## 编程知识 cdmana.com

### 用 JavaScript 实现寻路算法 —— 编程训练

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[x, y]);\n await insert(x + 1, y, [x, y]);\n await insert(x, y + 1, [x, y]);\n\n // 把 4 个 斜边推入队列\n await insert(x - 1, y - 1, [x, y]);\n await insert(x + 1, y - 1, [x, y]);\n await insert(x - 1, y + 1, [x, y]);\n await insert(x + 1, y + 1, [x, y]);\n }\n\n return null;\n}","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"注意：这里我们把原来的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"path","attrs":{}}],"attrs":{}},{"type":"text","text":" 函数名改为了 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"findPath","attrs":{}}],"attrs":{}},{"type":"text","text":"，因为在寻找路径的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"while","attrs":{}}],"attrs":{}},{"type":"text","text":" 循环里面我们用了 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"path","attrs":{}}],"attrs":{}},{"type":"text","text":" 做为记录路径的变量。这里还需要注意的就是，我们的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"find","attrs":{}}],"attrs":{}},{"type":"text","text":" 按钮里面的函数调用也需要一并修改哦。","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"html"},"content":[{"type":"text","text":"\n
\n \n \n
","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":" ","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"运行最终效果如下：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/eb/eb81f224a7a560665193edbe218d5829.png","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"link","attrs":{"href":"http://tridiamond.tech/frontend-tutorials/exercises/path-finder/4-map-find-path.html","title":""},"content":[{"type":"text","text":"查看效果","attrs":{}}]},{"type":"text","text":" ｜ ","attrs":{}},{"type":"link","attrs":{"href":"https://github.com/TriDiamond/frontend-tutorials/blob/master/exercises/path-finder/4-map-find-path.html","title":""},"content":[{"type":"text","text":"查看代码","attrs":{}}]},{"type":"text","text":" ｜ ","attrs":{}},{"type":"text","marks":[{"type":"strong","attrs":{}}],"text":"喜欢的同学 star 一下谢谢！","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"heading","attrs":{"align":null,"level":1},"content":[{"type":"text","text":"启发式寻路（A*）","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"到这里我们已经完成了整个广度优先寻路的算法。但是广搜式寻路是不是最好的寻路方案呢？","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"其实并不是的","attrs":{}}],"attrs":{}},{"type":"text","text":"!","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"image","attrs":{"src":"https://static001.geekbang.org/infoq/bc/bc8b68ef9eb75f70203c94c48089c90b.gif","alt":null,"title":null,"style":[{"key":"width","value":"75%"},{"key":"bordertype","value":"none"}],"href":null,"fromPaste":true,"pastePass":true}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"通过各位数学科学家的努力下，他们证明了一件事情。我们是可以有一种方法能够加速寻路的，通过用这个方法我们不需要使用一个非常傻的方式来挨个去找。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这种寻路的方式叫做 “","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"启发式寻路","attrs":{}}],"attrs":{}},{"type":"text","text":"”","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"启发式寻路就是用一个函数去判断这些点扩展的优先级。只要我们判断好了优先级，我们就可以有目的的去验者格子的方向做优先找路。","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"“但是这个找到的路径是不是最佳路径呀？说的那么神奇的。“ 说实话，这个我们普通人的思路就排不上用场了。但是数学家证明了一件事情，只要我们使用启发式函数来估计值，并且这些值能够一定小于当前点到终点的路径的长度，这样就一定能找到最优路径。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这种能找到最优路径的启发式寻路，在计算机里面我们叫它做 “","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"A*","attrs":{}}],"attrs":{}},{"type":"text","text":"”。这里面的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"A","attrs":{}}],"attrs":{}},{"type":"text","text":" 代表着一种不一定能找到最优路径的启发式寻路。所以 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"A*","attrs":{}}],"attrs":{}},{"type":"text","text":" 就是 A 寻路的一个特例，是一种可以找到最佳路径的一种算法。","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"要实现这个启发式寻路，其实我们是不需要改过多我们 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"findPath()","attrs":{}}],"attrs":{}},{"type":"text","text":"函数里面的代码的。我们要改的是我们存储的数据结构，也就是我们的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"queue","attrs":{}}],"attrs":{}},{"type":"text","text":" 队列。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"我们要把 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"queue","attrs":{}}],"attrs":{}},{"type":"text","text":" 的先进先出变成一个","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"优先队列 (Prioritized Queue)","attrs":{}}],"attrs":{}},{"type":"text","text":"。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"所以我们需要构建一个 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"Sorted","attrs":{}}],"attrs":{}},{"type":"text","text":" 类，这个类有几个工作：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"numberedlist","attrs":{"start":"1","normalizeStart":1},"content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":1,"align":null,"origin":null},"content":[{"type":"text","text":"这个类可以存储我们之前 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"queue","attrs":{}}],"attrs":{}},{"type":"text","text":" 队列里面的数据","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":2,"align":null,"origin":null},"content":[{"type":"text","text":"可以支持传入排序函数（也就是和我们 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"array sort","attrs":{}}],"attrs":{}},{"type":"text","text":" 函数一样的功能，可以传入一个排序规则函数，也叫 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"compare","attrs":{}}],"attrs":{}},{"type":"text","text":" 函数）","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":3,"align":null,"origin":null},"content":[{"type":"text","text":"在我们通过这个类获取值的时候给我们数据里面的最小值","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":4,"align":null,"origin":null},"content":[{"type":"text","text":"在我们插入数据的时候不需要排序，只是单纯的保存","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":5,"align":null,"origin":null},"content":[{"type":"text","text":"每次去除数据的时候，可以把输出的数据在类的数据里面删除掉","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":6,"align":null,"origin":null},"content":[{"type":"text","text":"这样我们就可以一直在里面获取数据，知道没有数据为止","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":7,"align":null,"origin":null},"content":[{"type":"text","text":"最后加入一个可以获取当前数据的长度（这个在我们的寻路算法中需要用到）","attrs":{}}]}],"attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"blockquote","content":[{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"这里我们用一个非常 “土鳖” 的数组来实现这个 Sorted 类，但是在计算机当中，我们还有很多其他方式可以实现这一种类。比如说 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"winner tree","attrs":{}}],"attrs":{}},{"type":"text","text":"，","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"堆 (heap)","attrs":{}}],"attrs":{}},{"type":"text","text":"，","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"排序二叉树","attrs":{}}],"attrs":{}},{"type":"text","text":" 等很多的不同思路来实现有序的数据结构。","attrs":{}}]}],"attrs":{}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"好废话少说，我们来看看怎么实现这个数据结构：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"javascript"},"content":[{"type":"text","text":"/** 排序数据类 */\nclass Sorted {\n constructor(data, compare) {\n this.data = data.slice();\n this.compare = compare || ((a, b) => a - b);\n }\n take() {\n // 考虑到 null 也是可以参与比较的，所以这里返回 null 是不合适的\n if (!this.data.length) return;\n // 记录最小的值\n // 默认第一个位置为最小值\n let min = this.data[0];\n // 记录最小值的位置\n let minIndex = 0;\n\n // 开始比较数组里面的所有值，找到更小的值，就记录为 min\n // 同时记录最小值，和最小值的位置\n for (let i = 1; i < this.data.length; i++) {\n if (this.compare(this.data[i], min) < 0) {\n min = this.data[i];\n minIndex = i;\n }\n }\n\n // 现在我们要把最小值拿出去了，所以要在我们当前的数据中移除\n // 这里我们不考虑使用 splice，因为 splice 移除会涉及数组内的元素都要往前挪动\n // 这样 splice 就会有一个 O(N) 的时间复杂度\n // 这里我们用一个小技巧，把数组里面最后一位的值挪动到当前发现最小值的位置\n // 最后使用 pop 把最后一位数据移除\n this.data[minIndex] = this.data[this.data.length - 1];\n this.data.pop();\n // 最后把最小值输出\n return min;\n }\n give(value) {\n this.data.push(value);\n }\n get length() {\n return this.data.length;\n }\n}","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"有了这个 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"Sorted","attrs":{}}],"attrs":{}},{"type":"text","text":" 的数据结构之后，我们就可以用来解决我们的寻路问题，让我们可以找到最佳的路径了。","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"加入这个最佳路径的逻辑，我们需要改到一下几个点：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"numberedlist","attrs":{"start":"1","normalizeStart":1},"content":[{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":1,"align":null,"origin":null},"content":[{"type":"text","text":"首先改写我们的存储数据的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"queue","attrs":{}}],"attrs":{}},{"type":"text","text":"，使用我们 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"Sorted","attrs":{}}],"attrs":{}},{"type":"text","text":" 的排序数据结构","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":2,"align":null,"origin":null},"content":[{"type":"text","text":"编写一个 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"distance()","attrs":{}}],"attrs":{}},{"type":"text","text":" 函数来运算任何一个格子与终点格子的直线距离","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":3,"align":null,"origin":null},"content":[{"type":"text","text":"把所有入队列和出队列的调用改为使用 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"Sorted","attrs":{}}],"attrs":{}},{"type":"text","text":" 类里面的 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"take","attrs":{}}],"attrs":{}},{"type":"text","text":" 取值 和 ","attrs":{}},{"type":"codeinline","content":[{"type":"text","text":"give","attrs":{}}],"attrs":{}},{"type":"text","text":" 插入值函数","attrs":{}}]}],"attrs":{}},{"type":"listitem","content":[{"type":"paragraph","attrs":{"indent":0,"number":4,"align":null,"origin":null},"content":[{"type":"text","text":"其他地方基本就没有什么改变了","attrs":{}}]}],"attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null},"content":[{"type":"text","text":"接下来我们来看看代码是怎么实现的：","attrs":{}}]},{"type":"paragraph","attrs":{"indent":0,"number":0,"align":null,"origin":null}},{"type":"codeblock","attrs":{"lang":"javascript"},"content":[{"type":"text","text":"// 上一部分的代码，这里就忽略了...\n// 只要在上部分的代码后面改造这部分即可\n\n/**\n * 寻路方法 (异步)\n * @param {Array} map 地图数据\n * @param {Array} start 起点 例如：[0, 0]\n * @param {Array} end 终点 例如：[50, 50]\n * @return Boolean\n */\nasync function findPath(map, start, end) {\n // 创建一个记录表格\n let table = Object.create(map);\n let queue = new Sorted([start], (a, b) => distance(a) - distance(b));\n\n async function insert(x, y, pre) {\n // 到达底盘边缘，直接停止\n if (x < 0 || x >= 100 || y < 0 || y >= 100) return;\n // 遇到地图的墙，也停止\n if (table[y * 100 + x]) return;\n // 加入 30 毫秒的停顿，让我们可以看到 UI 上面的变化\n await sleep(1);\n // 给搜索到的路径的格子加上背景颜色\n container.children[y * 100 + x].style.backgroundColor = 'DARKSLATEBLUE';\n // 标记走过的格子的值，标记为上一个格子的 x，y 位置\n table[y * 100 + x] = pre;\n // 把可走的路推入队列\n queue.give([x, y]);\n }\n\n /**\n * 获取格与格之前的距离\n * @param {Array} point 当前格子的坐标：[x,y]\n */\n function distance(point) {\n // 使用三角形 x^2 + y^2 = z^2 的方式来计算距离\n return (point[0] - end[0]) ** 2 + (point[1] - end[1]) ** 2;\n }\n\n // 循环格子 4 边的格子\n while (queue.length) {\n let [x, y] = queue.take();\n // console.log(x, y);\n\n // 遇到了终点位置就可以返回了\n if (x === end[0] && y === end[1]) {\n let path = [];\n\n // 往回走，直到走到起点\n // 这样就能画出最佳路径了\n while (x != start[0] || y != start[1]) {\n path.push(map[y * 100 + x]);\n [x, y] = table[y * 100 + x];\n container.children[y * 100 + x].style.backgroundColor = 'fuchsia';\n }\n\n return path;\n }\n\n // 把上下左右推入队列\n await insert(x - 1, y, [x, y]);\n await insert(x, y - 1, [x, y]);\n await insert(x + 1, y, [x, y]);\n await insert(x, y + 1, [x, y]);\n\n // 把 4 个 斜边推入队列\n await insert(x - 1, y - 1, [x, y]);\n await insert(x + 1, y - 1, [x, y]);\n await insert(x - 1, y + 1, [x, y]);\n await insert(x + 1, y + 1, [x, y]);\n }\n\n return 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