Let’s say there are two persons, **Composer** and **Performer**.

The **Composer** randomly selects three different **Pitch** which constructed by two part, **Note** and **Octave**. **Note** in the range of “A” to “G”, **Octave** in the range of “1” to “3”.

For example, here is a typical **Pitch** combined by ‘A’ and ‘1’, in which ‘A’ is the **Note**, and ‘1’ is the **Octave**.

Once **Composer** selected a Combination, **Performer** needs to guess it as quick as possible. After each guess, **Performer** get a feedback which indicates that:

- how many pitches in the guess are included in the target (
**correct pitches**) - how many pitches have the right note but the wrong octave (
**correct notes**) - how many pitches have the right octave but the wrong note (
**correct octaves**)

Now, the question is how to get the corrected answer as less times as possible.

The core idea is that when we get a feedback from the previous guess, we’d check out combinations that have identical feedback in the remind possible set, in which the problem scale can be reduced effectively.

Now, the question is how to get the corrected answer as less times as possible.

The core idea is that when we get a feedback from the previous guess, we are able to check out combinations that have identical feedback in the remaining possible set, by which the problem scale can be pruned effectively.

possible set, in which the problem scale can be reduced effectively.

```
-- Subject : UniMelb 2019 SM1 COMP90048 Declarative Programming
-- File : Proj1.hs
-- Author : Mingzhe Du
-- Origin : Mon Apr 8 2019
-- Purpose : This program for guessing a target chord. In each round of the game,
-- the program will generate a chord from a possible set, and then a feedback
-- against the guess will be given. Depanding on these feedbacks, the aim of this
-- program is get the correct chord with as less as possible guess times.
module Proj1 (Pitch, GameState, toPitch, feedback, initialGuess, nextGuess) where
-- Pitch structure
data Pitch = Pitch { note :: Char,
octave :: Char
} deriving (Eq)
instance Show Pitch where
show (Pitch note octave) = [note, octave]
-- Game State
data GameState = GameState { times :: Int, -- Guess times
cCombinations :: [[[Char]]] -- Possible set
} deriving (Eq, Show)
-- Converting String to Pitch
toPitch :: String -> Maybe Pitch
toPitch (a:b:t)
| not (null t) = Nothing
| (elem note' ['A'..'G']) && (elem octave' ['1'..'3']) = Just Pitch {note = note', octave = octave'}
| otherwise = Nothing
where note' = a
octave' = b
-- Comparing target chord and guessed chord
feedback :: [Pitch] -> [Pitch] -> (Int,Int,Int)
feedback pitch_a pitch_b
| (length pitch_a == 3) && (length pitch_b == 3) = (c_p, c_n - c_p, c_o - c_p)
| otherwise = (0,0,0)
where get_key key = foldr (\x acc -> key x:acc) []
c_p = getCounter pitch_a pitch_b 0 -- Correct pitches
c_n = getCounter (map note pitch_a) (map note pitch_b) 0 -- Correct notes
c_o = getCounter (map octave pitch_a) (map octave pitch_b) 0 -- Correct Octaves
-- Initial guess
initialGuess :: ([Pitch], GameState)
initialGuess = (currentGuess, gameState)
where currentGuess = combinationToPitch (cGuess)
gameState = GameState 0 all_combinations
all_items = getCombination "ABCDEFG" "123"
cGuess:all_combinations = subsequencesOfSize 3 all_items -- New guess and new possible set
getCombination p_note p_octave = foldr (\x acc -> (map (\y -> y:[x]) p_note) ++ acc) [] p_octave
combinationToPitch combinations = map (\(Just x) -> x) $ map toPitch combinations -- Converting String to Pitch
-- Get the next guess
nextGuess :: ([Pitch], GameState) -> (Int,Int,Int) -> ([Pitch],GameState)
nextGuess (pGuess, pGameState) pFeedback = (cGuess, cGameState)
where cGuess':cCombs = getNewCombination pGuess pCombinations pFeedback
pCombinations = cCombinations pGameState
cGuess = toChord cGuess'
cGameState = GameState ((times pGameState) + 1) cCombs
toChord = map (\x -> Pitch (x !! 0) (x !! 1))
-- Help Functions
-- remove an item from a list
removeItem :: (Eq a) => a -> [a] -> [a]
removeItem _ [] = []
removeItem x (y:ys)
| x == y = ys
| otherwise = y : removeItem x ys
-- get the number of same elements in two lists
getCounter :: (Eq a) => [a] -> [a] -> Int -> Int
getCounter [] y c = c
getCounter (x:xs) y c
| elem x y = getCounter xs (removeItem x y) (c+1)
| otherwise = getCounter xs y c
-- Generate combinations by a specifc size
subsequencesOfSize :: Int -> [a] -> [[a]]
subsequencesOfSize n xs = let l = length xs in if n>l then [] else subsequencesBySize xs !! (l-n)
where subsequencesBySize [] = [[[]]]
subsequencesBySize (x:xs) = let next = subsequencesBySize xs in zipWith (++) ([]:next) (map (map (x:)) next ++ [[]])
-- Converting a string list to pitch list
toChord :: [[Char]] -> [Pitch]
toChord a = map (\x -> Pitch (x !! 0) (x !! 1)) a
-- retrive a new guess
getNewCombination :: [Pitch] -> [[[Char]]] -> (Int, Int, Int) -> [[[Char]]]
getNewCombination guess allCombinations pFeedback = foldr (\x acc -> if checkFeedback (toChord x) then x:acc else acc) [] allCombinations
where checkFeedback nChord = if pFeedback == (feedback guess nChord) then True else False
```