经典图算法Java代码实践：BFS,DFS以及几种最短路径算法
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public class City
{
String name;
int id;
static int idCounter = 0;
public City(String name)
{
this.name=name;
id = idCounter++;
}
}
import java.util.ArrayList;
public class Graph {
public static void main(String[] args)
{
// TODO Auto-generated method stub
Map M = new Map(12);
City a = new City("a");
City b = new City("b");
City c = new City("c");
City d = new City("d");
City e = new City("e");
City f = new City("f");
City g = new City("g");
City h = new City("h");
City i = new City("i");
City j = new City("j");
City k = new City("k");
City l = new City("l");
M.createEdge(a,b,3);
M.createEdge(a,c,5);
M.createEdge(a,d,4);
M.createEdge(b,f,6);
M.createEdge(c,d,2);
M.createEdge(c,g,4);
M.createEdge(d,e,1);
M.createEdge(d,h,5);
M.createEdge(e,f,2);
M.createEdge(e,i,4);
M.createEdge(f,j,5);
M.createEdge(g,h,3);
M.createEdge(g,k,6);
M.createEdge(h,i,6);
M.createEdge(h,k,7);
M.createEdge(i,j,3);
M.createEdge(i,l,5);
M.createEdge(j,l,9);
M.createEdge(k,l,8);
System.out.println("the graph is:\n");
System.out.println(M);
System.out.println();
System.out.println("findPathByDFS:a to k");
M.findPathByDFS(a,k);
System.out.println();
System.out.println("findPathByBFS:a to k");
M.findPathByBFS(a,k);
System.out.println();
System.out.println("bellmanFord from a:");
M.bellmanFord(a);
System.out.println();
System.out.println("dijkstra from a:");
M.dijkstra(a);
System.out.println();
System.out.println("bellmanFord,print example from a:");
M.floydWarshall();
M.printFloydWarshallForOneCity(a);
}
}
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
public class Map
{
double[][] A;
public Map(int n)
{
A = new double[n][n];
for(int i = 0;i < A.length;i++)
{
for(int j = 0;j < A.length;j++)
{
if(i == j) A[i][j] = 0;
else A[i][j] = -1;
}
}
}
ArrayList<City> cities = new ArrayList<City>();
private double[] D;
private void relax(int u,int v)
{
if(D[v]>D[u]+A[v][u])
D[v]=D[u]+A[v][u];
}
private double[][] DD = null;
public void floydWarshall()
{
DD = new double[A.length][A.length];
int i,j,k;
for(i = 0;i < A.length;i++)
{
for(j = 0;j < A.length;j++)
{
if(A[i][j]>0)
DD[i][j] = A[i][j];
else if(i == j) DD[i][j] = 0;
else DD[i][j] = 99999999;
}
}
for(k = 0;k < A.length;k++)
for(i = 0;i < A.length;i++)
for(j = 0;j < A.length;j++)
{
if(DD[i][j] > DD[i][k] + DD[k][j])
{
DD[i][j] = DD[i][k] + DD[k][j];
}
}
}
public void printFloydWarshallForOneCity(City city)
{
System.out.println("floydWarshall:");
if(DD == null)
{
floydWarshall();
}
for(int i=0;i<A.length;i++)
{
System.out.printf("from %s to %s shortest path is:%f\n",city.name,cities.get(i).name,DD[city.id][i]);
}
}
public void dijkstra(City city)
{
dijkstra(city.id);
System.out.println("dijkstra:");
for(int i=0;i<A.length;i++)
{
System.out.printf("from %s to %s shortest path is:%f\n", city.name,cities.get(i).name,D[i]);
}
}
public void dijkstra(int srcId)
{
D = new double[A.length];
for(int i=0;i<A.length;i++)
{
D[i]=999999999;
}
D[srcId]=0;
int[] q = new int[A.length];
int ql=0,qf=0; //队列
for(int i=0;i<A.length;i++) q[ql++]=i;
while(qf!=ql)
{
int min=qf;
for(int i=qf;i<ql;i++)
{
if(D[q[i]]<D[q[min]])
{
min=i;
}
}
int id = q[qf];
q[qf] = q[min];
q[min] = id; //q[qf] is the min
int u=q[qf++];
for(int i=0;i<A.length;i++)
{
if(A[u][i]>0)
{
relax(u,i);
}
}
}
}
public void bellmanFord(City city)
{
bellmanFord(city.id);
System.out.println("bellmanFord:");
for(int i=0;i<A.length;i++)
{
System.out.printf("from %s to %s shortest path is:%f\n", city.name,cities.get(i).name,D[i]);
}
}
public void bellmanFord(int srcId)
{
D = new double[A.length];
for(int i=0;i<A.length;i++)
{
D[i] = 99999999;//无穷大
}
D[srcId] = 0;
for(int i=0;i<A.length;i++)//外层循环次数
{
for(int j=0;j<A.length;j++)
{
for(int k=0;k<A.length;k++)
{
if(A[j][k]>0)
{
relax(j,k);
}
}
}
}
}
Queue<Integer> bfsQueue = new LinkedList<Integer>();
boolean[] bfsFlag;
int bsfPre[];
public void findPathByBFS(City src,City dst)
{
System.out.printf("bfs find path between ‘%s‘ and ‘%s‘!\n",src.name,dst.name);
findPathByBFS( src.id, dst.id);
printBFS(dst.id);
}
public void findPathByBFS(int srcId,int dstId)
{
bsfPre = new int[A.length];
bfsQueue.clear();
bfsFlag = new boolean[A.length];
for(int i=0;i<A.length;i++)
{
bfsFlag[i] = false;
bsfPre[i] = -1;
}
bfsQueue.offer(srcId);
bfsFlag[srcId] = true;
while(!bfsQueue.isEmpty())
{
int current = bfsQueue.poll();
for(int index=0;index<A.length;index++)
{
if(current == index) continue;
if(A[current][index]>0) //两者相连
{
if(index == dstId)//找到目标了
{
bfsFlag[index] = true;
bsfPre[index] = current;
return;//直接返回
}
if(bfsFlag[index] == false)//假设未訪问过
{
bfsFlag[index] = true;
bsfPre[index] = current;
bfsQueue.offer(index);
}
}
}
}
}
private void printBFS(int dstId)
{
int index = dstId;
do
{
System.out.printf("<-%s", cities.get(index).name);
index = bsfPre[index];
}while(index != -1);
System.out.println();
}
ArrayList<Integer> dfsPath = new ArrayList<Integer>();
boolean[] dfsFlag;
private void printDFS()
{
for(Integer node:dfsPath)
{
System.out.printf("->%s", cities.get(node).name);
}
System.out.println();
}
public void findPathByDFS(City src,City dst)
{
System.out.printf("dfs find path between ‘%s‘ and ‘%s‘!\n",src.name,dst.name);
findPathByDFS(src.id, dst.id);
}
public void findPathByDFS(int srcId,int dstId)
{
dfsPath.clear();
dfsFlag = new boolean[A.length];
for(int i=0;i<A.length;i++)
{
dfsFlag[i] = false;
}
dfsPath.add(srcId);
dfsFlag[srcId] = true;
dfs( srcId, dstId);
printDFS();
}
private void dfs(int srcId,int dstId)
{
for(int index=0;index<A[srcId].length;index++)
{
if(srcId == index) continue;
if(A[srcId][index]>0)//两者连接
{
if(index == dstId)//找到目标了
{
dfsFlag[index] = true;
dfsPath.add(index);
return;
}
if(dfsFlag[index] == false)//假设该节点未訪问过
{
dfsFlag[index] = true;
dfsPath.add(index);
dfs(index,dstId);
if(dfsFlag[dstId] == false)//目标没找到
dfsPath.remove(index);
else return;
}
}
}
}
public void createEdge(City a, City b, double w)
{
A[a.id][b.id]=w;
A[b.id][a.id]=w;//added by me!
cities.add(a.id,a);
cities.add(b.id,b);
}
public String toString()
{
String r = "I am a map of " + A.length + " cities.";
r += " My connections are:\n";
for (int i=0;i<A.length;i++)
{
for (int j=0;j<A[0].length;j++)
r+=A[i][j]+"\t";
r+="\n";
}
return r;
}
}
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