This question should be answered with OCaml. All functions must be implemented with the Continuation Passing Style. Do not use ChatGPT. Oftentimes we want to traverse an entire tree in a certain order. One common way of traversing a tree is postorder traversal. In postorder traversal, we traverse the left subtree first, then traverse the right subtree, then visit the node. Our job is to create a function that returns a list of the values of the tree visited in postorder traversal. This function should be implemented with the Continuation Passing Style. Our function would have the following signature: traverse : 'a tree -> 'a list Example 1: For the tree in the image above, traverse should return the list [2; 5; 11; 6; 7; 5; 9; 9; 1]. Example 2: Input: Tree (Tree (Empty, 2, Empty), 1, Tree (Empty, 3, Empty)) Output: [2; 3; 1] Example 3: Input: Tree (Tree (Tree (Empty, 4, Empty), 2, Tree (Empty, 5, Empty)), 1, Tree (Empty, 3, Empty)) Output: [4; 5; 2; 3; 1]   1. Write a good set of tests for testing your tree traversal function. let traverse_tests : (int tree * int list) list = [] 2. Implement a CPS style postorder traversal function. let traverse (tree : 'a tree) : 'a list =     let rec helper (tree : 'a tree) (sc : 'a list -> 'r) =         raise NotImplemented     in     raise NotImplemented

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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This question should be answered with OCamlAll functions must be implemented with the Continuation Passing Style. Do not use ChatGPT.

Oftentimes we want to traverse an entire tree in a certain order. One common way of traversing a tree is postorder traversal. In postorder traversal, we traverse the left subtree first, then traverse the right subtree, then visit the node.

Our job is to create a function that returns a list of the values of the tree visited in postorder traversal. This function should be implemented with the Continuation Passing Style.

Our function would have the following signature: traverse : 'a tree -> 'a list

Example 1: For the tree in the image above, traverse should return the list [2; 5; 11; 6; 7; 5; 9; 9; 1].

Example 2:

Input: Tree (Tree (Empty, 2, Empty), 1, Tree (Empty, 3, Empty))

Output: [2; 3; 1]

Example 3:

Input: Tree (Tree (Tree (Empty, 4, Empty), 2, Tree (Empty, 5, Empty)), 1, Tree (Empty, 3, Empty))

Output: [4; 5; 2; 3; 1]

 

1. Write a good set of tests for testing your tree traversal function.

let traverse_tests : (int tree * int list) list = []

2. Implement a CPS style postorder traversal function.

let traverse (tree : 'a tree) : 'a list =

    let rec helper (tree : 'a tree) (sc : 'a list -> 'r) =

        raise NotImplemented

    in

    raise NotImplemented

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