in C++ code

Your ShelterBST class should implement the following functions. However, this time, you will sort your ShelterBST by Pet Name A. Insert a node to ShelterBST This time, you will need to ensure there are no duplicates in your insert function (i.e., the tree should refuse to insert a Pet with a duplicate name). B. Search and InOrder, PreOrder, PostOrder traversals as defined in Lab3. You can reuse this code, but modify it to use Pet name for all comparisons (instead of age). C. Find the parent for a given pet name Your private method should take as input an existing Pet name stored in your tree, and return the TreeNode* that is its ancestor/parent node. Your public method should display the Pet name and age of the parent node. You do not need to consider the situation when the input value is not stored in your BST. Only input the values already stored in your BST. D. Find the successor for a given node with 2 children. You do not need to consider the situation when the input node has one no children. Your private method should take as input an existing Pet name stored in your tree, and return the TreeNode* that is its successor node. Your public method should display the Pet name and age of the successor node. E. Number of nodes in your tree Return the number of total nodes in your BST. The return value should be an integer. F. Find the number of leaf nodes in your tree Return the number of leaf nodes in BST. The return value should be an integer. G. Find the number of nodes at a given level Return the number of nodes at a given in your BST. For example, if your BST is not empty, at level zero there is one node (the root). H. Find the height of the tree Return the height of your BST. The return value should be an integer. I. Balance check Input the root node of this tree. If this BST is balanced, return true; otherwise, return false. J. Delete a node based on a Pet name Delete a node based on the pet name given by the user. After deleting the node, your BST should be reconstructed. If the node to be deleted has two children, reconstruct the tree using the inorder successor (you should use the method you will write for D). You do not need to consider the situation when the input value is not stored in your BST. Only input the values already stored in your BST