你那個(gè)文字我看不懂，路由器的路由算法其實(shí)就兩類：1、距離矢量算法（如RIP協(xié)議），2、鏈路狀態(tài)協(xié)議（如OSPF協(xié)議）。路由器不一定按最短路徑轉(zhuǎn)發(fā)（如OSPF協(xié)議），還要看他的路徑開銷等參數(shù)。如果你不考慮其他因素，僅考慮最短路徑，可以用Dijistra算法寫。
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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(hào)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(chǔ)未遍歷的節(jié)點(diǎn)，close用來存儲(chǔ)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(duì)象用于封裝節(jié)點(diǎn)信息，包括名字和子節(jié)點(diǎn)
[java] view plain copy
public class Node {
private String name;
private MapNode,Integer child=new HashMapNode,Integer();
public Node(String name){
this.name=name;
}
public String getName() {
return name;
}
public void setName(String name) {
this.name = name;
}
public MapNode, Integer getChild() {
return child;
}
public void setChild(MapNode, 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)
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public class MapBuilder {
public Node build(SetNode open, SetNode 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(duì)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 plain copy
public class Dijkstra {
SetNode open=new HashSetNode();
SetNode close=new HashSetNode();
MapString,Integer path=new HashMapString,Integer();//封裝路徑距離
MapString,String pathInfo=new HashMapString,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);
MapNode,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(){
SetMap.EntryString, String pathInfos=pathInfo.entrySet();
for(Map.EntryString, 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;
MapNode,Integer childs=node.getChild();
for(Node child:childs.keySet()){
if(open.contains(child)){
int distance=childs.get(child);
if(distanceminDis){
minDis=distance;
res=child;
}
}
}
return res;
}
}
Main用于測(cè)試Dijkstra對(duì)象
[java] view plain copy
public class Main {
public static void main(String[] args) {
Dijkstra test=new Dijkstra();
Node start=test.init();
test.computePath(start);
test.printPathInfo();
}
}
有什么無權(quán)無向圖的最短路徑算法比較好
帶權(quán)圖也分有向和無向兩種，基本的算法可以看看書咯。 帶權(quán)的無向圖的最短路徑又叫最小生成樹，Prim算法和Kruskal算法； 帶權(quán)的有向圖的最短路徑算法有迪杰斯特拉算法和佛洛依德算法；
String[]?s={"January",?"February",?"March",?"April",?"May",?"June",?"July",?"August",?"September",?"October",?"November",?"December"};
System.out.print("請(qǐng)輸入數(shù)字（1-12）：");
BufferedReader?br=new?BufferedReader(new?InputStreamReader(System.in));
String?str=br.readLine();
int?m=Integer.parseInt(str);
if?(m=0||m=13)
{
import java.util.Vector;
public class Link {
private Vector link = new Vector();
// private Link next = null;
public Link() {
}
public boolean addNode(Node setNode){//增加一個(gè)節(jié)點(diǎn)
setNode = checkNode(setNode);
if(setNode != null){
this.link.addElement((Node)setNode);
return true;
}
return false;
}
public void delNode(Node setNode){ //刪除一個(gè)節(jié)點(diǎn)
if(!this.link.isEmpty()){
for(int i=0;i this.link.size(); i++)
{
if(setNode.getPos() == ((Node)this.link.elementAt(i)).getPos()){
this.link.remove(i);
//System.out.println("asdfasdfas:"+this.link.size());
break;
}
}
}
}
public Node checkNode(Node setNode){//判斷節(jié)點(diǎn)是否在鏈表里面并取得兩者的最佳值
if(!this.link.isEmpty() setNode!=null){
for(int i=0;i this.link.size(); i++)
{
if(setNode.getPos() == ((Node)this.link.elementAt(i)).getPos()){
if(setNode.getStep() ((Node)this.link.elementAt(i)).getStep()){
setNode = (Node)this.link.elementAt(i);
this.link.remove(i);
}
else
return null;
break;
}
}
}
return setNode;
}
public boolean isEmpty(){
return this.link.isEmpty();
}
public Node getBestNode(){ //得到最好的節(jié)點(diǎn)
Node tmpNode = null;
if(!this.link.isEmpty()){
tmpNode = (Node)this.link.elementAt(0);
//System.out.println("tmpNodeStep:"+tmpNode.getStep());
//System.out.print("OpenNode(pos,step):");
for(int i=1;i this.link.size(); i++)
{
//System.out.print("("+((Node)this.link.elementAt(i)).getPos()+","+((Node)this.link.elementAt(i)).getStep()+")");
if(tmpNode.getJudgeNum() = ((Node)this.link.elementAt(i)).getJudgeNum()){
tmpNode = (Node)this.link.elementAt(i);
}
}
}
return tmpNode;
}
}
public class FindBestPath {
private char[][] map = null;//地圖
private int maxX,maxY;//最大的地圖邊界大小
Node startNode = null;//入口
Node endNode = null;//出口
private int endX,endY;
/*初始化
*@param setMap 地圖
*@param setX,setY 邊界值
//////////*@param startNode 入口
//////////*param endNode 出口
*@param sX,sY:開始點(diǎn)
*@param eX,eY:結(jié)束點(diǎn)
*/
public FindBestPath(char[][] setMap,int setX,int setY,int sX,int sY,int eX,int eY) {
this.map = setMap;
this.maxY = setX - 1; //x,y互換
this.maxX = setY - 1; //x,y互換
//this.startNode = sNode;
//this.endNode = eNode;
Node sNode = new Node();
Node eNode = new Node();
sNode.setFarther(null);
sNode.setPos(posToNum(sX,sY));
sNode.setStep(0);
eNode.setPos(posToNum(eX,eY));
this.startNode = sNode;
this.endNode = eNode;
this.endX = eX;//numToX(eNode.getPos());
this.endY = eY;//numToY(eNode.getPos());
}
public int posToNum(int x,int y){//從xy坐標(biāo)獲得編號(hào)
return (x+y*(this.maxY+1));
}
public int numToX(int num){//從編號(hào)獲得x坐標(biāo)
return (num%(this.maxY+1));
}
public int numToY(int num){//從編號(hào)獲得y坐標(biāo)
return (int)(num/(this.maxY+1));
}
public boolean checkVal(int x,int y){//判斷是否為障礙
//System.out.println("map["+x+"]["+y+"]="+map[x][y]);
if(this.map[x][y] == 'N')
return false;
else
return true;
}
public int judge(Node nowNode){//一定要比實(shí)際距離小
//System.out.println("nowNodePos:"+nowNode.getPos());
int nowX = numToX(nowNode.getPos());
int nowY = numToY(nowNode.getPos());
int distance = Math.abs((nowX-this.endX))+Math.abs((nowY-this.endY));
// System.out.println("distance:"+distance);
return distance;
}
public Node getLeft(Node nowNode){//取得左節(jié)點(diǎn)
int nowX = numToX(nowNode.getPos());
int nowY = numToY(nowNode.getPos());
Node tmpNode = new Node();
if(nowY 0){//判斷節(jié)點(diǎn)是否到最左
if(checkVal(nowX,nowY-1)){
tmpNode.setFarther(nowNode);
tmpNode.setPos(posToNum(nowX,nowY-1));
tmpNode.setStep(nowNode.getStep()+1);
tmpNode.setJudgeNum(tmpNode.getStep()+judge(tmpNode));
return tmpNode;
}
}
return null;
}
public Node getRight(Node nowNode){//取得右節(jié)點(diǎn)
int nowX = numToX(nowNode.getPos());
int nowY = numToY(nowNode.getPos());
Node tmpNode = new Node();
if(nowY this.maxX){//判斷節(jié)點(diǎn)是否到最左
if(checkVal(nowX,nowY+1)){
tmpNode.setFarther(nowNode);
tmpNode.setPos(posToNum(nowX,nowY+1));
tmpNode.setStep(nowNode.getStep()+1);
tmpNode.setJudgeNum(tmpNode.getStep()+judge(tmpNode));
return tmpNode;
}
}
return null;
}
public Node getTop(Node nowNode){//取得上節(jié)點(diǎn)
int nowX = numToX(nowNode.getPos());
int nowY = numToY(nowNode.getPos());
Node tmpNode = new Node();
if(nowX 0){//判斷節(jié)點(diǎn)是否到最左
if(checkVal(nowX-1,nowY)){
tmpNode.setFarther(nowNode);
tmpNode.setPos(posToNum(nowX-1,nowY));
tmpNode.setStep(nowNode.getStep()+1);
tmpNode.setJudgeNum(tmpNode.getStep()+judge(tmpNode));
return tmpNode;
}
}
return null;
}
public Node getBottom(Node nowNode){//取得下節(jié)點(diǎn)
int nowX = numToX(nowNode.getPos());
int nowY = numToY(nowNode.getPos());
Node tmpNode = new Node();
if(nowX this.maxY){//判斷節(jié)點(diǎn)是否到最左
if(checkVal(nowX+1,nowY)){
tmpNode.setFarther(nowNode);
tmpNode.setPos(posToNum(nowX+1,nowY));
tmpNode.setStep(nowNode.getStep()+1);
tmpNode.setJudgeNum(tmpNode.getStep()+judge(tmpNode));
return tmpNode;
}
}
return null;
}
public Link getBestPath(){//尋找路徑
Link openLink = new Link();//沒有訪問的路徑
Link closeLink = new Link();//訪問過的路徑
Link path = null;//最短路徑
Node bestNode = null;
Node tmpNode = null;
openLink.addNode(this.startNode);
while(!openLink.isEmpty())//openLink is not null
{
bestNode = openLink.getBestNode();//取得最好的節(jié)點(diǎn)
//System.out.println("bestNode:("+numToX(bestNode.getPos())+","+numToY(bestNode.getPos())+")step:"+bestNode.getJudgeNum());
if(bestNode.getPos()==this.endNode.getPos())
{
/*this.endNode.setStep(bestNode.getStep()+1);
this.endNode.setFarther(bestNode);
this.endNode.setJudgeNum(bestNode.getStep()+1);*/
path = makePath(bestNode);
break;
}
else
{
tmpNode = closeLink.checkNode(getLeft(bestNode));
if(tmpNode != null)
//System.out.println("("+numToY(tmpNode.getPos())+","+numToX(tmpNode.getPos())+")");
openLink.addNode(tmpNode);
tmpNode = closeLink.checkNode(getRight(bestNode));
if(tmpNode != null)
// System.out.println("("+numToY(tmpNode.getPos())+","+numToX(tmpNode.getPos())+")");
openLink.addNode(tmpNode);
tmpNode = closeLink.checkNode(getTop(bestNode));
if(tmpNode != null)
// System.out.println("("+numToY(tmpNode.getPos())+","+numToX(tmpNode.getPos())+")");
openLink.addNode(tmpNode);
tmpNode = closeLink.checkNode(getBottom(bestNode));
if(tmpNode != null)
// System.out.println("("+numToY(tmpNode.getPos())+","+numToX(tmpNode.getPos())+")");
openLink.addNode(tmpNode);
openLink.delNode(bestNode);
closeLink.addNode(bestNode);
}
}
return path;
}
public Link makePath(Node lastNode){//制造路徑
Link tmpLink = new Link();
Node tmpNode = new Node();
int x,y;
tmpNode = lastNode;
if(tmpNode != null){
do{
x=numToX(tmpNode.getPos());
y=numToY(tmpNode.getPos());
System.out.println("map["+x+"]["+y+"]="+map[x][y]);
tmpLink.addNode(tmpNode);
tmpNode = tmpNode.getFarther();
}while(tmpNode != null);
}else
{
System.out.println("Couldn't find the path!");
}
return tmpLink;
}
/**
* @param args the command line arguments
*/
public static void main(String[] args) {
char[][] map ={
{'Y', 'N', 'z', 'y', 'x', 'w', 'v', 'N', 'N', 'N'},
{'Y', 'N', '1', 'N', 'N', 'N', 'u', 't', 'N', 'N'},
{'N', '1', '2', '1', '1', '1', 'N', 's', 'N', 'N'},
{'N', 'N', '1', 'N', '9', 'N', 'q', 'r', 'N', 'N'},
{'N', 'N', '1', 'N', 'n', 'o', 'p', 'N', 'N', 'N'},
{'N', '4', '5', '6', 'm', 'N', 'N', 'N', 'N', 'N'},
{'N', '3', 'N', '5', 'l', 'k', 'j', 'N', 'N', 'N'},
{'N', 'N', '3', '4', 'N', 'd', 'i', 'd', 'N', 'N'},
{'N', '1', 'N', 'N', '1', 'N', 'h', 'N', 'N', 'N'},
{'N', '1', 'N', 'N', '1', 'N', 'g', 'N', 'N', 'N'},
{'N', 'a', 'b', 'c', 'd', 'e', 'f', 'N', 'N', 'N'}
};
/*map[x][y]
*如上所示：maxY=10 maxX=11 橫的代表maxY,豎的代表maxX 可以自己替換
*地圖的讀取是
*for(i=1;i行的最大值;i++)
* for(j=1;j列的最大值;j++)
* map[i][j] = 地圖[i][j]
*/
Link bestPath = new Link();
/*startNode.setFarther(null);
startNode.setPos(21);
startNode.setStep(0);
//endNode.setFarther(startNode);
endNode.setPos(79);
//endNode.setStep(0);*/
FindBestPath path = new FindBestPath(map, 11, 10, 10, 1, 0, 2);
//FindBestPath path = new FindBestPath(map, 11, 10, startNode, endNode);
bestPath = path.getBestPath();
//bestPath.printLink();
}
}
public class Node {
private int step;//從入口到該節(jié)點(diǎn)經(jīng)歷的步數(shù)
private int pos;//位置
private Node farther;//上一個(gè)結(jié)點(diǎn)
private int judgeNum;
public Node() {
}
public void setStep(int setStep){
this.step = setStep;
}
public int getStep(){
return this.step;
}
public void setPos(int setPos){
this.pos = setPos;
}
public int getPos(){
return this.pos;
}
public void setFarther(Node setNode){
this.farther = setNode;;
}
public Node getFarther(){
return this.farther;
}
public void setJudgeNum (int setInt){
this.judgeNum = setInt;;
}
public int getJudgeNum(){
return this.judgeNum;
}
}
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