-- Interface for a group of functions that implement a Board data structure.
--
-- Alyce Brady

module Board where

type Row = [Integer]
type Column = [Integer]
type Board = [Row]

-- *******************************
-- *           INTERFACE 
-- *******************************

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-- FUNCTIONS TO CREATE A BOARD
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-- mkRow N
--   Creates an "empty" row of length N (actually a row of 0's).
mkRow :: Int -> Row

-- mkBoard N
--   Creates an "empty" N x N board (actually filled with 0's).
mkBoard :: Int -> Board

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-- FUNCTIONS TO ACCESS ELEMENTS OF A BOARD
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-- getRow board rowIndex
--   Returns the row at index rowIndex.
getRow :: Board -> Int -> Row

-- getCol board colIndex
--   Returns the column at index colIndex.
getCol :: Board -> Int -> Column

-- getCol board rowIndex colIndex
--   Returns the contents of the cell at location (rowIndex, colIndex)
--   on the board.
getCell :: Board -> Int -> Int -> Integer

-- validIndex board index
--   Returns True if the index (a row or column index) is in range.
validIndex :: Board -> Int -> Bool

-- validLoc board rowIndex colIndex
--   Returns True if location (rowIndex, colIndex) is in range (on the board).
validLoc :: Board -> Int -> Int -> Bool

-- setVal board rowIndex colIndex newValue
--   Returns a new board equivalent to board EXCEPT
--   that the value at location (rowIndex, colIndex) is newValue.
setVal :: Board -> Int -> Int ->Integer -> Board
  -- USES
     -- setValInRow R colIndex newValue
     --   Returns a new row equivalent to R EXCEPT
     --   that the value in column colIndex is newValue.
     -- setValInRow :: Row -> Int ->Integer -> Row

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-- USEFUL FUNCTION FOR TESTING PURPOSES
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-- mkTestBoard N
--   Creates an N x N board whose 2-digit values encode their location:
--   the first digit is the row number (starting at 1) and the second is
--   the column number (starting at 1).  For example,
--     mkTestBoard 3
--   creates the following board:
--     [[11,12,13],[21,22,23],[31,32,33]]
mkTestBoard :: Integer -> Board

-- ************************************
-- *           IMPLEMENTATION 
-- ************************************

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-- FUNCTIONS TO CREATE A BOARD
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-- mkRow N
--   Creates an "empty" row of length N (actually a row of 0's).
mkRow n =