重复访问顶点就不叫做遍历了。
关于图的基本概念,理论知识不想说了。太繁琐~
[v0][v1]代表v0顶点到v1顶点的路径权重为10
可以看见右图,权重为0的都是顶点自己到自己,这根本就没有意义。
而无限大符号表示到达不了,比如[v0][v2]。可以看左图,v0只能到达v1和v5,到不了v2。
第一幅图的矩阵可以看到有9个顶点,组成二维数组。
我们可以先生成这个矩阵:
public class Graph {
private int vertexSize; // 顶点数量
private int[] vertexs; // 顶点数组
private int[][] matrix; // 包含所有顶点的数组
// 路径权重
// 0意味着顶点自己到自己,无意义
// MAX_WEIGHT也意味着到目的顶点不可达
private static final int MAX_WEIGHT = 1000;
public Graph(int vertextSize) {
this.vertexSize = vertextSize;
matrix = new int[vertextSize][vertextSize];
vertexs = new int[vertextSize];
for (int i = 0; i < vertextSize; i++) {
vertexs[i] = i;
}
}
public static void main(String[] args) {
Graph graph = new Graph(9);
// 顶点的矩阵设置
int[] a1 = new int[] { 0, 10, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT };
int[] a2 = new int[] { 10, 0, 18, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, MAX_WEIGHT, 12 };
int[] a3 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 0, 22, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 8 };
int[] a4 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, 24, 16, 21 };
//int[] a4 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, MAX_WEIGHT, 16, 21 };
int[] a5 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 20, 0, 26, MAX_WEIGHT, 7, MAX_WEIGHT };
int[] a6 = new int[] { 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 26, 0, 17, MAX_WEIGHT, MAX_WEIGHT };
int[] a7 = new int[] { MAX_WEIGHT, 16, MAX_WEIGHT, 24, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
//int[] a7 = new int[] { MAX_WEIGHT, 16, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
int[] a8 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, 7, MAX_WEIGHT, 19, 0, MAX_WEIGHT };
int[] a9 = new int[] { MAX_WEIGHT, 12, 8, 21, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 0 };
graph.matrix[0] = a1;
graph.matrix[1] = a2;
graph.matrix[2] = a3;
graph.matrix[3] = a4;
graph.matrix[4] = a5;
graph.matrix[5] = a6;
graph.matrix[6] = a7;
graph.matrix[7] = a8;
graph.matrix[8] = a9;
}
}
matrix
二维数组存放所有顶点0
表示自己到自己,MAX_WEIGHT
表示无限大======================================
private boolean[] isVisited = new boolean[vertextSize];
/**
* 获取指定顶点的第一个邻接点
*
* @param index
* 指定邻接点
* @return
*/
private int getFirstNeighbor(int index) {
for (int i = 0; i < vertexSize; i++) {
if (matrix[index][i] < MAX_WEIGHT && matrix[index][i] > 0) {
return i;
}
}
return -1;
}
/**
* 获取指定顶点的下一个邻接点
*
* @param v
* 指定的顶点
* @param index
* 从哪个邻接点开始
* @return
*/
private int getNextNeighbor(int v, int index) {
for (int i = index+1; i < vertexSize; i++) {
if (matrix[v][i] < MAX_WEIGHT && matrix[v][i] > 0) {
return i;
}
}
return -1;
}
核心代码很简单,经上述分析过后:
/**
* 图的深度优先遍历算法
*/
private void depthFirstSearch(int i) {
isVisited[i] = true;
int w = getFirstNeighbor(i);
while (w != -1) {
if (!isVisited[w]) {
// 需要遍历该顶点
System.out.println("访问到了:" + w + "顶点");
depthFirstSearch(w); // 进行深度遍历
}
w = getNextNeighbor(i, w); // 第一个相对于w的邻接点
}
}
0
进去,表示v0
。设置v0
已访问过,获取v0
的第一个邻接点。w != -1
说明有这个邻接点,然后对这个临界点进行判断。
算法还是很简单的!
v0
有3个邻接点,v1 v2 v3
。 LinkedList
,因为它适合增删。而且这里不需要遍历集合。while(!queue.isEmpty())
或while(queue.size() > 0)
都行。开始循环。核心代码:
/**
* 图的广度优先遍历算法
*/
private void boardFirstSearch(int i) {
LinkedList queue = new LinkedList<>();
System.out.println("访问到了:" + i + "顶点");
isVisited[i] = true;
queue.add(i);
while (queue.size() > 0) {
int w = queue.removeFirst().intValue();
int n = getFirstNeighbor(w);
while (n != -1) {
if (!isVisited[n]) {
System.out.println("访问到了:" + n + "顶点");
isVisited[n] = true;
queue.add(n);
}
n = getNextNeighbor(w, n);
}
}
}
完整代码
复制即可运行
import java.util.LinkedList;
public class Graph {
private int vertexSize; // 顶点数量
private int[] vertexs; // 顶点数组
private int[][] matrix; // 包含所有顶点的数组
// 路径权重
// 0意味着顶点自己到自己,无意义
// MAX_WEIGHT也意味着到目的顶点不可达
private static final int MAX_WEIGHT = 1000;
private boolean[] isVisited; // 某顶点是否被访问过
public Graph(int vertextSize) {
this.vertexSize = vertextSize;
matrix = new int[vertextSize][vertextSize];
vertexs = new int[vertextSize];
for (int i = 0; i < vertextSize; i++) {
vertexs[i] = i;
}
isVisited = new boolean[vertextSize];
}
/**
* 获取指定顶点的第一个邻接点
*
* @param index
* 指定邻接点
* @return
*/
private int getFirstNeighbor(int index) {
for (int i = 0; i < vertexSize; i++) {
if (matrix[index][i] < MAX_WEIGHT && matrix[index][i] > 0) {
return i;
}
}
return -1;
}
/**
* 获取指定顶点的下一个邻接点
*
* @param v
* 指定的顶点
* @param index
* 从哪个邻接点开始
* @return
*/
private int getNextNeighbor(int v, int index) {
for (int i = index+1; i < vertexSize; i++) {
if (matrix[v][i] < MAX_WEIGHT && matrix[v][i] > 0) {
return i;
}
}
return -1;
}
/**
* 图的深度优先遍历算法
*/
private void depthFirstSearch(int i) {
isVisited[i] = true;
int w = getFirstNeighbor(i);
while (w != -1) {
if (!isVisited[w]) {
// 需要遍历该顶点
System.out.println("访问到了:" + w + "顶点");
depthFirstSearch(w); // 进行深度遍历
}
w = getNextNeighbor(i, w); // 第一个相对于w的邻接点
}
}
/**
* 图的广度优先遍历算法
*/
private void boardFirstSearch(int i) {
LinkedList queue = new LinkedList<>();
System.out.println("访问到了:" + i + "顶点");
isVisited[i] = true;
queue.add(i);
while (queue.size() > 0) {
int w = queue.removeFirst().intValue();
int n = getFirstNeighbor(w);
while (n != -1) {
if (!isVisited[n]) {
System.out.println("访问到了:" + n + "顶点");
isVisited[n] = true;
queue.add(n);
}
n = getNextNeighbor(w, n);
}
}
}
public static void main(String[] args) {
Graph graph = new Graph(9);
// 顶点的矩阵设置
int[] a1 = new int[] { 0, 10, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT };
int[] a2 = new int[] { 10, 0, 18, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, MAX_WEIGHT, 12 };
int[] a3 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 0, 22, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 8 };
int[] a4 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, 24, 16, 21 };
//int[] a4 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, MAX_WEIGHT, 16, 21 };
int[] a5 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 20, 0, 26, MAX_WEIGHT, 7, MAX_WEIGHT };
int[] a6 = new int[] { 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 26, 0, 17, MAX_WEIGHT, MAX_WEIGHT };
int[] a7 = new int[] { MAX_WEIGHT, 16, MAX_WEIGHT, 24, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
//int[] a7 = new int[] { MAX_WEIGHT, 16, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
int[] a8 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, 7, MAX_WEIGHT, 19, 0, MAX_WEIGHT };
int[] a9 = new int[] { MAX_WEIGHT, 12, 8, 21, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 0 };
graph.matrix[0] = a1;
graph.matrix[1] = a2;
graph.matrix[2] = a3;
graph.matrix[3] = a4;
graph.matrix[4] = a5;
graph.matrix[5] = a6;
graph.matrix[6] = a7;
graph.matrix[7] = a8;
graph.matrix[8] = a9;
graph.depthFirstSearch(0);
//graph.boardFirstSearch(0);
}
}