Day 9 (#10)

Went with Lagrange interpolation instead because that seemed easier.

Co-authored-by: Smaug123 <patrick+github@patrickstevens.co.uk>
Reviewed-on: #10

AdventOfCode2023.FSharp/AdventOfCode2023.FSharp.Lib/Day9.fs

@@ -0,0 +1,55 @@
+namespace AdventOfCode2023
+
+open System
+
+[<RequireQualifiedAccess>]
+module Day9 =
+
+    let extrapolate (isStart : bool) (arr : ResizeArray<int64>) =
+        let mutable answer = 0L
+        let pos = if isStart then -1L else int64 arr.Count
+
+        for i = 0 to arr.Count - 1 do
+            let mutable product = Rational.ofInt arr.[i]
+
+            for j = 0 to arr.Count - 1 do
+                if j <> i then
+                    product <- product * Rational.make (pos - int64 j) (int64 i - int64 j)
+
+            answer <- answer + Rational.assertIntegral product
+
+        answer
+
+    let part1 (s : string) =
+        use s = StringSplitEnumerator.make '\n' s
+        let mutable answer = 0L
+        let arr = ResizeArray ()
+
+        for line in s do
+            arr.Clear ()
+            use line = StringSplitEnumerator.make' ' ' line
+
+            for number in line do
+                let number = Int64.Parse number
+                arr.Add number
+
+            answer <- answer + extrapolate false arr
+
+        answer
+
+    let part2 (s : string) =
+        use s = StringSplitEnumerator.make '\n' s
+        let mutable answer = 0L
+        let arr = ResizeArray ()
+
+        for line in s do
+            arr.Clear ()
+            use line = StringSplitEnumerator.make' ' ' line
+
+            for number in line do
+                let number = Int64.Parse number
+                arr.Add number
+
+            answer <- answer + extrapolate true arr
+
+        answer