Skip to content

Latest commit

 

History

History
46 lines (35 loc) · 2.16 KB

exercises-1.md

File metadata and controls

46 lines (35 loc) · 2.16 KB

Exercises on OCaml Programming (Part 1)

Exercise 1

The series expansion of $e^x$ is given by:

$$1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \dots$$

Evaluate $e^x$ for given values of x by using the above expansion for the first 10 terms.

Exercise 2

We define super digit of an integer x as follows:

  1. if x has only 1 digit, then its super digit is x;
  2. otherwise, the super digit of x is equal to the super digit of the sum of its digits.

For example, the super digit of 3 is calculated as

super_digit(3) = 3

Instead, the super digit of

super_digit(148148148) = super_digit(1+4+8+1+4+8+1+4+8)
                       = super_digit(39)
                       = super_digit(3+9)
                       = super_digit(12)
                       = super_digit(1+2)
                       = super_digit(3)
                       = 3.

Write a function super_digit that given an integer n returns the super digit of n.

Exercise 3

Write a function list_replication that, given a list l and a natural number n, returns a new list where each element is replicated n times. For example, if l = [1;2;3;4] and n = 3, the result of list_replication l n is [1;1;1;2;2;2;3;3;3;4;4;4].

Exercise 4

Write a function list_replication1 that, given a list l and a natural number n, returns a new list that is obtained by concatenating l with itself n times. For example, if l = [1;2;3;4] and n = 3, the result of list_replication l n is [1;2;3;4;1;2;3;4;1;2;3;4].

Exercise 5

Write a function is_function that takes a relation r on integers as input, i.e., a list of pair (x,y) of integers, and returns true if r represents a valid function. For example, is_function r1 where r1 = [(1,1); (2,2); (3,3)] returns true because r1 represents the identity function on the set {1,2,3}. Instead, is_function r2 with r2 = [(1,2); (2,4); (3,6); (4,8); (1,0)] returns false because r2 cannot be a function.

Exercise 6

Write a function mingle_string that given two string p and q of the same lenght and mingles them together. For example, mingle_string "abcde" "pqrst" returns "apbqcrdset".