Given a binary search tree, rearrange the tree in in-order so that the leftmost node in the tree is now the root of the tree, and every node has no left child and only 1 right child.

Example 1:

Input: [5,3,6,2,4,null,8,1,null,null,null,7,9]

5
/ \
3    6
/ \    \
2   4    8
/        / \
1        7   9

Output: [1,null,2,null,3,null,4,null,5,null,6,null,7,null,8,null,9]

1
\
2
\
3
\
4
\
5
\
6
\
7
\
8
\
9


Note:

1. The number of nodes in the given tree will be between 1 and 100.
2. Each node will have a unique integer value from 0 to 1000.

## Solutions

### 1. DFS-中序遍历

比较 naive 的解法……

# Time Complexity: O(n)
# Space Complexity: O(n)
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
def increasingBST(self, root: TreeNode) -> TreeNode:
if not root:
return None
seq = []
self.dfs(root, seq)
return self.build(seq)

def dfs(self, root, seq):
if not root:
return
self.dfs(root.left, seq)
seq.append(root.val)
self.dfs(root.right, seq)

def build(self, seq):
if not seq:
return None
root = TreeNode(seq)
node = root
for i in range(1, len(seq)):
cur_node = TreeNode(seq[i])
node.right = cur_node
node = cur_node
return root
# Runtime: 104 ms, faster than 41.51% of Python3 online submissions for Increasing Order Search Tree.
# Memory Usage: 14 MB, less than 8.33% of Python3 online submissions for Increasing Order Search Tree.


### 2. DFS-递归

待解释。

# Time Complexity: O(n)
# Space Complexity: O(n)
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
def increasingBST(self, root: TreeNode) -> TreeNode:
return self.dfs(root, None)

def dfs(self, root, pre):
if not root:
return pre
res = self.dfs(root.left, root)
root.left = None
root.right = self.dfs(root.right, pre)
return res
# Runtime: 104 ms, faster than 41.51% of Python3 online submissions for Increasing Order Search Tree.
# Memory Usage: 13.9 MB, less than 8.33% of Python3 online submissions for Increasing Order Search Tree.