Question

998. Maximum Binary Tree II

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Description

A maximum tree is a tree where every node has a value greater than any other value in its subtree.

You are given the root of a maximum binary tree and an integer val .

Just as in the previous problem , the given tree was constructed from a list a ( root = Construct(a) ) recursively with the following Construct(a) routine:

• If a is empty, return null .
• Otherwise, let a[i] be the largest element of a . Create a root node with the value a[i] .
• The left child of root will be Construct([a[0], a[1], ..., a[i - 1]]) .
• The right child of root will be Construct([a[i + 1], a[i + 2], ..., a[a.length - 1]]) .
• Return root .

Note that we were not given a directly, only a root node root = Construct(a) .

Suppose b is a copy of a with the value val appended to it. It is guaranteed that b has unique values.

Return Construct(b) .

Example 1:

Input: root = [4,1,3,null,null,2], val = 5
Output: [5,4,null,1,3,null,null,2]
Explanation: a = [1,4,2,3], b = [1,4,2,3,5]

Example 2:

Input: root = [5,2,4,null,1], val = 3
Output: [5,2,4,null,1,null,3]
Explanation: a = [2,1,5,4], b = [2,1,5,4,3]

 

Constraints:

• The number of nodes in the tree is in the range [1, 100] .
• 1 <= Node.val <= 100
• All the values of the tree are unique.
• 1 <= val <= 100

Solutions

Solution 1: Recursion

If $val$ is the maximum number, then make $val$ the new root node, and $root$ the left subtree of the new root node.

If $val$ is not the maximum number, since $val$ is the last appended number, it must be on the right side of $root$. Therefore, we can insert $val$ as a new node into the right subtree of $root$.

The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ is the number of nodes in the tree.

# 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 insertIntoMaxTree(
    self, root: Optional[TreeNode], val: int
  ) -> Optional[TreeNode]:
    if root is None or root.val < val:
      return TreeNode(val, root)
    root.right = self.insertIntoMaxTree(root.right, val)
    return root

/**
 * 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 {
  public TreeNode insertIntoMaxTree(TreeNode root, int val) {
    if (root == null || root.val < val) {
      return new TreeNode(val, root, null);
    }
    root.right = insertIntoMaxTree(root.right, val);
    return root;
  }
}

/**
 * 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* insertIntoMaxTree(TreeNode* root, int val) {
    if (!root || root->val < val) return new TreeNode(val, root, nullptr);
    root->right = insertIntoMaxTree(root->right, val);
    return root;
  }
};

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *   Val int
 *   Left *TreeNode
 *   Right *TreeNode
 * }
 */
func insertIntoMaxTree(root *TreeNode, val int) *TreeNode {
  if root == nil || root.Val < val {
    return &TreeNode{val, root, nil}
  }
  root.Right = insertIntoMaxTree(root.Right, val)
  return root
}

/**
 * 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 insertIntoMaxTree(root: TreeNode | null, val: number): TreeNode | null {
  if (!root || root.val < val) {
    return new TreeNode(val, root);
  }
  root.right = insertIntoMaxTree(root.right, val);
  return root;
}

// Definition for a binary tree node.
// #[derive(Debug, PartialEq, Eq)]
// pub struct TreeNode {
//   pub val: i32,
//   pub left: Option<Rc<RefCell<TreeNode>>>,
//   pub right: Option<Rc<RefCell<TreeNode>>>,
// }
//
// impl TreeNode {
//   #[inline]
//   pub fn new(val: i32) -> Self {
//   TreeNode {
//     val,
//     left: None,
//     right: None
//   }
//   }
// }
use std::rc::Rc;
use std::cell::RefCell;
impl Solution {
  pub fn insert_into_max_tree(
    mut root: Option<Rc<RefCell<TreeNode>>>,
    val: i32
  ) -> Option<Rc<RefCell<TreeNode>>> {
    if root.is_none() || root.as_ref().unwrap().as_ref().borrow().val < val {
      return Some(
        Rc::new(
          RefCell::new(TreeNode {
            val,
            left: root.take(),
            right: None,
          })
        )
      );
    }
    {
      let mut root = root.as_ref().unwrap().as_ref().borrow_mut();
      root.right = Self::insert_into_max_tree(root.right.take(), val);
    }
    root
  }
}

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *   int val;
 *   struct TreeNode *left;
 *   struct TreeNode *right;
 * };
 */

struct TreeNode* insertIntoMaxTree(struct TreeNode* root, int val) {
  if (!root || root->val < val) {
    struct TreeNode* res = (struct TreeNode*) malloc(sizeof(struct TreeNode));
    res->val = val;
    res->left = root;
    res->right = NULL;
    return res;
  }
  root->right = insertIntoMaxTree(root->right, val);
  return root;
}

Solution 2: Iteration

Search the right subtree, find the node where $curr.val \gt val \gt curr.right.val$, then create a new node $node$, point $node.left$ to $curr.right$, and then point $curr.right$ to $node$.

Finally, return $root$.

The time complexity is $O(n)$, where $n$ is the number of nodes in the tree. The space complexity is $O(1)$.

# 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 insertIntoMaxTree(
    self, root: Optional[TreeNode], val: int
  ) -> Optional[TreeNode]:
    if root.val < val:
      return TreeNode(val, root)
    curr = root
    node = TreeNode(val)
    while curr.right and curr.right.val > val:
      curr = curr.right
    node.left = curr.right
    curr.right = node
    return root

/**
 * 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 {
  public TreeNode insertIntoMaxTree(TreeNode root, int val) {
    if (root.val < val) {
      return new TreeNode(val, root, null);
    }
    TreeNode curr = root;
    TreeNode node = new TreeNode(val);
    while (curr.right != null && curr.right.val > val) {
      curr = curr.right;
    }
    node.left = curr.right;
    curr.right = node;
    return root;
  }
}

/**
 * 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* insertIntoMaxTree(TreeNode* root, int val) {
    if (root->val < val) return new TreeNode(val, root, nullptr);
    TreeNode* curr = root;
    TreeNode* node = new TreeNode(val);
    while (curr->right && curr->right->val > val) curr = curr->right;
    node->left = curr->right;
    curr->right = node;
    return root;
  }
};

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *   Val int
 *   Left *TreeNode
 *   Right *TreeNode
 * }
 */
func insertIntoMaxTree(root *TreeNode, val int) *TreeNode {
  if root.Val < val {
    return &TreeNode{val, root, nil}
  }
  node := &TreeNode{Val: val}
  curr := root
  for curr.Right != nil && curr.Right.Val > val {
    curr = curr.Right
  }
  node.Left = curr.Right
  curr.Right = node
  return root
}

/**
 * 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 insertIntoMaxTree(root: TreeNode | null, val: number): TreeNode | null {
  if (root.val < val) {
    return new TreeNode(val, root);
  }
  const node = new TreeNode(val);
  let curr = root;
  while (curr.right && curr.right.val > val) {
    curr = curr.right;
  }
  node.left = curr.right;
  curr.right = node;
  return root;
}