In [ ] Problem 3 Write a function buckets : ('a -> 'a -> bool) -> 'a list -> 'a list list that partitions a list into equivalence classes. That is, buckets equiv 1st should return a list of lists where each sublist in the result contains equivalent elements, where two elements are considered equivalent if equiv returns true. For example: buckets () [1; 2; 3; 4] = [[1]; [2]; [3]; [4]] buckets () [1; 2; 3; 4; 2; 3; 4; 3; 4] = buckets (fun x y-> (=) (x mod 3) The order of the buckets must reflect the order in which the elements appear in the original list. For example, the output of buckets (=) [1;2;3;4] should be [[1]; [2]; [3]; [4]] and not [[2]; [1]; [3];[4]] or any other permutation. [[1]; [2; 2]; [3; 3; 3]; [4; 4; 4]] (y mod 3)) [1; 2; 3; 4; 5; 6] = [[1;4]; [2;5]; [3;6]] The order of the elements in each bucket must reflect the order in which the elements appear in the original list. For example, the output of buckets (fun x y-> (=) (x mod 3) (y mod 3)) [1;2;3; 4; 5; 6] should be [[1;4]; [2;5]; [3;6]] and not [[4;1]; [5;2]; [3;6]] or any other permutations. Assume that the comparison function ('a -> 'a -> bool) is commutative, associative and idempotent. Just use lists. Do not use sets or hash tables. List append function @ may come in handy. [1;2;3] @[4;5;6] = [1;2;3; 4; 5;6]. let buckets p 1 = (* YOUR CODE HERE *) In [ ]: assert (buckets (=) [1;2;3;4] = [[1]; [2]; [3]; [4]]); assert (buckets (=) [1; 2; 3; 4; 2; 3; 4;3;4] = [[1]; [2; 2]; [3; 3; 3]; [4;4;4]]); assert (buckets (fun x y-> (=) (x mod 3) (y mod 3)) [1; 2; 3; 4; 5; 6] = [[1;4]; [2;5]; [3; 6]])
In [ ] Problem 3 Write a function buckets : ('a -> 'a -> bool) -> 'a list -> 'a list list that partitions a list into equivalence classes. That is, buckets equiv 1st should return a list of lists where each sublist in the result contains equivalent elements, where two elements are considered equivalent if equiv returns true. For example: buckets () [1; 2; 3; 4] = [[1]; [2]; [3]; [4]] buckets () [1; 2; 3; 4; 2; 3; 4; 3; 4] = buckets (fun x y-> (=) (x mod 3) The order of the buckets must reflect the order in which the elements appear in the original list. For example, the output of buckets (=) [1;2;3;4] should be [[1]; [2]; [3]; [4]] and not [[2]; [1]; [3];[4]] or any other permutation. [[1]; [2; 2]; [3; 3; 3]; [4; 4; 4]] (y mod 3)) [1; 2; 3; 4; 5; 6] = [[1;4]; [2;5]; [3;6]] The order of the elements in each bucket must reflect the order in which the elements appear in the original list. For example, the output of buckets (fun x y-> (=) (x mod 3) (y mod 3)) [1;2;3; 4; 5; 6] should be [[1;4]; [2;5]; [3;6]] and not [[4;1]; [5;2]; [3;6]] or any other permutations. Assume that the comparison function ('a -> 'a -> bool) is commutative, associative and idempotent. Just use lists. Do not use sets or hash tables. List append function @ may come in handy. [1;2;3] @[4;5;6] = [1;2;3; 4; 5;6]. let buckets p 1 = (* YOUR CODE HERE *) In [ ]: assert (buckets (=) [1;2;3;4] = [[1]; [2]; [3]; [4]]); assert (buckets (=) [1; 2; 3; 4; 2; 3; 4;3;4] = [[1]; [2; 2]; [3; 3; 3]; [4;4;4]]); assert (buckets (fun x y-> (=) (x mod 3) (y mod 3)) [1; 2; 3; 4; 5; 6] = [[1;4]; [2;5]; [3; 6]])
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
Problem 1PE
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OCAML Problem
![# Problem 3
### Write a function
**Type Signature**
```
buckets : ('a -> 'a -> bool) -> 'a list -> 'a list list
```
**Description**:
This function partitions a list into equivalence classes. Specifically, the function `buckets equiv lst` returns a list of lists, where each sublist contains elements considered equivalent if `equiv` returns `true`.
**Example**:
- `buckets (=) [1;2;3;4] = [[1];[2];[3];[4]]`
- `buckets (=) [1;2;3;4;2;3;4;3;4] = [[1];[2;2];[3;3;3];[4;4;4]]`
- `buckets (fun x y -> (=) (x mod 3) (y mod 3)) [1;2;3;4;5;6] = [[1;4];[2;5];[3;6]]`
The order of the buckets should reflect the order in the original list. For example:
- The output of `buckets (=) [1;2;3;4]` should be `[[1];[2];[3];[4]]` not `[[2];[1];[3];[4]]` or any permutation.
Similarly, the order of elements within each bucket should reflect their original order. Thus, the output of:
- `buckets (fun x y -> (=) (x mod 3) (y mod 3)) [1;2;3;4;5;6]` should be `[[1;4];[2;5];[3;6]]` not `[[4;1];[5;2];[3;6]]` or any permutation.
**Assumptions**:
- The comparison function `('a -> 'a -> bool)` is commutative, associative, and idempotent.
**Requirements**:
- Use lists only. Do not use sets or hash tables.
- The list append function `@` may be useful. For example, `[1;2;3] @ [4;5;6] = [1;2;3;4;5;6]`.
**Implementation**:
```ocaml
let buckets p l =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95a918cc-648a-4ba1-8333-a4ee16085cbc%2F5b7bcad7-047f-4bb4-94df-2a769a47648f%2Fwztcxg_processed.png&w=3840&q=75)
Transcribed Image Text:# Problem 3
### Write a function
**Type Signature**
```
buckets : ('a -> 'a -> bool) -> 'a list -> 'a list list
```
**Description**:
This function partitions a list into equivalence classes. Specifically, the function `buckets equiv lst` returns a list of lists, where each sublist contains elements considered equivalent if `equiv` returns `true`.
**Example**:
- `buckets (=) [1;2;3;4] = [[1];[2];[3];[4]]`
- `buckets (=) [1;2;3;4;2;3;4;3;4] = [[1];[2;2];[3;3;3];[4;4;4]]`
- `buckets (fun x y -> (=) (x mod 3) (y mod 3)) [1;2;3;4;5;6] = [[1;4];[2;5];[3;6]]`
The order of the buckets should reflect the order in the original list. For example:
- The output of `buckets (=) [1;2;3;4]` should be `[[1];[2];[3];[4]]` not `[[2];[1];[3];[4]]` or any permutation.
Similarly, the order of elements within each bucket should reflect their original order. Thus, the output of:
- `buckets (fun x y -> (=) (x mod 3) (y mod 3)) [1;2;3;4;5;6]` should be `[[1;4];[2;5];[3;6]]` not `[[4;1];[5;2];[3;6]]` or any permutation.
**Assumptions**:
- The comparison function `('a -> 'a -> bool)` is commutative, associative, and idempotent.
**Requirements**:
- Use lists only. Do not use sets or hash tables.
- The list append function `@` may be useful. For example, `[1;2;3] @ [4;5;6] = [1;2;3;4;5;6]`.
**Implementation**:
```ocaml
let buckets p l =
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