# Find Elements in a Contaminated Binary Tree

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:**

![](https://assets.leetcode.com/uploads/2019/11/06/untitled-diagram-4-1.jpg)

```
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:**

![](https://assets.leetcode.com/uploads/2019/11/06/untitled-diagram-4.jpg)

```
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:**

![](https://assets.leetcode.com/uploads/2019/11/07/untitled-diagram-4-1-1.jpg)

```
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`

```java
class FindElements {
    TreeNode root;
    Set<Integer> set;

    public FindElements(TreeNode root) {
        this.root = root;
        set = new HashSet<>();
        fillTree(this.root, 0);
    }

    public void fillTree(TreeNode root, int val) {
        if (root == null)
            return;
        set.add(val);
        root.val = val;
        fillTree(root.left, 2 * val + 1);
        fillTree(root.right, 2 * val + 2);
    }

    public boolean find(int target) {
        return set.contains(target);
    }
}
```


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