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may also ask you to solve a related problem.
Write an insertion sort function for lists of integers
for example,
sort [6;7;1] = [1;6;7]
Hint: use the following helper function
let rec insert (i: int) (list: int list): int list = failwith “unimplemented”
that takes a a number, an already sorted ls and returns a new sorted list with that number inserted
for example,
insert 5 [1;3;5;7] = [1;3;5;5;7]
let rec sort (ls: int list): int list = failwith “unimplemented”
Write a zip function that takes two lists of integers and combines them into a list of pairs of ints
If the two input list are of unequal lengths, return None
your method should be tail recursive.
For example,
safe_zip_int [1;2;3;5] [6;7;8;9] = Some [(1,6);(2,7);(3,8);(5,9)]
safe_zip_int [1] [2;4;6;8] = None
safe_zip_int (between 0 1000000) (between 0 1000000) does not stack overflow
let rec safe_zip_int (ls1: int list) (ls2: int list) : ((int * int) list) option = failwith “unimplemented”
Write a function that produces the ith Pell number:
https://en.wikipedia.org/wiki/Pell_number
https://oeis.org/A000129
your function should be tail recursive, but only needs to have the correct output up to integer overflow
pell 0 = 0
pell 1 = 1
pell 7 = 169
pell 1000000 does not stack overflow
let rec pell (i: int) : int = failwith “unimplemented”
infinite precision natural numbers can be represented as lists of ints between 0 and 9
Write a function that takes an integer and represents it with a list of integers between 0 and 9 where the head ias the least signifigant digit.
If the input is negative return None
toDec 1234 = Some [4; 3; 2; 1]
toDec 0 = Some []
toDec (-1234) = None
(* Hint use
let rec toDec (i : int) : int list option = failwith “unimplemented”
Write a function that sums 2 natrual numbers as represented by a list of integers between 0 and 9 where the head ias the least signifigant digit.
Your function should be tail recursive
sum [4; 3; 2; 1] [1;0;1] = [5; 3; 3; 1]
sum [1] [9;9;9] = [0; 0; 0; 1]
sum [] [] = []
sum (nines 1000000) [1] does not stack overflow, when (nines 1000000) provides a list of 1000000 9s
let rec sum (a : int list) (b : int list) : int list = failwith “unimplemented”
Write an infinite precision version of the pel function from before
pell2 0 = []
pell2 1 = [1]
pell2 7 = [9; 6; 1]
pell2 50 = [2; 2; 5; 3; 5; 1; 4; 2; 9; 2; 4; 6; 2; 5; 7; 6; 6; 8; 4]
let rec pell2 (i: int) : int list = failwith “unimplemented”
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