Solving sudokus using core.logic

(ns sudoku

  (:refer-clojure :exclude [==])

  (:use clojure.core.logic)

  (:require [clojure.core.logic.fd :as fd]))

(defn get-square [rows x y]

  (for [x (range x (+ x 3))

        y (range y (+ y 3))]

    (get-in rows [x y])))

(defn bind [var hint]

  (if-not (zero? hint)

    (== var hint)

    succeed))

(defn bind-all [vars hints]

  (and* (map bind vars hints)))

(defn sudokufd [hints]

  (let [vars (repeatedly 81 lvar)

        rows (->> vars (partition 9) (map vec) (into []))

        cols (apply map vector rows)

        sqs  (for [x (range 0 9 3)

                   y (range 0 9 3)]

               (get-square rows x y))]

    (run 1 [q]

      (== q vars)

      (everyg #(fd/in % (fd/domain 1 2 3 4 5 6 7 8 9)) vars)

      (bind-all vars hints)

      (everyg fd/distinct rows)

      (everyg fd/distinct cols)

      (everyg fd/distinct sqs))))

(def hints

  [2 0 7 0 1 0 5 0 8

   0 0 0 6 7 8 0 0 0

   8 0 0 0 0 0 0 0 6

   0 7 0 9 0 6 0 5 0

   4 9 0 0 0 0 0 1 3

   0 3 0 4 0 1 0 2 0

   5 0 0 0 0 0 0 0 1

   0 0 0 2 9 4 0 0 0

   3 0 6 0 8 0 4 0 9])

;; Print the solution

(->> (sudokufd hints)

     (first) 

     (partition-all 9)

     (clojure.pprint/pprint))