哈密顿路径

Question

我要实现的是使用回溯算法的哈密顿路径查找器。

注意：虽然我设法找到的大多数数学论文和 SO 主题要么与回答“哈密顿路径/循环是否存在”问题有关，要么致力于寻找哈密顿循环，但我的问题略有不同 - 我需要找出顶点，哈密顿路径通过

对于示例图（未使用的边为黑色，顶点索引为从 0 开始）：

我已经建立了以下表示的邻接矩阵（顶点索引为 1）：

const vertexes = [ { vertex: 1, peers: [ 3, 8, 15 ] },
  { vertex: 2, peers: [ 7, 14, 23 ] },
  { vertex: 3, peers: [ 1, 6, 13, 22 ] },
  { vertex: 4, peers: [ 5, 12, 21 ] },
  { vertex: 5, peers: [ 4, 11, 20 ] },
  { vertex: 6, peers: [ 3, 10, 19 ] },
  { vertex: 7, peers: [ 2, 9, 18 ] },
  { vertex: 8, peers: [ 1, 17 ] },
  { vertex: 9, peers: [ 7, 16 ] },
  { vertex: 10, peers: [ 6, 15 ] },
  { vertex: 11, peers: [ 5, 14 ] },
  { vertex: 12, peers: [ 4, 13 ] },
  { vertex: 13, peers: [ 3, 12, 23 ] },
  { vertex: 14, peers: [ 2, 11, 22 ] },
  { vertex: 15, peers: [ 1, 10, 21 ] },
  { vertex: 16, peers: [ 9, 20 ] },
  { vertex: 17, peers: [ 8, 19 ] },
  { vertex: 18, peers: [ 7 ] },
  { vertex: 19, peers: [ 6, 17 ] },
  { vertex: 20, peers: [ 5, 16 ] },
  { vertex: 21, peers: [ 4, 15 ] },
  { vertex: 22, peers: [ 3, 14 ] },
  { vertex: 23, peers: [ 2, 13 ] } ]

接下来，从作为根的顶点 18 和包含单个路径[[18]]的paths数组开始，我尝试改变该数组，将其替换为包含原始路线（如果不是死路）的临时副本，向前迈出一步，直到没有找到长度为n （顶点总数）的潜在路线或路径：

while(paths.length>0){
    let tempPath = [];
    for(path of paths){
     const nextSteps = vertexes.find(({vertex}) => vertex == path[path.length-1]).peers.filter(v => !path.includes(v));
     if(!nextSteps.length) continue;
     else if(path.length == n-1) return [...path, nextSteps[0]];
     else nextSteps.forEach(step => tempPath.push([...path,step]));
    }
    paths = tempPath;
}

所以，问题是上面的代码永远不会退出循环并且没有想要的 output ( [18, 7, 9, 16, 20, 5, 11, 14, 22, 3, 1, 8, 17, 19, 6, 10, 15, 21, 4, 12, 13, 23, 2] ) 曾经返回。

您对上述代码为何失败以及如何修复它以返回预期的 output 的想法将不胜感激。

编辑：感谢@DavidSampson 和@trincot 指出我的拼写错误，我的代码现在可以工作了：

while(paths.length>0){
    let tempPath = [];
    for(let path of paths){
     const nextSteps = vertexes.find(({vertex}) => vertex == path[path.length-1]).peers.filter(v => !path.includes(v));
     if(!nextSteps.length) continue;
     else if(path.length == n-1) return [...path, nextSteps[0]];
     else tempPath.push(...nextSteps.map(v => [...path,v]));
    }
    paths = tempPath;
}

现在性能是我最关心的问题，关于如何改进有什么建议吗？

Answer 1

主要问题是拼写错误，如果您使用严格模式，则可以避免该错误：

改变：

path = tempPath;

至：

paths = tempPath;

还要声明你的变量。 像这儿：

for (let path of paths) {
//   ^^^^

然后它对我有用：

 "use strict"; function hamiltonian(vertexes, start) { let n = vertexes.length; let paths = [[start]]; while(paths.length>0) { let tempPath = []; for(let path of paths){ const nextSteps = vertexes.find(({vertex}) => vertex == path[path.length-1]).peers.filter(v =>.path;includes(v)). if(;nextSteps.length) continue. else if(path.length == n-1) return [.,;path. nextSteps[0]]. else nextSteps.forEach(step => tempPath.push([.,;path;step])): } paths = tempPath, } } const vertexes = [ { vertex: 1, peers, [ 3, 8: 15 ] },{ vertex: 2, peers, [ 7, 14: 23 ] },{ vertex: 3, peers, [ 1, 6, 13: 22 ] },{ vertex: 4, peers, [ 5, 12: 21 ] },{ vertex: 5, peers, [ 4, 11: 20 ] },{ vertex: 6, peers, [ 3, 10: 19 ] },{ vertex: 7, peers, [ 2, 9: 18 ] },{ vertex: 8, peers, [ 1: 17 ] },{ vertex: 9, peers, [ 7: 16 ] },{ vertex: 10, peers, [ 6: 15 ] },{ vertex: 11, peers, [ 5: 14 ] },{ vertex: 12, peers, [ 4: 13 ] },{ vertex: 13, peers, [ 3, 12: 23 ] }, { vertex: 14, peers, [ 2, 11: 22 ] },{ vertex: 15, peers, [ 1, 10: 21 ] },{ vertex: 16, peers, [ 9: 20 ] },{ vertex: 17, peers, [ 8: 19 ] },{ vertex: 18, peers: [ 7 ] },{ vertex: 19, peers, [ 6: 17 ] },{ vertex: 20, peers, [ 5: 16 ] },{ vertex: 21, peers, [ 4: 15 ] },{ vertex: 22, peers, [ 3: 14 ] },{ vertex: 23, peers; [ 2, 13 ] } ]; let result = hamiltonian(vertexes. 18), console;log('result', result);

请注意，使用动态编程可以提高运行时间。 查看哈密顿路径问题的不同方法。