Search and extract node in a BST

SearchBST.cpp

struct Node
{
	Node* left;
	Node* right;
	int value;
};

Node* insert(Node* tree, int value) {
	if (tree == nullptr) {
		Node* temp = new Node;
		temp->left = nullptr;
		temp->right = nullptr;
		temp->value = value;
		return temp;
	}

	if (tree->value > value) {
		tree->left = insert(tree->left, value);
	}
	else
	{
		tree->right = insert(tree->right, value);
	}

	return tree;
}




void transverse(Node* tree) {
	if (tree == nullptr) {
		return;
	}

	transverse(tree->left);

	std::cout << tree->value << " ";

	transverse(tree->right);
}

Node* search(Node* tree, int value) {
	Node* ptr = tree;

	if (ptr->value == value) {
		tree = ptr;
		return tree;
	}

	while (ptr != nullptr && ptr->value != value)
	{
		if (ptr->value > value) {
			ptr = ptr->left;
		}
		else if (ptr->value < value) {
			ptr = ptr->right;
		}
	}
	tree = ptr;
	return tree;
}
int main() {
	Node* list = nullptr;
	list = insert(list, 5);
	list = insert(list, 0);
	list = insert(list, 9);
	list = insert(list, 1);
	list = insert(list, 10);
	list = insert(list, -1);
	list = insert(list, 10);
	list = insert(list, 20);
	list = insert(list, 40);

	transverse(list);
	
	Node * list2 = search(list, 20);

	std::cout << "\n";

	transverse(list2);

	std::cout << "\n";

	transverse(list);
}