Java数据结构——图的DFS和BFS

1.图的DFS:
即Breadth First Search,深度优先搜索是从起始顶点开始，递归访问其所有邻近节点，比如A节点是其第一个邻近节点，而B节点又是A的一个邻近节点，则DFS访问A节点后再访问B节点，如果B节点有未访问的邻近节点的话将继续访问其邻近节点，否则继续访问A的未访问邻近节点，当所有从A节点出去的路径都访问完之后，继续递归访问除A以外未被访问的邻近节点。

/*
* 深度优先遍历
*/
public void DFS(int i) {
isVisited[i] = true;
int weight = getFirstNeighbor(i);
while (weight != -1) {
if (!isVisited[weight]) {
System.out.print("v" + weight + " ");
DFS(weight);
}
weight = getNextNeighbor(i, weight);
}
}

/*
* 提供访问的DFS,强制每一次的遍历，防止在有向图和非连通图中有些顶点访问不到的情况
*/
public void DFS() {
isVisited = new boolean[size];
for (int i = 0; i < size; i++) {
if (!isVisited[i]) {
System.out.print("v" + i + " ");
DFS(i);
}
}
isVisited = new boolean[size];
}

2.图的BFS:
即Breadth First Search，其主要思想是从起始点开始，将其邻近的所有顶点都加到一个队列（FIFO）中去，然后标记下这些顶点离起始顶点的距离为1.最后将起始顶点标记为已访问，今后就不会再访问。然后再从队列中取出最先进队的顶点A，也取出其周边邻近节点，加入队列末尾，将这些顶点的距离相对A再加1，最后离开这个顶点A。依次下去，直到队列为空为止。

/*
* 广度优先遍历
*/
public void BFS(int i) {
int temp, weight;
LinkedList<Integer> queue = new LinkedList<>();
System.out.print("v" + i + " ");
isVisited[i] = true;
queue.add(i);
while (!queue.isEmpty()) {
temp = queue.removeFirst().intValue();
weight = getFirstNeighbor(temp);
while (weight != -1) {
if (!isVisited[weight]) {
System.out.print("v" + weight + " ");
isVisited[weight] = true;
queue.add(weight);
}
weight = getNextNeighbor(temp, weight);
}
}
}

/*
* 提供访问的BFS,强制每一次的遍历，防止在有向图和非连通图中有些顶点访问不到的情况
* 
*/
public void BFS() {
isVisited = new boolean[size];
for (int i = 0; i < size; i++) {
if (!isVisited[i]) {
BFS(i);
}
}
isVisited = new boolean[size];
}

3.全部java实现：

import java.util.LinkedList;

public class Graph {
private int size; // 顶点数量
private int[] vertexs; // 顶点数组
private int[][] matrix; // 邻接矩阵
private boolean[] isVisited;
private static final int MAX_WEIGHT = 10000;

public Graph(int size) {
super();
this.size = size;
vertexs = new int[size];
for (int i = 0; i < size; i++) {
vertexs[i] = i;
}
matrix = new int[size][size];
isVisited = new boolean[size];
}

public int getSize() {
return size;
}

public void setSize(int size) {
this.size = size;
}

public int[] getVertexs() {
return vertexs;
}

public void setVertexs(int[] vertexs) {
this.vertexs = vertexs;
}

/*
* 获取指定顶点的第一个邻接点
*/
public int getFirstNeighbor(int index) {
for (int i = 0; i < matrix[index].length; i++) {
if (matrix[index][i] != 0 && matrix[index][i] != MAX_WEIGHT) {
return i;
}
}
return -1;
}

/*
* 根据前一个邻接点的下标来获取下一个邻接点
* 
* @param v 表示要找的顶点
* 
* @param index 表示该顶点相对于哪个邻接点去获取下一个邻接点
*/
public int getNextNeighbor(int v, int index) {
for (int i = (index + 1); i < size; i++) {
if (matrix[v][i] != 0 && matrix[v][i] != MAX_WEIGHT) {
return i;
}
}
return -1;
}

/*
* 深度优先遍历
*/
public void DFS(int i) {
isVisited[i] = true;
int weight = getFirstNeighbor(i);
while (weight != -1) {
if (!isVisited[weight]) {
System.out.print("v" + weight + " ");
DFS(weight);
}
weight = getNextNeighbor(i, weight);
}
}

/*
* 提供访问的DFS,强制每一次的遍历，防止在有向图和非连通图中有些顶点访问不到的情况
*/
public void DFS() {
isVisited = new boolean[size];
for (int i = 0; i < size; i++) {
if (!isVisited[i]) {
System.out.print("v" + i + " ");
DFS(i);
}
}
isVisited = new boolean[size];
}

/*
* 广度优先遍历
*/
public void BFS(int i) {
int temp, weight;
LinkedList<Integer> queue = new LinkedList<>();
System.out.print("v" + i + " ");
isVisited[i] = true;
queue.add(i);
while (!queue.isEmpty()) {
temp = queue.removeFirst().intValue();
weight = getFirstNeighbor(temp);
while (weight != -1) {
if (!isVisited[weight]) {
System.out.print("v" + weight + " ");
isVisited[weight] = true;
queue.add(weight);
}
weight = getNextNeighbor(temp, weight);
}
}
}

/*
* 提供访问的BFS,强制每一次的遍历，防止在有向图和非连通图中有些顶点访问不到的情况
* 
*/
public void BFS() {
isVisited = new boolean[size];
for (int i = 0; i < size; i++) {
if (!isVisited[i]) {
BFS(i);
}
}
isVisited = new boolean[size];
}

public static void main(String[] args) {
Lfw_41 graph = new Lfw_41(9);
int[] a0 = new int[] { 0, 10, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT };
int[] a1 = new int[] { 10, 0, 18, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, MAX_WEIGHT, 12 };
int[] a2 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 0, 22, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 8 };
int[] a3 = new int[] { MAX_WEIGHT, MAX_WEIGHT, 22, 0, 20, MAX_WEIGHT, MAX_WEIGHT, 16, 21 };
int[] a4 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 20, 0, 26, MAX_WEIGHT, 7, MAX_WEIGHT };
int[] a5 = new int[] { 11, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 26, 0, 17, MAX_WEIGHT, MAX_WEIGHT };
int[] a6 = new int[] { MAX_WEIGHT, 16, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 17, 0, 19, MAX_WEIGHT };
int[] a7 = new int[] { MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 16, 7, MAX_WEIGHT, 19, 0, MAX_WEIGHT };
int[] a8 = new int[] { MAX_WEIGHT, 12, 8, 21, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, MAX_WEIGHT, 0 };
graph.matrix[0] = a0;
graph.matrix[1] = a1;
graph.matrix[2] = a2;
graph.matrix[3] = a3;
graph.matrix[4] = a4;
graph.matrix[5] = a5;
graph.matrix[6] = a6;
graph.matrix[7] = a7;
graph.matrix[8] = a8;
System.out.print("DFS: ");
graph.DFS();
System.out.println();
System.out.print("BFS: ");
graph.BFS();
System.out.println();
}
}