Description
Write the functions in problem 1 – 5 in a single file, named “sol1.sml”. Then upload the file to the uni06.unist.ac.kr server (under your account), run the following command in the same directory where you have sol1.sml file. plsubmit assign1 sol1.sml You can submit the file multiple times, and the last one before the deadline will be used for grading. Please test submitting your solution a couple of days before the deadline to make sure the submission works for you. If it does not work, please contact the TA. Problems 1. Merge Lists (10pt) Write merge function that takes two sorted lists (in ascending order) and returns a sorted list that contains all the elements in the two lists. The signature of the function is as following: merge: int list * int list – int list For example, merge([1,4,5], [2,6,7]) should return [1,2,4,5,6,7]. You may assume that each of the input lists does not have repeating elements. For example, [1,1,4,5] cannot be used as an input to merge function because 1 is repeated. 2. Reverse List (10pt) Write reverse function that takes a list and returns the reversed list. For example, reverse([1,5,4]) returns [4,5,1]. The signature of the function is as following: reverse: int list – int list For problem 2, you should not use the ML’s built-‐in function rev. 3. Sigma Function (10pt) Write sigma function that takes two integers, a and b, and a function f and returns the following: ?(?) ! !!! The signature of sigma is as following: sigma: int * int * (int – int) – int
In other words, sigma(a,b,f) computes ?(?) ! !!! 4. Digits Function (10pt) Write digits function that takes a positive integer and returns the list of digits of the integer. For example, digits(253) returns [2,5,3] . The function’s signature should be: digits: int – int list You may assume that the input is a positive number. 5. Digital Roots and Additive Persistence (20pt: 10pt for each function) Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The number of additions required to obtain a single digit from a number n is called the additive persistence of n, and the digit obtained is called the digital root of n. For example, the sequence obtained from the starting number 9876 is (9876, 30, 3), so 9876 has an additive persistence of 2 and a digital root of 3. For the starting number 12349, the process produces (12349, 19, 10, 1), so 12349 has an additive persistence of 3 and a digital root of 1. Write two functions additivePersistence and digitalRoot that take positive integer argument n and return the additive persistence and the digital root of n respectively. The signatures of the functions are as following: additivePersistence: int – int digitalRoot: int – int You can use digits function defined in the previous question.
