-- Name: Stefan Russell
-- Date: 9/1/23
-- Class: COP 4020

{-
Assignment Instructions:
1. (33 pts) Create a function named problem1. Use a list comprehension for the main function. This function will take a single integer parameter. It indicates the number of primes that will be the final list. The final solution will output a list of every other prime.
problem1 10 --> [2,5,11,17,23,31,41,47,59,67]
problem1 7 --> [2,5,11,17,23,31,41]

2. (33 pts) Create a function named problem2. Use recursion to solve this problem. This function will take a single integer parameter. It indicates the maximum value of Fibonacci numbers that will be in the list. The final solution will be a list of Fibonacci numbers that have a three as their right-most digit and are less than or equal to n. (For this problem, Fibonacci starts 1,1,2,…)
problem2 100 --> [3,13]
problem2 10000 --> [3,13,233]

3. (34 pts) Create a function named problem3. For this problem, you can solve it any way you’d like. You may (and should) use helper functions. Create a list from numbers from 1 to n. The numbers must be either a multiple of five or have exactly three factors.
problem3 100 --> [4,5,9,10,15,20,25,30,35,40,45,49,50,55,60,65,70,75,80,85,90,95,100]
-}

{-
How to interpret:
In order to run Haskell code, make sure to 'ghci' then ':l secondAssignment.hs' then use the function you want to call:

Example:

problem1 10
problem1 7
problem2 100
problem2 10000
problem3 100
-}

--------------------Question1--------------------
-- Helper function to check if its prime (Given from class)
checkIfPrime n = ip n [2..(isqrt (n))]
 where
 ip _ [] = True
 ip n (x:xs)
  | n `mod` x == 0 = False
  | otherwise = ip n xs
isqrt :: Integral i => i -> i
isqrt = floor . sqrt . fromIntegral

-- Helper function to list every prime number
listOfPrimes n = take (2*n) [x | x <- [1..], checkIfPrime x]

-- Actual function to take in an integer and get fluctuating primes
problem1 n = skipEvenNumOfPrimes (listOfPrimes n)
 where 
 skipEvenNumOfPrimes (x:y:xs) = y : skipEvenNumOfPrimes xs
 skipEvenNumOfPrimes _ = []

--------------------Question2--------------------
-- Actual function (Partially from class)
problem2 n = go n 1 1 --Given--
    where --Given--
    go n f s --Given--
        | (f+s) > n = [] --Given--
        | (f+s) `mod` 10 == 3 = (f+s) : go n s (f+s) --In order to find all right most 3 #'s--
        | otherwise = go n s (f+s) --Given--

--------------------Question3--------------------
-- Helper function checks if the number of factors for a number
factorsP n = sum([ 1 | x <- [1..n], n `mod` x == 0])
-- Actual function checks if the number is a multiple of 5 or has 3 factors
problem3 n = [x | x <- [1..n],  (x `mod` 5 == 0 || factorsP x == 3)]