# 08. Binary Tree to BST

The problem can be found at the following link: [Question Link](https://practice.geeksforgeeks.org/problems/binary-tree-to-bst/1)

## My Approach

I solved this problem by utilizing the BST property, where the inorder traversal of the tree results in sorted values. In this context, I reversed this process by:

* First obtaining the inorder order of the binary tree.
* Sorting the values of the binary tree.
* Subsequently updating the binary tree with the sorted values.

Here are the steps to do so:

* Conduct an in-order traversal of the binary tree to obtain the nodes in inorder order.
* Store these nodes in a `nodes` vector and also collect the binary tree values in a `values` vector.
* Sort the `values` vector to arrange the values in ascending order.
* Assign these sorted `values` to the corresponding `nodes` in the vector.

## Time and Auxiliary Space Complexity

* **Time Complexity**: `O(NlogN)` (due to sorting), where N is the number of nodes in the binary tree.
* **Auxiliary Space Complexity**: `O(N)` (for the vector to store nodes).

## Code (C++)

```cpp
class Solution {
public:
    void inorder(Node *root, vector<Node*>& nodes) {
        if (!root)
            return;

        inorder(root->left, nodes);
        nodes.push_back(root);
        inorder(root->right, nodes);
    }

    Node *binaryTreeToBST(Node *root) {
        vector<Node*> nodes;
        inorder(root, nodes);
        vector<int> values;
        
        for (auto node : nodes)
            values.push_back(node->data);

        sort(values.begin(), values.end());

        for (int i = 0; i < nodes.size(); ++i)
            nodes[i]->data = values[i];

        return root;
    }
};
```

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