We can represent a maze on a rectangular grid as a list of paths. Each path consists of a pair of coordinates which are the ends of the path, where a coordinate is a pair of non$-$negative integers $($x$,$ y$).$ All paths run either horizontally $($same y$-$value for both ends$)$ or vertically $($same x$-$value for both ends$).$ A path of length $1$ is considered to be both horizontal and vertical. $$The order of the ends of a paths is not important; the path $((0,2),(2,2))$ is equivalent to the path $((2,2),(0,2)).$ Similarly, the order of the paths in the maze is unimportant. $$

Write a function:

renderMaze :: $[(($Int$,$ Int$),($Int$,$ Int$))]->[$String$]$

that renders the maze row$-$by$-$row as a list of strings. Each character in each string represents a coordinate within the maze. If a horizontal path is present at that coordinate, the character should be a hyphen symbol $\text{'}-\text{'}.$ If a vertical path is present at that coordinate, the character should be a bar symbol $\text{'}|\text{'}.$ If that coordinate lies on both a horizontal and vertical path, the character should be a plus symbol $\text{'}+\text{'}.$If a path is not present, the character should be a space.

For example, if we have defined:

maze $=[((0,0),(0,3)),((0,2),(2,2)),((2,1),(4,1)),((4,0),(4,2)),((4,2),(5,2)),((2,1),(2,5)),((1,5),(4,5))]$

then renderMaze maze should return:$["||","|+-+","+-++-","||","|","-+--"].$ Written an way that is easier to read, this is$$

$["||",$

$"|+-+",$

$"+-++-",$

$"||",$

$"|",$

$"-+--"]$

The grid in the rendering should run from $(0,0)$ in the top left corner to $($maxX$,$maxY$)$ in the bottom right, where maxX and maxY are the largest x and y values to appear in any path in the maze.

Hint: you may find it useful to use list comprehensions to calculate all of the $($x$,$y$)$ points that appear in a maze.

For example:

TestResult

renderMaze $[]$

$[]$

renderMaze $[((0,0),(0,0))]-$ Singleton Path

$["+"]$

renderMaze $[((1,1),(1,1))]-$ Singleton Path, maze size $2$x$2$

$["","+"]$

renderMaze $[((0,1),(1,1))]-$ Horizontal Path

$["","--"]$

renderMaze $[((1,1),(0,1))]-$ Horizontal Path, switched endpoints

$["","--"]$

renderMaze $[((1,0),(1,1))]-$ Vertical Path

$["|","|"]$

renderMaze $[((1,1),(1,0))]-$ Vertical Path, switched endpoints

$["|","|"]$

renderMaze $[((0,1),(1,1)),((1,0),(1,1))]-$ Intersecting Paths

$["|","-+"]$

renderMaze $[((0,1),(3,1)),((2,1),(4,1))]-$ Overlapping Paths

$["","-----"]$

renderMaze $[((0,0),(0,1)),((0,2),(3,2))]-$ Non$-$Intersecting Paths

$["|","|","----"]$

renderMaze $[((2,0),(2,3)),((0,1),(4,1)),((1,3),(3,3)),((1,3),(1,5)),((3,3),(3,5))]-$ person$-$like shape

$["|","--+--","|","+++","||","||"]$

renderMaze $[((0,0),(0,1)),((0,1),(1,1)),((1,1),(1,2)),((1,2),(2,2)),((2,2),(2,3)),((2,3),(3,3)),((3,3),(3,5)),((3,4),(4,4)),((2,5),(5,5)),((2,5),(2,6)),((1,6),(2,6)),((1,7),(1,6)),((0,7),(1,7)),((5,5),(5,6)),((5,6),(6,6)),((6,6),(6,7)),((6,7),(7,7))]-$ lambda shape

$["|","++","++","++","+-","++-+","++++","-++-"]$