实验一：判断一个无向图是不是一棵树
public boolean isTree()
实验二：判断两个图是否相同
public boolean equlas(Object obj)
实验方法与步骤（需求分析、算法设计思路、流程图等）
- 判断一个无向图是不是一棵树
判断一个图有n个结点，同时具有n-1条边，同时该图是个连通图。若满足条件，则是二叉树，否则并不是二叉树。
- 判断两个图是否相同
通过遍历，比较结点和边的数量，同时比较边的权值，若都相同，则返回true，否则返回false。
四、实验原始纪录（源程序、数据结构等）
public abstract class AbstractGraph<T>
{
protected static final int MAX_WEIGHT=99999;
protected SeqList<T> vertexlist;
boolean directed;
public AbstractGraph(int length)
{
this.vertexlist = new SeqList<T>(length);
// System.out.println(this.vertexlist);
}
public AbstractGraph()
{
this(10);
}
public int vertexCount()
{
return this.vertexlist.size();
}
public int edeCount()
{
return 0;
}
public String toString()
{
return "顶点集合："+this.vertexlist.toString()+"\n";
}
public T getVertex(int i)
{
return this.vertexlist.get(i);
}
public void setVertex(int i, T x)
{
this.vertexlist.set(i,x);
}
public abstract int insertVertex(T x);
public abstract void removeVertex(int i);
public abstract int weight(int i, int j);
protected abstract int next(int i, int j);
public void DFSTraverse(int i)
{
boolean[] visited=new boolean[this.vertexCount()];
int j=i;
do
{ if (!visited[j])
{
System.out.print("{ ");
this.depthfs(j, visited);
System.out.print("} ");
}
j = (j+1) % this.vertexCount();
} while (j!=i);
System.out.println();
}
private void depthfs(int i, boolean[] visited)
{
System.out.print(this.getVertex(i)+" ");
visited[i] = true;
for (int j=this.next(i,-1); j!=-1; j=this.next(i,j))
if(!visited[j])
depthfs(j, visited);
}
public void BFSTraverse(int i)
{
boolean[] visited = new boolean[this.vertexCount()];
int j=i;
do
{ if (!visited[j])
{
System.out.print("{ ");
breadthfs(j, visited);
System.out.print("} ");
}
j = (j+1) % this.vertexCount();
} while (j!=i);
System.out.println();
}
private void breadthfs(int i, boolean[] visited)
{
System.out.print(this.getVertex(i)+" ");
visited[i] = true;
LinkedQueue<Integer> que = new LinkedQueue<Integer>();
que.add(i);
while (!que.isEmpty())
{
i = que.poll();
for (int j=next(i,-1); j!=-1; j=next(i,j))
if (!visited[j])
{
System.out.print(this.getVertex(j)+" ");
visited[j] = true;
que.add(j);
}
}
}
public void minSpanTree()
{
Triple[] mst = new Triple[vertexCount()-1];
for (int i=0; i<mst.length; i++)
mst[i]=new Triple(0,i+1,this.weight(0,i+1));
for (int i=0; i<mst.length; i++)
{
System.out.print("mst边集合：");
for(int j=0; j<mst.length; j++)
System.out.print(mst[j].toString()+",");
System.out.println();
int min=i;
for (int j=i+1; j<mst.length; j++)
if (mst[j].value < mst[min].value)
{
min = j;
}
Triple edge = mst[min];
if (min!=i)
{
mst[min] = mst[i];
mst[i] = edge;
}
int tv = edge.column;
for (int j=i+1; j<mst.length; j++)
{
int v = mst[j].column;
int weight = this.weight(tv,v);
if (weight<mst[j].value)
mst[j] = new Triple(tv,v,weight);
}
}
System.out.print("\n最小生成树的边集合：");
int mincost=0;
for (int i=0; i<mst.length; i++)
{
System.out.print(mst[i]+" ");
mincost += mst[i].value;
}
System.out.println("，最小代价为"+mincost);
}
public void shortestPath(int i)
{
int n = this.vertexCount();
boolean[] vset = new boolean[n];
vset[i] = true;
int[] dist = new int[n];
int[] path = new int[n];
for (int j=0; j<n; j++)
{
dist[j] = this.weight(i,j);
path[j] = (j!=i && dist[j]<MAX_WEIGHT) ? i : -1;
}
// System.out.print("\nvset数组"+toString(vset));
// System.out.print("\tpath数组"+toString(path));
// System.out.print("\tdist数组"+toString(dist));
for (int j=(i+1)%n; j!=i; j=(j+1)%n)
{
int mindist=MAX_WEIGHT, min=0;
for (int k=0; k<n; k++)
if (!vset[k] && dist[k]<mindist)
{
mindist = dist[k];
min = k;
}
if (mindist==MAX_WEIGHT)
break;
vset[min] = true;
for (int k=0; k<n; k++)
if (!vset[k] && this.weight(min,k)<MAX_WEIGHT && dist[min]+this.weight(min,k)<dist[k])
{
dist[k] = dist[min] + this.weight(min,k);
path[k] = min;
}
// System.out.print("\nvset数组"+toString(vset));
// System.out.print("\tpath数组"+toString(path));
// System.out.print("\tdist数组"+toString(dist));
}
System.out.print(this.getVertex(i)+"的单源最短路径：");
for (int j=0; j<n; j++)
if (j!=i)
{
SinglyList<T> pathlink = new SinglyList<T>();
pathlink.insert(0, this.getVertex(j));
for (int k=path[j]; k!=i && k!=j && k!=-1; k=path[k])
pathlink.insert(0, this.getVertex(k));
pathlink.insert(0, this.getVertex(i));
System.out.print(pathlink.toString()+"长度"+(dist[j]==MAX_WEIGHT ? "∞" : dist[j])+"，");
}
System.out.println();
}
private static String toString(int[] value)
{
if (value!=null && value.length>0)
{
String str="{";
int i=0;
for(i=0; i<value.length-1; i++)
str += (value[i]==MAX_WEIGHT ? "∞" : value[i])+",";
return str+(value[i]==MAX_WEIGHT ? "∞" : value[i])+"}";
}
return null;
}
public void shortestPath()
{
int n=this.vertexCount();
Matrix path=new Matrix(n), dist=new Matrix(n);
for (int i=0; i<n; i++)
for (int j=0; j<n; j++)
{ int w=this.weight(i,j);
dist.set(i,j,w);
path.set(i,j, (i!=j && w<MAX_WEIGHT ? i : -1));
}
System.out.println("dist"+dist.toString()+"path"+path.toString()+"路径矩阵：");
printPathAll(path);
for (int k=0; k<n; k++)
{
System.out.println("\n以"+this.getVertex(k)+"作为中间顶点，替换路径如下：");
for (int i=0; i<n; i++)
if (i!=k)
for (int j=0; j<n; j++)
if (j!=k && j!=i)
{
System.out.print(toPath(path,i,j)+"路径长度"+dist.get(i,j)+"，替换为"+
toPath(path,i,k)+","+toPath(path,k,j)+"路径长度"+(dist.get(i,k)+dist.get(k,j))+"？");
if (j!=k && j!=i && dist.get(i,j) > dist.get(i,k)+dist.get(k,j))
{
dist.set(i, j, dist.get(i,k)+dist.get(k,j));
path.set(i, j, path.get(k,j));
System.out.println("是，d"+i+j+"="+dist.get(i,j)+"，p"+i+j+"="+path.get(i,j));
}
else
System.out.println("否");
}
System.out.println("dist"+dist.toString()+"path"+path.toString()+"路径矩阵：");
printPathAll(path);
}
System.out.println("\n每对顶点间的最短路径如下：");
for (int i=0; i<n; i++)
{
for (int j=0; j<n; j++)
if (i!=j)
System.out.print(toPath(path,i,j)+"长度"+(dist.get(i,j)==MAX_WEIGHT ? "∞" : dist.get(i,j))+"，");
System.out.println();
}
}
private String toPath(Matrix path, int i, int j)
{
SinglyList<T> pathlink = new SinglyList<T>();
pathlink.insert(0, this.getVertex(j));
for (int k=path.get(i,j); k!=i && k!=j && k!=-1; k=path.get(i,k))
pathlink.insert(0, this.getVertex(k));
pathlink.insert(0, this.getVertex(i));
return pathlink.toString();
}
private void printPathAll(Matrix path) //输出path路径矩阵中每对顶点间的路径字符串
{
for (int i=0; i<path.getRows(); i++)
{
for (int j=0; j<path.getRows(); j++)
System.out.print(toPath(path,i,j)+" ");
System.out.println();
}
}
public boolean equlas(Object obj)
{
if(obj==this)
return true;
if(!(obj instanceof AbstractGraph))
return false;
if(this.vertexCount()!=((AbstractGraph)obj).vertexCount())
return false;
for(int i=0;i<this.vertexCount();i++)
{
int one=this.weight(i, i+1);
System.out.println("one的大小是"+one);
int two=((AbstractGraph) obj).weight(i, i+1);
if(one!=two)
return false;
}
return true;
}
public boolean isTree()
{
if(this.DFS()==this.vertexCount()-1)
return true;
return false;
}
int edge=0,vertex=0;
public int DFS()
{
boolean[] visited=new boolean[this.vertexCount()];
int j=0;
do
{ if (!visited[j])
{
if((this.next(j, j+1))!=-1)
edge++;
this.dept(j, visited);
}
j = (j+1) % this.vertexCount();
} while (j!=0);
return edge;
}
private void dept(int i, boolean[] visited)
{
visited[i] = true;
for (int j=this.next(i,-1); j!=-1; j=this.next(i,j))
if(!visited[j])
dept(j, visited);
}
五、实验结果及分析（计算过程与结果、数据曲线、图表等）
（1）判断一个无向图是不是一棵树：
（2）判断两个图是否相同：
