FP Homework 2

Basic notes

In all exercises you are required to write something to standard output. You can use the same strategy as in Laboratory 7.

Lets define a type for the result:

type Result = [String]

Now, if you want to print this result nicely on the screen, you can use:

pp :: Result -> IO ()
pp x = putStr (concat (map (++"\n") x))

1 - Painting

Lets define a new data types representing a circle and a rectangle.

data Point = Point Int Int
data Shape = Circle Point Int
           | Rectangle {topLeft:: Point, bottomRight::Point}

Using these types write a function view that creates a view of defined shapes. The first parameter is a tuple (columns, rows) defining the size of the resulting view. Left top corner has a coordinate (0,0). Second argument is a list of shapes (either circles or rectangles).

view :: (Int,Int) -> [Shape] -> Result

The result may differ based on rounding. In following example '.' was used for the free spot, '#' for the filled spot.

Prelude>pp(view (40,15) [Circle (Point 8 4) 5, Box {topLeft = (Point 15 5), bottomRight = (Point 35 12) }, Circle (Point 30 12) 8] )
....###...###...........................
....#.......#...........................
...##.......##..........................
...#.........#..........................
...#.........#.............#######......
...#.........#.#####################....
...##.......##.#........##.........##...
....#.......#..#.......##..........###..
....###...###..#.......#...........#.#..
......#####....#......##...........#.##.
...............#......#............#..#.
...............#......#............#..#.
...............#####################..#.
......................#...............#.
......................#...............#.

2 - Drawing

Lets define a new data types representing a point and a line.

data Point = Point Int Int
data Line = Line Point Point

Using these types write a function drawLines that creates a view of defined lines. The first parameter is a tuple (columns, rows) defining the size of the resulting view. Left top corner has a coordinate (0,0). Second argument is a list of lines.

drawLines :: (Int,Int) -> [Line] -> Result

The result may differ based on rounding. In following example '.' was used for the free spot, '#' for the filled spot.

Prelude>pp(drawLines (31,15) [Line (Point x y) (Point 15 7)|(x,y)<-concat [[(x,y)|y<-[0,7,14]]|x<-[0,15,30]]])
##.............#.............##
..##...........#...........##..
....##.........#.........##....
.....###.......#.......###.....
........##.....#.....##........
..........###..#..###..........
.............#####.............
###############################
.............#####.............
..........###..#..###..........
........##.....#.....##........
.....###.......#.......###.....
....##.........#.........##....
..##...........#...........##..
##.............#.............##

3 - Filling

Lets define a picture that is composed from '.' which is used for a free spot and '#' is used for the filled spot.

sampleInput = 
   ["....................",
    "....................",
    "....#####...........",
    "...##...##..........",
    "..##.....##.........",
    "..#.......#.........",
    "..#...############..",
    "..#...#...#......#..",
    "..##..#..##......#..",
    "...##.#.##.......#..",
    "....#####........#..",
    "......#..........#..",
    "......############..",
    "....................",
    "...................."]

Write a function fill that takes a defined picture and a starting position and it fills the continuous area of free cells starting from the defined starting position.

fill :: Result -> (Int,Int) -> Result

Prelude> pp(fill sampleInput (0,0))
********************
********************
****#####***********
***##...##**********
**##.....##*********
**#.......#*********
**#...############**
**#...#...#......#**
**##..#..##......#**
***##.#.##.......#**
****#####........#**
******#..........#**
******############**
********************
********************