常见图算法总结与Java实现

下面的代码中实现了基于邻接表的图算法包括广度优先遍历、深度优先遍历、最小生成树算法Prim和Kruskal、单源最短路径算法Bellman-Ford和Dijkstra

代码参考算法导论和https://github.com/wangkuiwu/datastructs_and_algorithm/blob/master/source/graph/prim/udg/java/ListUDG.java

package Graph;import java.util.Arrays;import java.util.HashSet;import java.util.LinkedList;public class Graph {class ENode{int num;int weight=0;ENode nextEdge;ENode(){num=0;nextEdge=null;}ENode(int num){this.num=num;nextEdge=null;}ENode(int num,int weight){this.num=num;this.weight=weight;nextEdge=null;}}class VNode{char vertex;ENode firstEdge=null;}class Edge{char start;char end;int weight;Edge(){}Edge(Edge edge){start=edge.start;end=edge.end;weight=edge.weight;}Edge(char start,char end,int weight){this.start=start;this.end=end;this.weight=weight;}}VNode[] mVertex;Edge[] medges;int edgeNum=0;int[][] mWeights;static int INF = Integer.MAX_VALUE;public int vertexToNum(char c){int res=0;for(int i=0;i<mVertex.length;i++){if(mVertex[i].vertex==c)return i;}return res;}public Graph(char[] vexs,char[][] edges){edgeNum=edges.length;mVertex=new VNode[vexs.length];for(int i=0;i<vexs.length;i++){mVertex[i]=new VNode();mVertex[i].vertex=vexs[i];}for(int i=0;i<edges.length;i++){ENode temp=new ENode(vertexToNum(edges[i][1]));if(mVertex[vertexToNum(edges[i][0])].firstEdge==null){mVertex[vertexToNum(edges[i][0])].firstEdge=temp;}else{ENode p=mVertex[vertexToNum(edges[i][0])].firstEdge;while(p.nextEdge!=null){p=p.nextEdge;}p.nextEdge=temp;}}}Graph(char[] vexs,char[][] edges,int[] weights,Boolean isDirected){edgeNum=edges.length;medges=new Edge[edgeNum];mWeights=new int[vexs.length][vexs.length];for(int i=0;i<vexs.length;i++){for(int j=0;j<vexs.length;j++){mWeights[i][j]=INF;}}mVertex=new VNode[vexs.length];for(int i=0;i<vexs.length;i++){mVertex[i]=new VNode();mVertex[i].vertex=vexs[i];}for(int i=0;i<edges.length;i++){ENode temp=new ENode(vertexToNum(edges[i][1]),weights[i]);medges[i]=new Edge(edges[i][0],edges[i][1],weights[i]);mWeights[vertexToNum(edges[i][0])][vertexToNum(edges[i][1])]=weights[i];if(mVertex[vertexToNum(edges[i][0])].firstEdge==null){mVertex[vertexToNum(edges[i][0])].firstEdge=temp;}else{ENode p=mVertex[vertexToNum(edges[i][0])].firstEdge;while(p.nextEdge!=null){p=p.nextEdge;}p.nextEdge=temp;}if(!isDirected){temp=new ENode(vertexToNum(edges[i][0]),weights[i]);mWeights[vertexToNum(edges[i][1])][vertexToNum(edges[i][0])]=weights[i];if(mVertex[vertexToNum(edges[i][1])].firstEdge==null){mVertex[vertexToNum(edges[i][1])].firstEdge=temp;}else{ENode p=mVertex[vertexToNum(edges[i][1])].firstEdge;while(p.nextEdge!=null){p=p.nextEdge;}p.nextEdge=temp;}}}}public void BFS(){LinkedList<VNode> queue=new LinkedList<VNode>();Boolean[] isVisited=new Boolean[mVertex.length];for(int i=0;i<mVertex.length;i++){isVisited[i]=false;}queue.offer(mVertex[0]);System.out.print(mVertex[0].vertex+" ");isVisited[0]=true;while(!queue.isEmpty()){VNode p=queue.remove(); ENode q=p.firstEdge;while(q!=null){if(!isVisited[q.num]){isVisited[q.num]=true;System.out.print(mVertex[q.num].vertex+" ");queue.offer(mVertex[q.num]);}q=q.nextEdge;}}System.out.println();}public void DFSfirst(VNode vertex,Boolean[] isVisited){int num=vertexToNum(vertex.vertex);if(!isVisited[num]){isVisited[num]=true;System.out.print(vertex.vertex+" ");}ENode p=vertex.firstEdge;while(p!=null){DFSfirst(mVertex[p.num],isVisited);p=p.nextEdge;}}public void DFS(){Boolean[] isVisited=new Boolean[mVertex.length];for(int i=0;i<mVertex.length;i++){isVisited[i]=false;}for(int i=0;i<mVertex.length;i++){if(!isVisited[i])DFSfirst(mVertex[i],isVisited);}System.out.println();}//walk all the edges in the nondecreasing order of weightpublic Edge[] Kruskal(){Edge[] res=new Edge[mVertex.length-1];if(edgeNum<1) return res;//bubble sortfor(int i=0;i<edgeNum-1;i++){for(int j=edgeNum-1;j>i;j--){if(medges[j].weight<medges[j-1].weight){Edge temp;temp=medges[j];medges[j]=medges[j-1];medges[j-1]=temp;}}}int j=0;char[] vends=new char[mVertex.length];for(int i=0;i<vends.length;i++){vends[i]=mVertex[i].vertex;}for(int i=0;i<edgeNum;i++){int s=vertexToNum(medges[i].start);int e=vertexToNum(medges[i].end);if(vends[s]!=vends[e]){char temp_c=vends[s];for(int k=0;k<vends.length;k++){if(vends[k]==temp_c)vends[k]=vends[e];}res[j]=medges[i];j++;}}int length = 0;        for (int i = 0; i < res.length; i++)            length += res[i].weight;        System.out.printf("Kruskal=%d: ", length);        for (int i = 0; i < res.length; i++)            System.out.printf("(%c,%c) ", res[i].start, res[i].end);        System.out.printf("\n");return res;}public void Prim(char c){int pos=vertexToNum(c);char[] res=new char[mVertex.length];int[] key=new int[mVertex.length];int[] front=new int[mVertex.length];int minKey=INF,minPos=0;for(int i=0;i<mVertex.length;i++){key[i]=mWeights[pos][i];front[i]=-1;if(key[i]<minKey){minKey=key[i];minPos=i;}}front[minPos]=pos;key[pos]=0;res[0]=mVertex[pos].vertex;int i=0,k=1,sum=0;while(i++<mVertex.length-1){minKey=INF;for(int j=0;j<mVertex.length;j++){if(key[j]!=0&&key[j]<minKey){minPos=j;minKey=key[j];}}res[k++]=mVertex[minPos].vertex;sum=sum+mWeights[front[vertexToNum(res[k-1])]][vertexToNum(res[k-1])];key[minPos]=0;for(int j=0;j<mVertex.length;j++){if(key[j]!=0&&mWeights[minPos][j]<key[j]){key[j]=mWeights[minPos][j];front[j]=minPos;}}} System.out.printf("PRIM(%c)=%d: ", mVertex[pos].vertex, sum);        for (i = 0; i < mVertex.length; i++)            System.out.printf("%c ", res[i]);        System.out.printf("\n");}public Boolean BellmanFord(char c){int s=vertexToNum(c);int[] d=new int[mVertex.length];int[] front=new int[mVertex.length];for(int i=0;i<mVertex.length;i++){d[i]=INF;front[i]=-1;}d[s]=0;for(int i=0;i<mVertex.length-1;i++){for(int j=0;j<edgeNum;j++){int start=vertexToNum(medges[j].start);int end=vertexToNum(medges[j].end);if(d[end]>d[start]+mWeights[start][end]){d[end]=d[start]+mWeights[start][end];front[end]=start;}}}for(int i=0;i<edgeNum;i++){int start=vertexToNum(medges[i].start);int end=vertexToNum(medges[i].end);if(d[end]>d[start]+mWeights[start][end]){return false;}}System.out.printf("BellmanFord:  ");for(int i=0;i<mVertex.length;i++){if(i==s) continue;System.out.print(mVertex[front[i]].vertex+" ");}System.out.println();return true;}public void Dijkstra(char c){int s=vertexToNum(c);int[] S=new int[mVertex.length];int[] d=new int[mVertex.length];int[] front=new int[mVertex.length];for(int i=0;i<mVertex.length;i++){d[i]=INF;S[i]=-1;front[i]=-1;}d[s]=0;//use array d[] to implement PriorityQueueint minPos=s,minD=INF;for(int i=0;i<mVertex.length;i++){minD=INF;for(int j=0;j<mVertex.length;j++){if(d[j]!=0&&d[j]<minD){minD=d[j];minPos=j;}}d[minPos]=0;int start=minPos;int end=0;ENode p=mVertex[start].firstEdge;while(p!=null){end=p.num;if(d[end]>d[start]+mWeights[start][end]){d[end]=d[start]+mWeights[start][end];front[end]=start;}p=p.nextEdge;}}System.out.printf("Dijkstra:  ");for(int i=0;i<mVertex.length;i++){if(i==s) continue;System.out.print(mVertex[front[i]].vertex+" ");}System.out.println();}public void printGraph(){for(int i=0;i<mVertex.length;i++){System.out.printf("%d%c:", i,mVertex[i].vertex);ENode p=mVertex[i].firstEdge;while(p!=null){System.out.printf("%d%c(%d) ", p.num,mVertex[p.num].vertex,p.weight);p=p.nextEdge;}System.out.println();}}public static void main(String[] args){char[] vexs = {'A', 'B', 'C', 'D', 'E', 'F', 'G'};        char[][] edges = new char[][]{            {'A', 'C'},             {'A', 'D'},             {'A', 'F'},             {'B', 'C'},             {'C', 'D'},             {'E', 'G'},             {'F', 'G'}};Graph mgraph=new Graph(vexs,edges);mgraph.printGraph();mgraph.BFS();mgraph.DFS();char[] vexs2={'A', 'B', 'C', 'D', 'E', 'F', 'G'};char[][] edges2={{'A','B'},{'A','F'},{'A','G'},{'B','C'},{'B','F'},{'C','D'},{'C','E'},{'C','F'},{'D','E'},{'E','F'},{'E','G'},{'F','G'},};int[] weight2={12,16,14,10,7,3,5,6,4,2,8,9};Graph mgraph2=new Graph(vexs2,edges2,weight2,false);mgraph2.printGraph();mgraph2.Kruskal();mgraph2.Prim('A');char[] vexs3={'s','t','x','y','z'};char[][] edges3={{'s','t'},{'s','y'},{'t','x'},{'t','y'},{'t','z'},{'x','t'},{'y','x'},{'y','z'},{'z','s'},{'z','x'}};int[] weights3={6,7,5,8,-4,-2,-3,9,2,7};Graph mgraph3=new Graph(vexs3,edges3,weights3,true);mgraph3.printGraph();mgraph3.BellmanFord('s');char[] vexs4={'s','t','x','y','z'};char[][] edges4={{'s','t'},{'s','y'},{'t','x'},{'t','y'},{'x','z'},{'y','t'},{'y','x'},{'y','z'},{'z','s'},{'z','x'}};int[] weights4={10,5,1,2,4,3,9,2,7,6};Graph mgraph4=new Graph(vexs4,edges4,weights4,true);mgraph4.Dijkstra('s');mgraph4.BellmanFord('s');}}