AST

.gitignore

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+*.cabal

Main.hs

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+{-# LANGUAGE OverloadedStrings #-}
+
+module Main where
+
+import Control.Applicative ((<|>),empty)
+import Data.Attoparsec.Text (Parser, parseOnly, decimal, choice, option, sepBy, endOfLine, endOfInput, many1)
+import qualified Data.Maybe as M
+import qualified Data.Text as T
+import qualified Data.Text.IO as T
+
+insuranceNetworkParser :: Parser InsuranceNetworkAST
+insuranceNetworkParser = many1 line
+  where
+    -- <line> ::= <insurer-id> ":" <percent> <optional-exprs>
+    -- <optional-exprs> ::= "" | "if" <exprs>
+    line :: Parser INASTLine
+    line = do
+      id <- insurerId
+      ": "
+      pc <- percent
+      oe <- option [] (" if " *> exprs)
+      endOfLine
+      pure $ INASTLine id pc oe
+    -- <exprs> ::= <expr> | <expr> "and" <exprs>
+    exprs :: Parser [ INASTExpr ]
+    exprs = expr `sepBy` " and "
+    -- <expr> ::= <lesser-than> | <greater-than> | <equals> | <insurer-id>
+    expr :: Parser INASTExpr
+    expr = choice [ INASTExprLt <$> lt
+                  , INASTExprGt <$> gt
+                  , INASTExprEq <$> eq
+                  , INASTExprInsurerId <$> insurerId ]
+    -- <lesser-than> ::= "<" <integer>
+    lt :: Parser INASTLt
+    lt = "<" *> integer
+    -- <greater-than> ::= ">" <integer>
+    gt :: Parser INASTGt
+    gt = ">" *> integer
+    -- <equals> ::= "=" <integer>
+    eq :: Parser INASTEq
+    eq = "=" *> integer
+    -- <insurer-id> ::= "I" <integer>
+    insurerId :: Parser INASTInsurerId
+    insurerId = "I" *> integer
+    -- <percent> ::= <integer> "%"
+    percent :: Parser INASTPercent
+    percent = integer <* "%"
+    -- <integer> ::= <digit> | <non-zero-digit> <integer>
+    -- Overapproximation of the grammar
+    integer :: Parser Int
+    integer = decimal
+
+type InsuranceNetworkAST = [INASTLine]
+
+data INASTLine = INASTLine INASTInsurerId INASTPercent [INASTExpr]
+  deriving (Show)
+
+data INASTExpr = INASTExprLt INASTLt
+               | INASTExprGt INASTGt
+               | INASTExprEq INASTEq
+               | INASTExprInsurerId INASTInsurerId
+  deriving (Show)
+
+type INASTLt = Int
+type INASTGt = Int
+type INASTEq = Int
+type INASTInsurerId = Int
+type INASTPercent = Int
+
+main :: IO ()
+main = do
+  inputNetwork <- T.readFile "./input.network"
+  T.putStrLn "Using the following input network:"
+  T.putStrLn inputNetwork
+  T.putStrLn "Parsed AST:"
+  print (parseOnly insuranceNetworkParser inputNetwork)
+
+

desc.md

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+# Insurance networks
+
+The following grammar:
+
+```
+<lines> ::= <line> | <line> "\n" <lines>
+<line> ::= <insurer-id> ":" <percent> <optional-exprs>
+<optional-exprs> ::= "" | "if" <exprs>
+<exprs> ::= <expr> | <expr> "and" <exprs>
+<expr> ::= <lesser-than> | <greater-than> | <equals> | <insurer-id>
+<lesser-than> ::= "<" <integer>
+<greater-than> ::= ">" <integer>
+<equals> ::= "=" <integer>
+<insurer-id> ::= "I" <integer>
+<percent> ::= <integer> "%"
+<integer> ::= <digit> | <non-zero-digit> <integer>
+<digit> ::= "0" | <non-zero-digit>
+<non-zero-digit> ::= "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
+```
+
+is used to represents insurance networks.
+
+Given a single input of type `Int`, the job of these networks is to provide, if possible, exactly 100% underwriting capital using the fewest insurers possible. Each insurer contributes their percentage only if their respective conditions are met.
+
+Below is a simple example of such a network:
+
+```
+I1: 50%
+I2: 50% if <5
+I3: 40% if I1
+I4: 30% if I2 and <5
+I5: 10% if I3 and I4
+I6: 10% if I3
+```
+
+where:
+- Insurer `I1` contributes 50% unconditionally, for any input
+- `I2` contributes 50% only if the input is `<5`
+- `I3` contributes 40% only if `I1` contributes
+- etc...
+
+Given the above, your task is to write a small command line program that takes 2 parameters:
+- the path to a file that defines a network
+- an integer input to the network
+
+and outputs a list of the fewest contributing insurers (by their integer ids).
+
+Eg. if your program was given the above example network and:
+- input `3` then it would output `[1, 2]` (representing insurers `I1` and `I2`)
+- input `6` then it would output `[1, 3, 6]`
+
+If a network is unable to collect exactly 100% for a given input then your program should output `[]`.
+
+Please create a new private github repository named `artificial-network`, commit all your code there and once finished please invite me, `pwm`, so we can check your solution.
+
+Good luck!

flake.lock

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+{
+  "nodes": {
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1628427351,
+        "narHash": "sha256-WuZUIQ07AvRw+T9wvQ3qFf8MXmKZ+ktZz9drNgWXDbs=",
+        "path": "/nix/store/aqinic6h77nrsrzwdsq2mxihw0kd87ml-source",
+        "rev": "348bc5de8bca09c624f5c4975f538684da4713d2",
+        "type": "path"
+      },
+      "original": {
+        "id": "nixpkgs",
+        "type": "indirect"
+      }
+    },
+    "root": {
+      "inputs": {
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

flake.nix

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+{
+  # inspired by: https://serokell.io/blog/practical-nix-flakes#packaging-existing-applications
+  description = "A Hello World in Haskell with a dependency and a devShell";
+  inputs.nixpkgs.url = "nixpkgs";
+  outputs = { self, nixpkgs }:
+    let
+      supportedSystems = [ "x86_64-linux" "x86_64-darwin" ];
+      forAllSystems = f: nixpkgs.lib.genAttrs supportedSystems (system: f system);
+      nixpkgsFor = forAllSystems (system: import nixpkgs {
+        inherit system;
+        overlays = [ self.overlay ];
+      });
+    in
+    {
+      overlay = (final: prev: {
+        interview-in = final.haskellPackages.callCabal2nix "in23" ./. {};
+      });
+      packages = forAllSystems (system: {
+         interview-in = nixpkgsFor.${system}.interview-in;
+      });
+      defaultPackage = forAllSystems (system: self.packages.${system}.interview-in);
+      checks = self.packages;
+      devShell = forAllSystems (system: let haskellPackages = nixpkgsFor.${system}.haskellPackages;
+        in haskellPackages.shellFor {
+          packages = p: [self.packages.${system}.interview-in];
+          withHoogle = true;
+          buildInputs = with haskellPackages; [
+            haskell-language-server
+            ghcid
+            cabal-install
+          ];
+        # Change the prompt to show that you are in a devShell
+        shellHook = "export PS1='\\e[1;34mdev > \\e[0m'";
+        });
+  };
+}

input.network

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+I1: 50%
+I2: 50% if <5
+I3: 40% if I1
+I4: 30% if I2 and <5
+I5: 10% if I3 and I4
+I6: 10% if I3

package.yaml

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+dependencies:
+  - base == 4.*
+  - attoparsec
+  - text
+executables:
+  interview-in:
+    main: Main.hs