Dijkstra算法求最短路径(java)
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Dijkstra算法求最短路径(java)
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任務(wù)描述：在一個(gè)無向圖中，獲取起始節(jié)點(diǎn)到所有其他節(jié)點(diǎn)的最短路徑描述
Dijkstra(迪杰斯特拉)算法是典型的最短路徑路由算法，用于計(jì)算一個(gè)節(jié)點(diǎn)到其他所有節(jié)點(diǎn)的最短路徑。主要特點(diǎn)是以起始點(diǎn)為中心向外層層擴(kuò)展，直到擴(kuò)展到終點(diǎn)為止。
Dijkstra一般的表述通常有兩種方式，一種用永久和臨時(shí)標(biāo)號方式，一種是用OPEN, CLOSE表方式
用OPEN,CLOSE表的方式，其采用的是貪心法的算法策略，大概過程如下：
1.聲明兩個(gè)集合，open和close，open用于存儲未遍歷的節(jié)點(diǎn)，close用來存儲已遍歷的節(jié)點(diǎn)
2.初始階段，將初始節(jié)點(diǎn)放入close，其他所有節(jié)點(diǎn)放入open
3.以初始節(jié)點(diǎn)為中心向外一層層遍歷，獲取離指定節(jié)點(diǎn)最近的子節(jié)點(diǎn)放入close并從新計(jì)算路徑，直至close包含所有子節(jié)點(diǎn)
代碼實(shí)例如下：
Node對象用于封裝節(jié)點(diǎn)信息，包括名字和子節(jié)點(diǎn)
[java]?view plaincopy 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用于初始化數(shù)據(jù)源，返回圖的起始節(jié)點(diǎn)
[java]?view plaincopy 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;?? ????}?? }??
圖的結(jié)構(gòu)如下圖所示：
Dijkstra對象用于計(jì)算起始節(jié)點(diǎn)到所有其他節(jié)點(diǎn)的最短路徑
[java]?view plaincopy public?class?Dijkstra?{?? ????Set<Node>?open=new?HashSet<Node>();?? ????Set<Node>?close=new?HashSet<Node>();?? ????Map<String,Integer>?path=new?HashMap<String,Integer>();//封裝路徑距離?? ????Map<String,String>?pathInfo=new?HashMap<String,String>();//封裝路徑信息?? ????public?Node?init(){?? ????????//初始路徑,因沒有A->E這條路徑,所以path(E)設(shè)置為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");?? ????????//將初始節(jié)點(diǎn)放入close,其他節(jié)點(diǎn)放入open?? ????????Node?start=new?MapBuilder().build(open,close);?? ????????return?start;?? ????}?? ????public?void?computePath(Node?start){?? ????????Node?nearest=getShortestPath(start);//取距離start節(jié)點(diǎn)最近的子節(jié)點(diǎn),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)){//如果子節(jié)點(diǎn)在open中?? ????????????????Integer?newCompute=path.get(nearest.getName())+childs.get(child);?? ????????????????if(path.get(child.getName())>newCompute){//之前設(shè)置的距離大于新計(jì)算出來的距離?? ????????????????????path.put(child.getName(),?newCompute);?? ????????????????????pathInfo.put(child.getName(),?pathInfo.get(nearest.getName())+"->"+child.getName());?? ????????????????}?? ????????????}?? ????????}?? ????????computePath(start);//重復(fù)執(zhí)行自己,確保所有子節(jié)點(diǎn)被遍歷?? ????????computePath(nearest);//向外一層層遞歸,直至所有頂點(diǎn)被遍歷?? ????}?? ????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());?? ????????}?? ????}?? ????/**? ?????*?獲取與node最近的子節(jié)點(diǎn)? ?????*/?? ????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用于測試Dijkstra對象
[java]?view plaincopy public?class?Main?{?? ????public?static?void?main(String[]?args)?{?? ????????Dijkstra?test=new?Dijkstra();?? ????????Node?start=test.init();?? ????????test.computePath(start);?? ????????test.printPathInfo();?? ????}?? }??
打印輸出如下：
D:A->D
E:A->F->E
F:A->F
G:A->C->G
B:A->B
C:A->C
H:A->B->H
Dijkstra(迪杰斯特拉)算法是典型的最短路徑路由算法，用于計(jì)算一個(gè)節(jié)點(diǎn)到其他所有節(jié)點(diǎn)的最短路徑。主要特點(diǎn)是以起始點(diǎn)為中心向外層層擴(kuò)展，直到擴(kuò)展到終點(diǎn)為止。
Dijkstra一般的表述通常有兩種方式，一種用永久和臨時(shí)標(biāo)號方式，一種是用OPEN, CLOSE表方式
用OPEN,CLOSE表的方式，其采用的是貪心法的算法策略，大概過程如下：
1.聲明兩個(gè)集合，open和close，open用于存儲未遍歷的節(jié)點(diǎn)，close用來存儲已遍歷的節(jié)點(diǎn)
2.初始階段，將初始節(jié)點(diǎn)放入close，其他所有節(jié)點(diǎn)放入open
3.以初始節(jié)點(diǎn)為中心向外一層層遍歷，獲取離指定節(jié)點(diǎn)最近的子節(jié)點(diǎn)放入close并從新計(jì)算路徑，直至close包含所有子節(jié)點(diǎn)
代碼實(shí)例如下：
Node對象用于封裝節(jié)點(diǎn)信息，包括名字和子節(jié)點(diǎn)
[java]?view plaincopy
MapBuilder用于初始化數(shù)據(jù)源，返回圖的起始節(jié)點(diǎn)
[java]?view plaincopy
Dijkstra對象用于計(jì)算起始節(jié)點(diǎn)到所有其他節(jié)點(diǎn)的最短路徑
[java]?view plaincopy
Main用于測試Dijkstra對象
[java]?view plaincopy
打印輸出如下：
D:A->D
E:A->F->E
F:A->F
G:A->C->G
B:A->B
C:A->C
H:A->B->H
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