Problem Set: Using the Sequence API

Objectives

During this activity, students should be able to:

Solve programming problems using the Clojure sequence API.

This activity helps the student develop the following skills, values and attitudes: ability to analyze and synthesize, capacity for identifying and solving problems, and efficient use of computer systems.

Activity Description

This activity can be developed individually or in pairs.

Solve the following set of programming exercises using the Clojure sequence API. Place all your functions and unit tests in a file called sequences.clj.

Important Note:

None of the following problems may use explicit recursion nor the loop/recur special forms. You may define any number of auxiliary functions as long as they don’t use explicit recursion nor the loop/recur special forms. You may only use functions defined in the clojure.core namespace.

The function positives takes a list of numbers lst as its argument, and returns a new list that only contains the positive numbers of lst. Unit tests:

(deftest test-positives
  (is (= () (positives '())))
  (is (= () (positives '(-4 -1 -10 -13 -5))))
  (is (= '(3 6) (positives '(-4 3 -1 -10 -13 6 -5))))
  (is (= '(4 3 1 10 13 6 5) (positives '(4 3 1 10 13 6 5)))))

The function dot-product takes two arguments: the lists a and b. It returns the result of performing the dot product of a times b. The dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and then summing those products. Unit tests:
```
(deftest test-dot-product
  (is (= 0 (dot-product () ())))
  (is (= 32 (dot-product '(1 2 3) '(4 5 6))))
  (is (= 21.45 (dot-product '(1.3 3.4 5.7 9.5 10.4) 
                            '(-4.5 3.0 1.5 0.9 0.0)))))
```

The function pow takes two arguments as input: a number a and a positive integer b. It returns the result of computing a raised to the power b. Unit tests:

(deftest test-pow
  (is (= 1 (pow 0 0)))
  (is (= 0 (pow 0 1)))
  (is (= 1 (pow 5 0)))
  (is (= 5 (pow 5 1)))
  (is (= 125 (pow 5 3)))
  (is (= 25 (pow -5 2)))
  (is (= -125 (pow -5 3)))
  (is (= 1024 (pow 2 10)))
  (is (= 525.21875 (pow 3.5 5)))
  (is (= 129746337890625 (pow 15 12)))
  (is (= 3909821048582988049 (pow 7 22))))

The function replic takes two arguments: a list lst and an integer number n, where n ≥ 0. It returns a new list that replicates n times each element contained in lst. Unit tests:

(deftest test-replic
  (is (= () (replic 7 ())))
  (is (= () (replic 0 '(a b c))))
  (is (= '(a a a) (replic 3 '(a))))
  (is (= '(1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4) 
         (replic 4 '(1 2 3 4)))))

The function expand takes a list lst as its argument. It returns a list where the first element of lst appears one time, the second elements appears two times, the third element appears three times, and so on. Unit test:

(deftest test-expand
  (is (= () (expand ())))
  (is (= '(a) (expand '(a))))
  (is (= '(1 2 2 3 3 3 4 4 4 4) (expand '(1 2 3 4))))
  (is (= '(a b b c c c d d d d e e e e e) 
         (expand '(a b c d e)))))

The function largest takes as argument a nonempty list of numbers lst. It returns the largest value contained in lst. Use the reduce function to solve this problem. Do not use the predefined max or min functions. Unit tests:

(deftest test-largest
  (is (= 31 (largest '(31))))
  (is (= 5 (largest '(1 2 3 4 5))))
  (is (= -1 (largest '(-1 -2 -3 -4 -5))))
  (is (= 52 (largest '(32 -1 45 12 -42 52 17 0 21 2)))))

The function drop-every takes two arguments: an integer number n, where n ≥ 1, and a list lst. It returns a new list that drops every n-th element from lst. Unit tests:

(deftest test-drop-every
  (is (= () (drop-every 5 ())))
  (is (= '(1 2 3) (drop-every 4 '(1 2 3 4))))
  (is (= '(1 3 5 7) (drop-every 2 '(1 2 3 4 5 6 7 8))))
  (is (= '(1 3 5 7 9) (drop-every 2 '(1 2 3 4 5 6 7 8 9))))
  (is (= '(a b d e g h j) 
         (drop-every 3 '(a b c d e f g h i j))))
  (is (= '(a b c d e f g h i j) 
         (drop-every 20 '(a b c d e f g h i j))))
  (is (= () (drop-every 1 '(a b c d e f g h i j)))))

The function rotate-left takes two arguments: an integer number n and a list lst. It returns the list that results from rotating lst a total of n elements to the left. If n is negative, it rotates to the right. Unit tests:

(deftest test-rotate-left
  (is (= () (rotate-left 5 ())))
  (is (= '(a b c d e f g) (rotate-left 0 '(a b c d e f g))))
  (is (= '(b c d e f g a) (rotate-left 1 '(a b c d e f g))))
  (is (= '(g a b c d e f) (rotate-left -1 '(a b c d e f g))))
  (is (= '(d e f g a b c) (rotate-left 3 '(a b c d e f g))))
  (is (= '(e f g a b c d) (rotate-left -3 '(a b c d e f g))))  
  (is (= '(a b c d e f g) (rotate-left 7 '(a b c d e f g))))
  (is (= '(a b c d e f g) (rotate-left -7 '(a b c d e f g))))
  (is (= '(b c d e f g a) (rotate-left 8 '(a b c d e f g))))
  (is (= '(g a b c d e f) (rotate-left -8 '(a b c d e f g))))
  (is (= '(d e f g a b c) (rotate-left 45 '(a b c d e f g))))
  (is (= '(e f g a b c d) (rotate-left -45 '(a b c d e f g)))))

The function gcd takes two positive integer arguments a and b as arguments, where a > 0 and b > 0. It returns the greatest common divisor (GCD) of a and b.

NOTE: The GCD of two integers is the largest positive integer that divides both numbers exactly. For example, the GCD of 20 and 16 is 4.

Unit tests:
```
(deftest test-gcd
  (is (= 1 (gcd 13 7919)))
  (is (= 4 (gcd 20 16)))
  (is (= 6 (gcd 54 24)))
  (is (= 7 (gcd 6307 1995)))
  (is (= 12 (gcd 48 180)))
  (is (= 14 (gcd 42 56))))
```

The function insert-everywhere takes two arguments as input: an object x and a list lst. It returns a new list with all the possible ways in which x can be inserted into every position of lst. Unit tests:

(deftest test-insert-everywhere
  (is (= '((1)) (insert-everywhere 1 ())))
  (is (= '((1 a) (a 1)) (insert-everywhere 1 '(a))))
  (is (= '((1 a b c) (a 1 b c) (a b 1 c) (a b c 1))
         (insert-everywhere 1 '(a b c))))
  (is (= '((1 a b c d e)
           (a 1 b c d e)
           (a b 1 c d e)
           (a b c 1 d e)
           (a b c d 1 e)
           (a b c d e 1))
          (insert-everywhere 1 '(a b c d e))))
  (is (= '((x 1 2 3 4 5 6 7 8 9 10)
           (1 x 2 3 4 5 6 7 8 9 10)
           (1 2 x 3 4 5 6 7 8 9 10)
           (1 2 3 x 4 5 6 7 8 9 10)
           (1 2 3 4 x 5 6 7 8 9 10)
           (1 2 3 4 5 x 6 7 8 9 10)
           (1 2 3 4 5 6 x 7 8 9 10)
           (1 2 3 4 5 6 7 x 8 9 10)
           (1 2 3 4 5 6 7 8 x 9 10)
           (1 2 3 4 5 6 7 8 9 x 10)
           (1 2 3 4 5 6 7 8 9 10 x))
          (insert-everywhere 'x '(1 2 3 4 5 6 7 8 9 10)))))

Source of several of these problems: Ninety-Nine Lisp Problems

Deliverables

The program source file must include at the top the authors’ personal information (name and student id) within comments. For example:

;----------------------------------------------------------
; Activity: Problem Set: Using the Sequence API
; Date: October 7, 2018.
; Authors:
;          A01166611 Pepper Pots
;          A01160611 Anthony Stark
;----------------------------------------------------------

Also, each function should include a documentation string (docstring) with a brief description of its behavior. For example:

(defn max2
  "Returns the largest of the two numbers x and y."
  [x y]
  (if (> x y) x y))

Upload Instructions

To deliver the sequences.clj file, please provide the following information:

Request PIN

Only one team member needs to upload the file.

Due date is Sunday, October 7.

Evaluation

This activity will be evaluated using the following criteria:

-10	The program doesn't contain within comments the author's personal information.
-30	A docstring is missing in one or more functions.
10	The program contains syntax errors.
1	The program was plagiarized in whole or in part.
10-100	Depending on the amount of exercises that were solved correctly.