Description#
Given the root of 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 one right child.
Example 1:
Input: root = [5,3,6,2,4,null,8,1,null,null,null,7,9]
Output: [1,null,2,null,3,null,4,null,5,null,6,null,7,null,8,null,9]
Example 2:
Input: root = [5,1,7]
Output: [1,null,5,null,7]
Constraints:
- The number of nodes in the given tree will be in the range
[1, 100]. 0 <= Node.val <= 1000
Solutions#
Solution 1: DFS In-order Traversal#
We define a virtual node $dummy$, initially the right child of $dummy$ points to the root node $root$, and a pointer $prev$ points to $dummy$.
We perform an in-order traversal on the binary search tree. During the traversal, each time we visit a node, we point the right child of $prev$ to it, then set the left child of the current node to null, and assign the current node to $prev$ for the next traversal.
After the traversal ends, the original binary search tree is modified into a singly linked list with only right child nodes. We then return the right child of the virtual node $dummy$.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the number of nodes in the binary search tree.
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| # Definition for a binary tree node.
# class TreeNode:
# def __init__(self, val=0, left=None, right=None):
# self.val = val
# self.left = left
# self.right = right
class Solution:
def increasingBST(self, root: TreeNode) -> TreeNode:
def dfs(root):
if root is None:
return
nonlocal prev
dfs(root.left)
prev.right = root
root.left = None
prev = root
dfs(root.right)
dummy = prev = TreeNode(right=root)
dfs(root)
return dummy.right
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| /**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
private TreeNode prev;
public TreeNode increasingBST(TreeNode root) {
TreeNode dummy = new TreeNode(0, null, root);
prev = dummy;
dfs(root);
return dummy.right;
}
private void dfs(TreeNode root) {
if (root == null) {
return;
}
dfs(root.left);
prev.right = root;
root.left = null;
prev = root;
dfs(root.right);
}
}
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| /**
* Definition for a binary tree node.
* struct TreeNode {
* int val;
* TreeNode *left;
* TreeNode *right;
* TreeNode() : val(0), left(nullptr), right(nullptr) {}
* TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
* TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
TreeNode* increasingBST(TreeNode* root) {
TreeNode* dummy = new TreeNode(0, nullptr, root);
TreeNode* prev = dummy;
function<void(TreeNode*)> dfs = [&](TreeNode* root) {
if (!root) {
return;
}
dfs(root->left);
prev->right = root;
root->left = nullptr;
prev = root;
dfs(root->right);
};
dfs(root);
return dummy->right;
}
};
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| /**
* Definition for a binary tree node.
* type TreeNode struct {
* Val int
* Left *TreeNode
* Right *TreeNode
* }
*/
func increasingBST(root *TreeNode) *TreeNode {
dummy := &TreeNode{Val: 0, Right: root}
prev := dummy
var dfs func(root *TreeNode)
dfs = func(root *TreeNode) {
if root == nil {
return
}
dfs(root.Left)
prev.Right = root
root.Left = nil
prev = root
dfs(root.Right)
}
dfs(root)
return dummy.Right
}
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| /**
* Definition for a binary tree node.
* class TreeNode {
* val: number
* left: TreeNode | null
* right: TreeNode | null
* constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
* this.val = (val===undefined ? 0 : val)
* this.left = (left===undefined ? null : left)
* this.right = (right===undefined ? null : right)
* }
* }
*/
function increasingBST(root: TreeNode | null): TreeNode | null {
const dummy = new TreeNode((right = root));
let prev = dummy;
const dfs = (root: TreeNode | null) => {
if (!root) {
return;
}
dfs(root.left);
prev.right = root;
root.left = null;
prev = root;
dfs(root.right);
};
dfs(root);
return dummy.right;
}
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