Clojure——学习迷宫生成

背景

初学clojure，想着看一些算法来熟悉clojure语法及相关算法实现。
找到一个各种语言生成迷宫的网站：http://rosettacode.org/wiki/Maze_generation
在上述网站可以看到clojure的实现版，本文就是以初学者的视角解读改程序。

小试牛刀

先看一些简单的示例，以帮助我们理解迷宫生成程序。

绑定符号x++

(defn f [x]
  (let [x++ (+ x 5)]
    #{[x x++]}))
(println (f 1))
=> #'sinlov.clojure.base-learn/f
#{[1 6]}
=> nil

Tips: 上述程序将x++绑定为x+5，不同于c语言中的自增运算符。

集合过滤

(select odd? (set [1 2 3 4 5]))
=> #{1 3 5}
(select (partial odd?) (set [1 2 3 4 5]))
=> #{1 3 5}

select语法参考文档：http://clojuredocs.org/clojure.set/select
partial解释见下文

vec交叉合并

(interleave [0 1 2] ['a 'b 'c])
=> (0 a 1 b 2 c)
(interleave [0 1 2] ['a 'b 'c] ['b])
=> (0 a b)
(interleave [0 1 2] ['a 'b 'c] (repeat 'z))
=> (0 a z 1 b z 2 c z)

文档：http://clojuredocs.org/clojure.core/interleave

transduce

transducer是clojure里面的一种编程思想，使用transducer可以简化很多语法。
可以参考这篇文章链接，帮助理解
文档：http://clojuredocs.org/clojure.core/transduce

思路

笔者阅读了迷宫生成算法，将思路整理如下

坐标点与符号映射关系

比如迷宫的左上角┌是如何生成的，不同大小的迷宫如何确定？
经过阅读源码发现，一个坐标点的符号与其周围4个临接点相关，如果按照坐标点表示，5个点排序顺序是一致的。

比如，上述坐标点(5,5)，和其4个临界点。可以看到在该坐标系内，一个点与其临界点做成的集合排序一定是下面的顺序：

比如迷宫左上角坐标是(0, 0)，该点五元组应该是

不在迷宫，不在迷宫，(0, 0), (0, 1), (1, 0)

假设不在迷宫或者该位置为空，记为0；如果是墙记为1
那么上述五元组可以换算为11100。

再比如迷宫右上角，五元组为

(n-1, 0), 不在迷宫, (n, 0), (n, 1), 不在迷宫

可换算为10110。

按照如上规则可以生成如下表：

["  " "  " "  " "  " "· " "╵ " "╴ " "┘ "
"  " "  " "  " "  " "╶─" "└─" "──" "┴─"
"  " "  " "  " "  " "╷ " "│ " "┐ " "┤ "
"  " "  " "  " "  " "┌─" "├─" "┬─" "┼─"]

程序代码

(ns maze.core
  (:require [clojure.set :refer [intersection
                                 select]]
            [clojure.string :as str]))

;; 得到周围临界点
(defn neighborhood
  ([] (neighborhood [0 0]))
  ([coord] (neighborhood coord 1))
  ([[y x] r]
   (let [y-- (- y r) y++ (+ y r)
         x-- (- x r) x++ (+ x r)]
     #{[y++ x] [y-- x] [y x--] [y x++]})))

;; 判断位置是否为空
(defn cell-empty? [maze coords]
  (= :empty (get-in maze coords)))

;; 判断位置是否为墙
(defn wall? [maze coords]
  (= :wall (get-in maze coords)))

;; 过滤迷宫中指定类型的点的集合
(defn filter-maze
  ([pred maze coords]
   (select (partial pred maze) (set coords)))
  ([pred maze]
   (filter-maze
     pred
     maze
     (for [y (range (count maze))
           x (range (count (nth maze y)))]
       [y x]))))

;; 创建新迷宫
(defn create-empty-maze [width height]
  (let [width (inc (* 2 width))
        height (inc (* 2 height))]
    (vec (take height
               (interleave
                 (repeat (vec (take width (repeat :wall))))
                 (repeat (vec (take width (cycle [:wall :empty])))))))))

(defn next-step [possible-steps]
  (rand-nth (vec possible-steps)))

;; 核心算法，深度优先递归
(defn create-random-maze [width height]
  (loop [maze (create-empty-maze width height)
         stack []
         nonvisited (filter-maze cell-empty? maze)
         visited #{}
         coords (next-step nonvisited)]
    (if (empty? nonvisited)
      maze
      (let [nonvisited-neighbors (intersection (neighborhood coords 2) nonvisited)]
        (cond
          (seq nonvisited-neighbors)
          (let [next-coords (next-step nonvisited-neighbors)
                wall-coords (map #(+ %1 (/ (- %2 %1) 2)) coords next-coords)]
            (recur (assoc-in maze wall-coords :empty)
                   (conj stack coords)
                   (disj nonvisited next-coords)
                   (conj visited next-coords)
                   next-coords))

          (seq stack)
          (recur maze (pop stack) nonvisited visited (last stack)))))))

;; 迷宫坐标与字符映射
(def cell-code->str
  ["  " "  " "  " "  " "· " "╵ " "╴ " "┘ "
   "  " "  " "  " "  " "╶─" "└─" "──" "┴─"
   "  " "  " "  " "  " "╷ " "│ " "┐ " "┤ "
   "  " "  " "  " "  " "┌─" "├─" "┬─" "┼─"])

;; 获取迷宫坐标的类型
;; 使用5 bit表示一个点对应的字符映射
;; 例如：00111对应┘ 
(defn cell-code [maze coord]
  (transduce
    (comp
      (map (partial wall? maze))
      (keep-indexed (fn [idx el] (when el idx)))
      (map (partial bit-shift-left 1)))
    (completing bit-or)
    0
    (sort (cons coord (neighborhood coord)))))

(defn cell->str [maze coord]
  (get cell-code->str (cell-code maze coord)))

;; 将迷宫坐标转换为字符
(defn maze->str [maze]
  (->> (for [y (range (count maze))]
         (for [x (range (count (nth maze y)))]
           (cell->str maze [y x])))
       (map str/join)
       (str/join \newline)))

;; 生成迷宫
(println (maze->str (create-random-maze 10 10)))

上述程序输出：