Haskell -- Generate Coordinates From Ends of the Path-CodePudding

I have an input of [ ( (Int,Int) , (Int,Int) ) ] which is the coordinate of the ends of the path. All paths run either horizontally (same y-value for both ends) or vertically (same x-value for both ends). So I want to write a function that generates all the coordinates of the path from the input.

For example, the input pair of ends is [((0, 0), (0, 3)), ((0, 2), (2, 2))](this is two paths), the output of the function I need is [[(0, 0), (0, 1), (0, 2), (0, 3)], [(0, 2), (1, 2), (2, 2)]]

getPaths :: [ ( (Integer,Integer) , (Integer,Integer) ) ] -> [[(Integer,Integer)]]
getPaths [((xa, ya), (xb, yb))]   
    | xa == xb : [(xa, yb   1) | yb < ya]  
    | xa == xb : [(xa, ya   1) | ya < yb]  
    | ya == yb : [(xa   1, ya) | xa < xb]  
    | ya == yb : [(xb   1, ya) | xb < xa]

I'm not sure if its right, could anyone have a look at it?

CodePudding user response：

I think it is better to first make a function that works with a single pair of coordinates:

path :: ((Int, Int), (Int, Int)) -> [(Int, Int)]
path = …

then getPaths is just a mapping of this:

getPaths :: [((Int, Int), (Int, Int))] -> [[(Int, Int)]]
getPaths = map path

as for the path, you can make use of ranges, indeed [x₁ .. x₂] will produce all (integral) values between x₁ and x₂ (both inclusive).

The function thus can be constructed with list comprehension with:

path :: ((Int, Int), (Int, Int)) -> [(Int, Int)]
path ((x₁, y₁), (x₂, y₂)) = [ … | … <- …, … <- … ]

where you still need to fill in the … parts.