任务描述:在一个无向图中,获取起始节点到所有其他节点的最短路径描述
dijkstra(迪杰斯特拉)算法是典型的最短路径路由算法,用于计算一个节点到其他所有节点的最短路径。主要特点是以起始点为中心向外层层扩展,直到扩展到终点为止。
dijkstra一般的表述通常有两种方式,一种用永久和临时标号方式,一种是用open, close表方式
用open,close表的方式,其采用的是贪心法的算法策略,大概过程如下:
1.声明两个集合,open和close,open用于存储未遍历的节点,close用来存储已遍历的节点
2.初始阶段,将初始节点放入close,其他所有节点放入open
3.以初始节点为中心向外一层层遍历,获取离指定节点最近的子节点放入close并从新计算路径,直至close包含所有子节点
代码实例如下:
node对象用于封装节点信息,包括名字和子节点
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public class node { private string name; private map<node,integer> child= new hashmap<node,integer>(); public node(string name){ this .name=name; } public string getname() { return name; } public void setname(string name) { this .name = name; } public map<node, integer> getchild() { return child; } public void setchild(map<node, integer> child) { this .child = child; } } |
mapbuilder用于初始化数据源,返回图的起始节点
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public class mapbuilder { public node build(set<node> open, set<node> close){ node nodea= new node( "a" ); node nodeb= new node( "b" ); node nodec= new node( "c" ); node noded= new node( "d" ); node nodee= new node( "e" ); node nodef= new node( "f" ); node nodeg= new node( "g" ); node nodeh= new node( "h" ); nodea.getchild().put(nodeb, 1 ); nodea.getchild().put(nodec, 1 ); nodea.getchild().put(noded, 4 ); nodea.getchild().put(nodeg, 5 ); nodea.getchild().put(nodef, 2 ); nodeb.getchild().put(nodea, 1 ); nodeb.getchild().put(nodef, 2 ); nodeb.getchild().put(nodeh, 4 ); nodec.getchild().put(nodea, 1 ); nodec.getchild().put(nodeg, 3 ); noded.getchild().put(nodea, 4 ); noded.getchild().put(nodee, 1 ); nodee.getchild().put(noded, 1 ); nodee.getchild().put(nodef, 1 ); nodef.getchild().put(nodee, 1 ); nodef.getchild().put(nodeb, 2 ); nodef.getchild().put(nodea, 2 ); nodeg.getchild().put(nodec, 3 ); nodeg.getchild().put(nodea, 5 ); nodeg.getchild().put(nodeh, 1 ); nodeh.getchild().put(nodeb, 4 ); nodeh.getchild().put(nodeg, 1 ); open.add(nodeb); open.add(nodec); open.add(noded); open.add(nodee); open.add(nodef); open.add(nodeg); open.add(nodeh); close.add(nodea); return nodea; } } |
图的结构如下图所示:
dijkstra对象用于计算起始节点到所有其他节点的最短路径
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public class dijkstra { set<node> open= new hashset<node>(); set<node> close= new hashset<node>(); map<string,integer> path= new hashmap<string,integer>(); //封装路径距离 map<string,string> pathinfo= new hashmap<string,string>(); //封装路径信息 public node init(){ //初始路径,因没有a->e这条路径,所以path(e)设置为integer.max_value path.put( "b" , 1 ); pathinfo.put( "b" , "a->b" ); path.put( "c" , 1 ); pathinfo.put( "c" , "a->c" ); path.put( "d" , 4 ); pathinfo.put( "d" , "a->d" ); path.put( "e" , integer.max_value); pathinfo.put( "e" , "a" ); path.put( "f" , 2 ); pathinfo.put( "f" , "a->f" ); path.put( "g" , 5 ); pathinfo.put( "g" , "a->g" ); path.put( "h" , integer.max_value); pathinfo.put( "h" , "a" ); //将初始节点放入close,其他节点放入open node start= new mapbuilder().build(open,close); return start; } public void computepath(node start){ node nearest=getshortestpath(start); //取距离start节点最近的子节点,放入close if (nearest== null ){ return ; } close.add(nearest); open.remove(nearest); map<node,integer> childs=nearest.getchild(); for (node child:childs.keyset()){ if (open.contains(child)){ //如果子节点在open中 integer newcompute=path.get(nearest.getname())+childs.get(child); if (path.get(child.getname())>newcompute){ //之前设置的距离大于新计算出来的距离 path.put(child.getname(), newcompute); pathinfo.put(child.getname(), pathinfo.get(nearest.getname())+ "->" +child.getname()); } } } computepath(start); //重复执行自己,确保所有子节点被遍历 computepath(nearest); //向外一层层递归,直至所有顶点被遍历 } public void printpathinfo(){ set<map.entry<string, string>> pathinfos=pathinfo.entryset(); for (map.entry<string, string> pathinfo:pathinfos){ system.out.println(pathinfo.getkey()+ ":" +pathinfo.getvalue()); } } /** * 获取与node最近的子节点 */ private node getshortestpath(node node){ node res= null ; int mindis=integer.max_value; map<node,integer> childs=node.getchild(); for (node child:childs.keyset()){ if (open.contains(child)){ int distance=childs.get(child); if (distance<mindis){ mindis=distance; res=child; } } } return res; } } |
main用于测试dijkstra对象
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public class main { public static void main(string[] args) { dijkstra test= new dijkstra(); node start=test.init(); test.computepath(start); test.printpathinfo(); } } |
打印输出如下:
d:a->d
e:a->f->e
f:a->f
g:a->c->g
b:a->b
c:a->c
h:a->b->h
以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持服务器之家。
原文链接:https://blog.csdn.net/javaman_chen/article/details/8254309