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module Darts
open System
let score (x: double) (y: double): int =
match Math.Sqrt(x * x + y * y) with
| distance when distance <= 1.0 -> 10
| distance when distance <= 5.0 -> 5
| distance when distance <= 10.0 -> 1
| _ -> 0
The first step is to calculate the distance from the center of the board, which we can with the cartesian coordinates distance formula:
Math.Sqrt(x * x + y * y)
Note
We open the System namespace to allows us to use Math.Sqrt instead of System.Math.Sqrt.
Before we'll look at the score calculation, let's re-iterate the games rules:
| Lands | Distance | Points |
|---|---|---|
| Outside | > 10 units | 0 |
| Outer circle | > 5 units and <= 10 units | 1 |
| Middle circle | > 1 unit and <= 5 units | 5 |
| Inner circle | <= 1 unit | 10 |
Directly translating this to code gives us:
match Math.Sqrt(x * x + y * y) with
| distance when distance <= 1.0 -> 10
| distance when distance > 1.0 && distance <= 5.0 -> 5
| distance when distance > 5.0 && <= 10.0 -> 1
| _ -> 0
However, due to the order of evaluation, we know in our second condition, distance > 1.0 must always true as otherwise distance <= 1.0 would have been true.
The same reasoning applies to the distandistance > 5.0 condition.
We can thus shorten our code to:
match Math.Sqrt(x * x + y * y) with
| distance when distance <= 1.0 -> 10
| distance when distance <= 5.0 -> 5
| distance when distance <= 10.0 -> 1
| _ -> 0
28th Aug 2024
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