Find Elements in a Contaminated Binary Tree

Description

Given a binary tree with the following rules:

1. root.val == 0
2. If treeNode.val == x and treeNode.left != null, then treeNode.left.val == 2 * x + 1
3. If treeNode.val == x and treeNode.right != null, then treeNode.right.val == 2 * x + 2

Now the binary tree is contaminated, which means all treeNode.val have been changed to -1.

You need to first recover the binary tree and then implement the FindElements class:

• FindElements(TreeNode* root) Initializes the object with a contamined binary tree, you need to recover it first.
• bool find(int target) Return if the target value exists in the recovered binary tree.

 

Example 1:

Input
["FindElements","find","find"]
[[[-1,null,-1]],[1],[2]]
Output
[null,false,true]
Explanation
FindElements findElements = new FindElements([-1,null,-1]); 
findElements.find(1); // return False 
findElements.find(2); // return True 

Example 2:

Input
["FindElements","find","find","find"]
[[[-1,-1,-1,-1,-1]],[1],[3],[5]]
Output
[null,true,true,false]
Explanation
FindElements findElements = new FindElements([-1,-1,-1,-1,-1]);
findElements.find(1); // return True
findElements.find(3); // return True
findElements.find(5); // return False

Example 3:

Input
["FindElements","find","find","find","find"]
[[[-1,null,-1,-1,null,-1]],[2],[3],[4],[5]]
Output
[null,true,false,false,true]
Explanation
FindElements findElements = new FindElements([-1,null,-1,-1,null,-1]);
findElements.find(2); // return True
findElements.find(3); // return False
findElements.find(4); // return False
findElements.find(5); // return True

 

Constraints:

• TreeNode.val == -1
• The height of the binary tree is less than or equal to 20
• The total number of nodes is between [1, 10^4]
• Total calls of find() is between [1, 10^4]
• 0 <= target <= 10^6

Solution(javascript)

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {TreeNode} root
 */
const FindElements = function (root) {
  root.val = 0
  const aux = (node, prev) => {
    if (node) {
      if (node === prev.left) {
        node.val = 2 * prev.val + 1
      } else if (node === prev.right) {
        node.val = 2 * prev.val + 2
      }
      aux(node.left, node)
      aux(node.right, node)
    }
  }
  aux(root, root)
  this.root = root
}

/**
 * @param {number} target
 * @return {boolean}
 */
//  O(h) time and space
FindElements.prototype.find = function (target) {
  const result = []
  while (target >= 0) {
    result.push(target)
    target = Math.floor((target - 1) / 2)
  }
  const index = result.length - 1
  if (this.root.val !== result[index]) {
    return false
  }
  const aux = (parent, index) => {
    if (index < 0) {
      return true
    }
    if (!parent) {
      return false
    }
    if (parent.left && parent.left.val === result[index]) {
      return aux(parent.left, index - 1)
    }
    if (parent.right && parent.right.val === result[index]) {
      return aux(parent.right, index - 1)
    }
    return false
  }
  return aux(this.root, index - 1)
}