java数据结构----带权图

Posted 2020-10-25 海的味道

1.带权图：要引入带权图，首先要引入最小生成树，当所有的边拥有相同的权值时。问题变得简单了，算法可以选择任意一条边加入最小生成树。但是当边有不同的权值时，需要用一些算法决策来选择正确的边。

2.带权图构建最小生成树算法：

　　2.1.从一个顶点开始，把它放入树的集合中，然后重复做下面的事情：

　　　　2.1.1.找到从最新的顶点到其他顶点的所有边，这些顶点不能在树的集合中，把这些边放入优先级队列，

　　　　2.1.2.找出权值最小的边，把它和它所到达的顶点放入树的集合中。重复直到所有顶点都在树的集合中。

3.实现代码：

　　3.1.Edge.java

 1 package com.cn.powergraph;
 2 /**
 3  * 带权图的边类
 4  * @author Administrator
 5  *
 6  */
 7 public class Edge {
 8 public int srcVert;
 9 public int destVert;
10 public int distance;
11 public Edge(int sv,int dv,int d){
12     srcVert = sv;
13     destVert = dv;
14     distance = d;
15 }
16 }

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　　3.2.PriorityQ.java

 1 package com.cn.powergraph;
 2 /**
 3  * 优先级队列来实现带权图
 4  * @author Administrator
 5  *
 6  */
 7 public class PriorityQ {
 8 private final int SIZE = 20;
 9 private Edge[] queArray;
10 private int size;
11 public PriorityQ(){
12     queArray = new Edge[SIZE];
13     size = 0;
14 }
15 public void insert(Edge item){
16     int i;
17     for ( i = 0; i < size; i++) {
18         if (item.distance >= queArray[i].distance)
19             break;
20     }
21     for (int j = size - 1; j >= i; j --) {
22         queArray[j + 1] = queArray[j];
23     }
24     queArray[i] = item;
25     size ++;
26 }
27 public Edge removeMin(){
28     return queArray[-- size];
29 }
30 public void removeN(int n){
31     for (int i = n; i < size - 1; i++) {
32         queArray[i] = queArray[i + 1];
33     }
34     size --;
35 }
36 public Edge peekMin(){
37     return queArray[size - 1];
38 }
39 public int size(){
40     return size;
41 }
42 public boolean isEmpty(){
43     return size == 0;
44 }
45 public Edge peekN(int n){
46     return queArray[n];
47 }
48 public int find(int index){
49     for (int i = 0; i < size; i++) {
50         if (queArray[i].destVert == index)
51             return i;
52     }
53     return -1;
54 }
55 }

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　　3.3.Vertex.java

 1 package com.cn.powergraph;
 2 /**
 3  * 带权图顶点类
 4  * @author Administrator
 5  *
 6  */
 7 public class Vertex {
 8 public char lable;
 9 public boolean isInTree;
10 public Vertex(char lab){
11     lable = lab;
12     isInTree = false;
13 }
14 }

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　　3.4.Graph.java

 1 package com.cn.powergraph;
 2 /**
 3  * 带权图的类
 4  * @author Administrator
 5  *
 6  */
 7 public class Graph {
 8 private final int MAX_VERTS = 20;
 9 private final int INFINITY = 1000000;
10 private Vertex[] vertList;
11 private int adjMat[][];
12 private int nVerts;
13 private int currentVert;
14 private PriorityQ thePQ;
15 private int nTree;
16 public Graph(){
17     vertList = new Vertex[MAX_VERTS];
18     adjMat = new int[MAX_VERTS][MAX_VERTS];
19     nVerts = 0;
20     for (int i = 0; i < MAX_VERTS; i++) {
21         for (int j = 0; j < MAX_VERTS; j++) {
22             adjMat[i][j] = INFINITY;
23         }
24     }
25     thePQ = new PriorityQ();
26 }
27 public void addVertex(char lab){
28     vertList[nVerts ++] = new Vertex(lab);
29 }
30 public void addEdge(int start,int end,int weight){
31     adjMat[start][end] = weight;
32     adjMat[end][start] = weight;
33 }
34 public void displayVertex(int v){
35     System.out.print(vertList[v].lable);
36 }
37 public void mstw(){
38     currentVert = 0;
39     while (nTree < nVerts - 1){
40         vertList[currentVert].isInTree = true;
41         nTree ++;
42         for (int i = 0; i < nVerts; i++) {
43             if (i == currentVert)
44                 continue;
45             if (vertList[i].isInTree)
46                 continue;
47             int distance = adjMat[currentVert][i];
48             if (distance == INFINITY)
49                 continue;
50             putInPQ(i,distance);
51         }
52         if (thePQ.size() == 0)
53         {
54             System.out.println("GRAPH NOT CONNECTED");
55             return;
56         }
57         Edge theedge = thePQ.removeMin();
58         int sourceVert = theedge.srcVert;
59         currentVert = theedge.destVert;
60         System.out.print(vertList[sourceVert].lable);
61         System.out.print(vertList[currentVert].lable);
62         System.out.print("  ");
63     }
64     for (int i = 0; i < nVerts; i++) {
65         vertList[i].isInTree = false;
66     }
67 }
68 public void putInPQ(int newVert,int newDist){
69     int queueIndex = thePQ.find(newDist);
70     if (queueIndex != -1){
71         Edge tempEdge = thePQ.peekN(queueIndex);
72         int oldDist = tempEdge.distance;
73         if (oldDist > newDist){
74             thePQ.removeN(queueIndex);
75             Edge theEdge = new Edge(currentVert, newVert,newDist);
76             thePQ.insert(theEdge);
77         }
78     }
79     else{
80         Edge theEdge = new Edge(currentVert, newVert,newDist);
81         thePQ.insert(theEdge);
82     }
83 }
84 }

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　　3.5.GTest.java

 1 package com.cn.powergraph;
 2 /**
 3  * 带权图的测试
 4  * @author Administrator
 5  *
 6  */
 7 public class GTest {
 8 public static void main(String[] args) {
 9     Graph g = new Graph();
10     g.addVertex(‘a‘);
11     g.addVertex(‘b‘);
12     g.addVertex(‘c‘);
13     g.addVertex(‘d‘);
14     g.addVertex(‘e‘);
15     g.addVertex(‘f‘);
16     g.addEdge(0, 1, 3);
17     g.addEdge(2, 1, 5);
18     g.addEdge(3, 1, 8);
19     g.addEdge(3, 2, 5);
20     g.addEdge(5, 4, 4);
21     g.addEdge(0, 4, 10);
22     g.mstw();
23 }
24 }

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