-tree-paths/

题解：

求Binary Tree所有路径。用Recursive解法会比较容易。逻辑是，假如为current root为leaf node，则在res中加入该节点，返回。否则，递归求解，在左子树和右子树每一个结果中，在String前面insert  root.val + "->"。

Time Complexity - O(n)， Space Complexity - O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> res = new ArrayList<>();
        if(root == null)
            return res;
        if(root.left == null && root.right == null) {
            res.add(String.valueOf(root.val));
        } else {
            for(String s : binaryTreePaths(root.left)) {
                res.add(String.valueOf(root.val) + "->" + s);
            }
            for(String s : binaryTreePaths(root.right)) {
                res.add(String.valueOf(root.val) + "->" + s);
            }
        }

        return res;
    }
}

二刷:

还是使用了最简单的DFS Recursive解法。更好的解法可能是stack DFS和queue BFS。

Java:

Time Complexity - O(n)， Space Complexity - O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> res = new ArrayList<>();
        if (root == null) {
            return res;
        }
        if (root.left == null && root.right == null) {
            res.add(root.val + "");
            return res;
        }
        List<String> left = binaryTreePaths(root.left);
        List<String> right = binaryTreePaths(root.right);
        for (String s : left) {
            res.add(root.val + "->" + s);
        }
        for (String s : right) {
            res.add(root.val + "->" + s);
        }
        return res;
    }
}

三刷:

完全忘了一刷二刷是怎么写的，直接就用dfs + backtracking了。辅助方法里面用的是in-order traversal。 这里使用了一个List<Integer>来辅助计算Path，否则单独使用一个StringBuilder并不十分方便。

Java:

Time Complexity - O(n)， Space Complexity - O(n)

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> res = new ArrayList<>();
        List<Integer> path = new ArrayList<>();
        getBinaryTreePaths(res, path, root);
        return res;
    }

    private void getBinaryTreePaths(List<String> res, List<Integer> path, TreeNode root) {
        if (root == null) return;
        path.add(root.val);
        if (root.left == null && root.right == null) {
            StringBuilder sb = new StringBuilder();
            for (int val : path) sb.append(val).append("->");
            sb.setLength(sb.length() - 2);
            res.add(sb.toString());
            path.remove(path.size() - 1);
            return;
        }
        getBinaryTreePaths(res, path, root.left);
        getBinaryTreePaths(res, path, root.right);
        path.remove(path.size() - 1);
    }
}

Update:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> res = new ArrayList<>();
        binaryTreePaths(res, new ArrayList<Integer>(), root);
        return res;
    }

    private void binaryTreePaths(List<String> res, List<Integer> path, TreeNode root) {
        if (root == null) return;
        path.add(root.val);
        if (root.left == null && root.right == null) {
            StringBuilder sb = new StringBuilder();
            for (int val : path) sb.append(val).append("->");
            sb.setLength(sb.length() - 2);
            res.add(sb.toString());
            path.remove(path.size() - 1);
            return;
        }
        binaryTreePaths(res, path, root.left);
        binaryTreePaths(res, path, root.right);
        path.remove(path.size() - 1);
    }
}

写在一个方法里，仿照一刷二刷的dfs:

这里每次递归都要创建新的ArrayList，并且左右子树都要计算，空间复杂度会比较高。怎么计算清楚，留给下一次了。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<String> binaryTreePaths(TreeNode root) {
        List<String> res = new ArrayList<>();
        if (root == null) return res;
        if (root.left == null && root.right == null) res.add(String.valueOf(root.val));

        List<String> left = binaryTreePaths(root.left);
        for (String leftPath :left) res.add(root.val + "->" + leftPath);

        List<String> right = binaryTreePaths(root.right);
        for (String rightPath :right) res.add(root.val + "->" + rightPath);

        return res;
    }
}

Reference:

https://leetcode.com/discuss/55451/clean-solution-accepted-without-helper-recursive-function

https://leetcode.com/discuss/52072/accepted-java-simple-solution-in-8-lines

https://leetcode.com/discuss/52020/5-lines-recursive-python

https://leetcode.com/discuss/65362/my-concise-java-dfs-solution

https://leetcode.com/discuss/67749/bfs-with-two-queue-java-solution