《漫画算法2》源码整理-2 图算法

GraphUtil

import java.util.LinkedList;public class GraphUtil {//深度优先遍历public static void dfs(Graph graph, int start, boolean[] visited) {System.out.println(graph.vertexes[start].data);visited[start] = true;for (int index : graph.adj[start]) {if (!visited[index]) {dfs(graph, index, visited);}}}//广度优先遍历public static void bfs(Graph graph, int start, boolean[] visited, LinkedList<Integer> queue) {queue.offer(start);while (!queue.isEmpty()) {int front = queue.poll();if (visited[front]) {continue;}System.out.println(graph.vertexes[front].data);visited[front] = true;for (int index : graph.adj[front]) {queue.offer(index);;}}}//图的顶点private static class Vertex {int data;Vertex(int data) {this.data = data;}}//图（邻接表形式）private static class Graph {private int size;private Vertex[] vertexes;private LinkedList<Integer>[] adj;Graph(int size) {this.size = size;//初始化顶点和邻接矩阵vertexes = new Vertex[size];adj = new LinkedList[size];for (int i = 0; i < size; i++) {vertexes[i] = new Vertex(i);adj[i] = new LinkedList();}}}public static void main(String[] args) {Graph graph = new Graph(6);graph.adj[0].add(1);graph.adj[0].add(2);graph.adj[0].add(3);graph.adj[1].add(0);graph.adj[1].add(3);graph.adj[1].add(4);graph.adj[2].add(0);graph.adj[3].add(0);graph.adj[3].add(1);graph.adj[3].add(4);graph.adj[3].add(5);graph.adj[4].add(1);graph.adj[4].add(3);graph.adj[4].add(5);graph.adj[5].add(3);graph.adj[5].add(4);System.out.println("图的深度优先遍历：");dfs(graph, 0, new boolean[graph.size]);System.out.println("图的广度优先遍历：");bfs(graph, 0, new boolean[graph.size], new LinkedList<Integer>());}
}

单源最短路径算法 Dijkstra 算法

import java.util.*;public class Dijkstra {// Dijkstra最短路径算法public static int[] dijkstra(Graph graph, int startIndex) {//图的顶点数量int size = graph.vertexes.length;//创建距离表，存储从起点到每一个顶点的临时距离int[] distances = new int[size];//记录顶点遍历状态boolean[] access = new boolean[size];//初始化最短路径表，到达每个顶点的路径代价默认为无穷大for (int i = 1; i < size; i++) {distances[i] = Integer.MAX_VALUE;}//遍历起点，刷新距离表access[0] = true;List<Edge> edgesFromStart = graph.adj[startIndex];for (Edge edge : edgesFromStart) {distances[edge.index] = edge.weight;}//主循环，重复遍历最短距离顶点和刷新距离表的操作for (int i = 1; i < size; i++) {//寻找最短距离顶点int minDistanceFromStart = Integer.MAX_VALUE;int minDistanceIndex = -1;for (int j = 1; j < size; j++) {if (!access[j] && (distances[j] < minDistanceFromStart)) {minDistanceFromStart = distances[j];minDistanceIndex = j;}}if (minDistanceIndex == -1) {break;}//遍历顶点，刷新距离表access[minDistanceIndex] = true;for (Edge edge : graph.adj[minDistanceIndex]) {if (access[edge.index]) {continue;}int weight = edge.weight;int preDistance = distances[edge.index];if ((weight != Integer.MAX_VALUE) &&((minDistanceFromStart + weight) < preDistance)) {distances[edge.index] = minDistanceFromStart + weight;}}}return distances;}// Dijkstra最短路径算法（返回完整路径）public static int[] dijkstraV2(Graph graph, int startIndex) {//图的顶点数量int size = graph.vertexes.length;//创建距离表，存储从起点到每一个顶点的临时距离int[] distances = new int[size];//创建前置定点表，存储从起点到每一个顶点的已知最短路径的前置节点int[] prevs = new int[size];//记录顶点遍历状态boolean[] access = new boolean[size];//初始化最短路径表，到达每个顶点的路径代价默认为无穷大for (int i = 0; i < size; i++) {distances[i] = Integer.MAX_VALUE;}//遍历起点，刷新距离表access[0] = true;List<Edge> edgesFromStart = graph.adj[startIndex];for (Edge edge : edgesFromStart) {distances[edge.index] = edge.weight;prevs[edge.index] = 0;}//主循环，重复 遍历最短距离顶点和刷新距离表 的操作for (int i = 1; i < size; i++) {//寻找最短距离顶点int minDistanceFromStart = Integer.MAX_VALUE;int minDistanceIndex = -1;for (int j = 1; j < size; j++) {if (!access[j] && (distances[j] < minDistanceFromStart)) {minDistanceFromStart = distances[j];minDistanceIndex = j;}}if (minDistanceIndex == -1) {break;}//遍历顶点，刷新距离表access[minDistanceIndex] = true;for (Edge edge : graph.adj[minDistanceIndex]) {if (access[edge.index]) {continue;}int weight = edge.weight;int preDistance = distances[edge.index];if ((weight != Integer.MAX_VALUE) &&((minDistanceFromStart + weight) < preDistance)) {distances[edge.index] = minDistanceFromStart + weight;prevs[edge.index] = minDistanceIndex;}}}return prevs;}private static void printPrevs(Vertex[] vertexes, int[] prev, int i) {if (i > 0) {printPrevs(vertexes, prev, prev[i]);}System.out.println(vertexes[i].data);}private static void initGraph(Graph graph) {graph.vertexes[0] = new Vertex("A");graph.vertexes[1] = new Vertex("B");graph.vertexes[2] = new Vertex("C");graph.vertexes[3] = new Vertex("D");graph.vertexes[4] = new Vertex("E");graph.vertexes[5] = new Vertex("F");graph.vertexes[6] = new Vertex("G");graph.adj[0].add(new Edge(1, 5));graph.adj[0].add(new Edge(2, 2));graph.adj[1].add(new Edge(0, 5));graph.adj[1].add(new Edge(3, 1));graph.adj[1].add(new Edge(4, 6));graph.adj[2].add(new Edge(0, 2));graph.adj[2].add(new Edge(3, 6));graph.adj[2].add(new Edge(5, 8));graph.adj[3].add(new Edge(1, 1));graph.adj[3].add(new Edge(2, 6));graph.adj[3].add(new Edge(4, 1));graph.adj[3].add(new Edge(5, 2));graph.adj[4].add(new Edge(1, 6));graph.adj[4].add(new Edge(3, 1));graph.adj[4].add(new Edge(6, 7));graph.adj[5].add(new Edge(2, 8));graph.adj[5].add(new Edge(3, 2));graph.adj[5].add(new Edge(6, 3));graph.adj[6].add(new Edge(4, 7));graph.adj[6].add(new Edge(5, 3));}//图的顶点private static class Vertex {String data;Vertex(String data) {this.data = data;}}//图的边private static class Edge {int index;int weight;Edge(int index, int weight) {this.index = index;this.weight = weight;}}// 图private static class Graph {private Vertex[] vertexes;private LinkedList<Edge>[] adj;Graph(int size) {//初始化顶点和邻接矩阵vertexes = new Vertex[size];adj = new LinkedList[size];for (int i = 0; i < adj.length; i++) {adj[i] = new LinkedList<Edge>();}}}public static void main(String[] args) {Graph graph = new Graph(7);initGraph(graph);int[] distances = dijkstra(graph, 0);System.out.println(distances[6]);System.out.println("输出完整路径：");int[] prevs = dijkstraV2(graph, 0);printPrevs(graph.vertexes, prevs, graph.vertexes.length- 1);}}

多源最短路径算法 Floyd 算法

public class Floyd {final static int INF = Integer.MAX_VALUE;public static void floyd(int[][] matrix) {//循环更新矩阵的值for (int k = 0; k < matrix.length; k++) {for (int i = 0; i < matrix.length; i++) {for (int j = 0; j < matrix.length; j++) {if ((matrix[i][k] == INF) || (matrix[k][j] == INF)) {continue;}matrix[i][j] = Math.min(matrix[i][j], matrix[i][k] + matrix[k][j]);}}}// 打印floyd最短路径的结果System.out.printf("最短路径矩阵: \n");for (int i = 0; i < matrix.length; i++) {for (int j = 0; j < matrix.length; j++) {System.out.printf("%3d  ", matrix[i][j]);}System.out.printf("\n");}}public static void main(String[] args) {int[][] matrix = {{ 0, 5, 2, INF, INF, INF, INF },{ 5, 0, INF, 1, 6, INF, INF },{ 2, INF, 0, 6, INF, 8, INF },{ INF, 1, 6, 0, 1, 2, INF },{ INF, 6, INF, 1, 0, INF, 7 },{ INF, INF, 8, 2, INF, 0, 3 },{ INF, INF, INF, INF, 7, 3, 0 }};floyd(matrix);}
}

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