-- CIS 252, Homework 2
-- VERSION 2, Wed Jan 30
--   Name:  FILL-IN
--   Email: FILL-IN

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 1
-----------------------------------------------------------------------

-- CONTRACT
distance :: (Float,Float) -> (Float,Float) -> Float

-- PURPOSE
-- distance (x1,y1) (x2,y2)
--   returns the Euclidian distance between points (x1,y1) and (x2,y2)

-- EXAMPLES
--   distance (0,0) (1,0)  -- should be 1
--   distance (0,1) (1,1)  -- should be about 1.414214
--   distance (-1,-1) (1,2)  -- should be about 3.605551
--   **ADD MORE**

-- DEFINITION
distance (x1,y1) (x2,y2) = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans1a = distance (0,0) (1,0)    -- should be 1
ans1b = distance (0,1) (1,1)    -- should be about 1.414214
ans1c = distance (-1,-1) (1,2)  -- should be about 3.605551
--   **ADD MORE**

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 2
-----------------------------------------------------------------------

-- CONTRACT
tcDistance :: (Float,Float) -> (Float,Float) -> Float
-- PURPOSE
-- tcDistance (x1,y1) (x2,y2)
--   returns the taxi-cab distance between points (x1,y1) and (x2,y2)

-- EXAMPLES
--   distance (0,0) (1,0)  -- should be 1
--   distance (0,1) (1,1)  -- should be 2
--   distance (-1,-1) (1,2)  -- should be about 3.605551
--   **ADD MORE**

-- DEFINITION
tcDistance  (x1,y1) (x2,y2) = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans2a = tcDistance (0,1) (1,1)    -- should be 1
ans2b = tcDistance (0,1) (1,1)    -- should be 2
ans2c = tcDistance (-1,-1) (1,2)  -- should be 5
--   **ADD MORE**

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 3
-----------------------------------------------------------------------

-- CONTRACT
insideCircle :: (Float,Float) -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- insideCircle (a,b) (x,y) r 
--   tests whether the point (a,b) is inside the circle having origin 
--   (x,y) and radius r. 

-- EXAMPLES
--   insideCircle (0,0) (1,1) 1 -- should be False
--   insideCircle (0,0) (1,1) 2 -- should be True
--   ** ADD MORE **

-- DEFINITION
insideCircle (a,b) (x,y) r = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans3a = insideCircle (0,0) (1,1) 1 -- should be False
ans3b = insideCircle (0,0) (1,1) 2 -- should be True
--   ** ADD MORE **

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 4
-----------------------------------------------------------------------

-- CONTRACT
insideDiamond :: (Float,Float) -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- insideCircle (a,b) (x,y) r 
--   tests whether the point (a,b) is inside the diamond having origin 
--   (x,y) and radius r. 

-- EXAMPLES
--   insideDiamond (0,0) (1,1) 1 -- should be True
--   insideDiamond (0,0) (1,1) 2 -- should be True
--   ** ADD MORE **

-- DEFINITION
insideDiamond (a,b) (x,y) r = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans4a = insideDiamond (0,0) (1,1) 1 -- should be False
ans4b = insideDiamond (0,0) (1,1) 2 -- should be True

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 5
-----------------------------------------------------------------------

-- CONTRACT
nestedCircle :: (Float,Float) -> Float -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- nestedCircle (x1,y1) r1 (x2,y2) r2 
--   tests whether the circle having origin (x1,y1) and radius r1 is 
--   completely inside the circle having origin (x2,y2) and radius r2. 

-- EXAMPLES
--   nestedCircle (3,4) 1 (0,0) 5 -- should return False
--   nestedCircle (2,2) 1 (0,0) 5 -- should return True
--   ****ADD MORE****

-- DEFINITION
nestedCircle (x1,y1) r1 (x2,y2) r2 = error "Change me!" -- << CHANGE THIS <<

-- TESTS
ans5a = nestedCircle (3,4) 1 (0,0) 5 -- should return False
ans5b = nestedCircle (2,2) 1 (0,0) 5 -- should return True
--   ****ADD MORE****

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 6
-----------------------------------------------------------------------

-- CONTRACT
nestedDiamond :: (Float,Float) -> Float -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- nestedDiamond (x1,y1) r1 (x2,y2) r2 
--   tests whether the diamond having origin (x1,y1) and radius r1 is 
--   completely inside the diamond having origin (x2,y2) and radius r2. 

-- EXAMPLES
--   nestedDiamond (3,4) 1 (0,0) 5 -- should return False
--   nestedDiamond (0,0) 1 (0,0) 5 -- should return True
--   ****ADD MORE****

-- DEFINITION
nestedDiamond (x1,y1) r1 (x2,y2) r2 = error "Change me!" -- << CHANGE THIS <<

-- TESTS
ans6a = nestedDiamond (3,4) 1 (0,0) 5 -- should return False
ans6b = nestedDiamond (0,0) 1 (0,0) 5 -- should return True
--   ****ADD MORE****

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 7
-----------------------------------------------------------------------

-- CONTRACT
circlesTouch :: (Float,Float) -> Float -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- circlesTouch (x1,y1) r1 (x2,y2) r2
--   determines whether the circle having origin (x1,y1) and radius r1
--        is touching the circle having origin (x2,y2) and radius r2

-- EXAMPLES
--   (circlesTouch (3,4) 1 (0,0) 5) should return True
--   (circlesTouch (3,4) 1 (0,0) 2) should return False
--   ****ADD MORE****

-- DEFINITION
circlesTouch (x1,y1) r1 (x2,y2) r2 = error "Change me!" -- << CHANGE THIS <<

-- TESTS
ans7a = circlesTouch (3,4) 1 (0,0) 5 -- should be True
ans7b = circlesTouch (3,4) 1 (0,0) 2 -- should be False
--   ****ADD MORE****

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 8
-----------------------------------------------------------------------

-- CONTRACT
diamondsTouch :: (Float,Float) -> Float -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- diamondsTouch (x1,y1) r1 (x2,y2) r2
--   determines whether the diamond having origin (x1,y1) and radius
--   r1 is touching the diamond having origin (x2,y2) and radius r2

-- EXAMPLES
--   (diamondsTouch (3,4) 1 (0,0) 5) should return False
--   (diamondsTouch (3,4) 1 (1,1) 5) should return True
--   ****ADD MORE****

-- DEFINITION
diamondsTouch (x1,y1) r1 (x2,y2) r2 = error "Change me!" -- << CHANGE THIS <<

-- TESTS
ans8a = diamondsTouch (3,4) 1 (0,0) 5 -- should be False
ans8b = diamondsTouch (3,4) 1 (1,1) 5 -- should be True   
--   ****ADD MORE****

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 9
-----------------------------------------------------------------------

-- CONTRACT
diamondCoord :: (Float,Float) -> Float -> Int -> (Float,Float)

-- PURPOSE
-- diamondCoord (x,y) r n 
--   returns the coordinates of the n-th base of the diamond with
--   origin (x,y) and radius r.  (1 == 1st base, 2 = 2nd base, 
--   3 == 3rd base, 4 == home base).

-- EXAMPLES
--   diamondCoord (0,0) 1 0 -- should return (0,-1)
--   diamondCoord (0,0) 1 1 -- should return (1,0)
--   diamondCoord (0,0) 1 2 -- should return (0,1)
--   diamondCoord (0,0) 1 3 -- should return (-1,0)
--   ****ADD MORE****

-- DEFINITION
diamondCoord (x,y) r n = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans9a = diamondCoord (0,0) 1 0 -- should return (0,-1)
ans9b = diamondCoord (0,0) 1 1 -- should return (1,0)
ans9c = diamondCoord (0,0) 1 2 -- should return (0,1)
ans9d = diamondCoord (0,0) 1 3 -- should return (-1,0)
--   ****ADD MORE****


-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- Problem 10
-----------------------------------------------------------------------

-- CONTRACT
insideDC :: (Float,Float) -> Float -> (Float,Float) -> Float -> Bool

-- PURPOSE
-- insideDC (x1,y1) r1 (x2,y2) r2 
--   determines whether the diamond having origin (x1,y1) and radius
--   r1 is completely inside the circle having origin (x2,y2) and
--   radius r2.

-- EXAMPLES
--   insideDC (0,0) 1 (1,0) 4 -- should return True
--   insideDC (0,0) 1 (1,0) 2 -- should return True
--   ****ADD MORE****

-- DEFINITION
insideDC (x1,y1) r1 (x2,y2) r2 = error "Change me!" -- <<<<< CHANGE THIS <<<<<

-- TESTS
ans10a = insideDC (0,0) 1 (1,0) 4 -- should return True
ans10b = insideDC (0,0) 1 (1,0) 2 -- should return True
--   ****ADD MORE****

-----------------------------------------------------------------------
-----------------------------------------------------------------------
-- CUT THE FOLLOWING OUT IN THE SUBMITTED HOMEWORK.
--
--   sqrt is a function that computes the square root of a number
--   abs  is a function that computes the absolute value of a number
--   x^2  is the square of x
-- Here are some sample uses of the above.

-- anyRoots a b c
--   tests if a*x^2+b*x+c has any real roots

anyRoots :: Float -> Float -> Float -> Bool
anyRoots a b c = (b^2-4*a*c >=0)

-- roots a b c
--   returns the real roots of a*x^2+b*x+c, if it has any,
--   and causes an error a*x^2+b*x+c has no real roots

roots :: Float -> Float -> Float -> (Float,Float)
roots a b c 
    | anyRoots a b c = ( (-b-sqrt(b^2-4*a*c))/(2*a), 
                         (-b+sqrt(b^2-4*a*c))/(2*a) )
    | otherwise      = error "no real roots"

-- difference a b
--   returns how far apart the values a and b are.
-- E.g.   (differnce 3 5) is 2
--        (differnce 5 3) is also 2.
difference :: Float -> Float -> Float
difference a b = abs(a - b)