ML practice problems

List processing

Easy

1. Write a function which, given a list of ints will return a list of int * int tuples containing each element of the list twice. For example, given the list [4,6,3,1], it will return the list [(4,4), (6,6), (3,3), (1,1)]. Solution.
   
   
2. Write a function which, given a list of ints and another int will determine whether or not the list contains a multiple of the given int. For example, given [1, 12, 8, 15] and 3, it will return true; given [1, 12, 8, 15] and 7, it will return false. Solution.
   
   
3. Write a function which, given a list of ints will return a list of ints like the one given except that each number is replaced by the sum of all numbers after it. For example, given the list [4,6,3,1], it will return the list [14, 10, 4, 1]. Solution.

Medium

1. Write a function which, given an int x will return a list containing the number x repeated x times. For example, given 0, it will return []; given 4, it will return [4, 4, 4, 4]. Solution.
   
   
2. Write a function deleteNth which takes a list and an integer and returns a list like the one it receives except that the nth element is deleted (counting from 1). For example, deleteNth([2, 5, 4, 3, 6, 3], 3) will return [2, 5, 3, 6, 3]. (You may assume that n is greater than or equal to zero. If n is 0 or if it is greater than the length of the list, then return the whole list.) Solution.

Hard

1. Write an ML function deleteEveryNth which takes a list and an integer and returns a list like the one it receives except th at every nth element is deleted. For example, deleteEveryNth([2, 5, 4, 3, 6, 3], 3) will return [2, 5, 3, 6]. (This time you may assume n is greater than zero.) Solution.
2. Write a function which, given a list will return the two halves of the list in a tuple (if the list has an odd number of elements, then one "half" will need to be one element longer than the other). For example, given [3, 12, 4, 6, 73, 34, 86], it will return ([3, 12, 4, 6], [73, 34, 86]) Solution.
3. Write a function which, given two lists of ints, which you may assumed to be sorted from smallest to largest, returns a list merged from the two given lists, with the numbers still in order. For example, given [3, 5, 13, 18] and [4, 8, 9, 10] will return [3, 4, 5, 8, 9, 10, 13, 18] Solution.
4. Using your answers to the two previous questions, write a function which, given a list of ints, will sort the list by splitting the list in half, recursively sorting each half list, and then merging the sorted results. Solution.

Relations

Easy

1. Write a function which, given the list representation of a relation and an element returns the image of that element under the relation (as a list). For example, given [(1, 3), (3, 6), (2, 1), (1, 6), (5, 4), (1,9)] and 1, it will return [3, 6, 9] (or the numbers could be in a different order). Solution.
   
   
2. Write a function which, given a list representation of a relation, returns the predicate representation of that relation. Solution.

Medium

1. Write a function which, given a predicate representation of a relation and a list of elements, tests whether or not the relation is reflexive for those elements. For example, given fn (x,y) => (x + y) mod 3 = 0 (that is, x and y are related if their sum is a multiple of 3) and [3, 9, 12] returns true, but given that function and [3,9,12,11] returns false. Solution.
   
   
2. Write a function which, given a list representation of a relation, will determine whether or not the relation is symmetric. Solution.
   
   
3. Write a function which, given a predicate representation of a relation, will return the inverse of that relation (as a predicate). Solution.

Hard

1. Suppose R is a relation from a set A to a set B and S is a relation from B to a set C. Write a function which, given the predicate representations of R and S and also the entire set B as a list will return the composition SoR as a predicate. Solution.

First class functions

Easy

1. Write a function which, given a list and a function, will return a list of containing the results of the given function applied to every element in the list. For example, given [1, 2, 3, 4] and fn (x) => 2 * x, it will return [2,4,6,8] Solution.
   
   
2. Write a function which, given a list, will return a function which, given an integer n will return the nth element in the given list. For example, if your function were named lister, then lister([1,2,3,4])(3) would return 3. Solution.