A complete binary search tree is a complete binary tree that satisfies the left-right ordering property of binary search tree as well as the structure of a complete binary tree. Since a complete binary tree can be perfectly stored in an array, we can also store the complete BST in an array. In this lab, you will be given an array of integers as input. The objective is to write a function to_bst(lst) to convert the array to a complete binary tree that stores in an array with the same length. For example, given an array [29, 72, 1, 34, 22], the corresponding complete BST is [34, 22, 72, 1, 29]. Hint: Consider the inorder traversal of the BST.

To convert the input array to a complete binary tree that stores in an array with the same length, we can follow these steps:

1. Sort the input array in ascending order.
2. Create an empty output array with the same length as the input array.
3. Perform an inorder traversal of the complete binary search tree and fill in the output array with the visited nodes in the order of the traversal.

Here is the Python code to implement this algorithm:

def to_bst(lst):
    # Sort the input array in ascending order
    lst.sort()

    # Create an empty output array with the same length as the input array
    output = [None] * len(lst)

    # Perform an inorder traversal of the complete binary search tree
    def inorder(node_index, start_index, end_index):
        if start_index <= end_index:
            # Calculate the index of the middle node
            mid_index = (start_index + end_index) // 2

            # Fill in the current node with the middle element
            output[node_index] = lst[mid_index]

            # Recursively fill in the left and right subtrees
            inorder(2 * node_index + 1, start_index, mid_index - 1)
            inorder(2 * node_index + 2, mid_index + 1, end_index)

    # Start the inorder traversal from the root node
    inorder(0, 0, len(lst) - 1)

    return output

This function uses recursion to perform an inorder traversal of the complete binary search tree and fill in the output array with the visited nodes in the order of the traversal. The time complexity of this algorithm is O(n log n) because of the sorting step.