📅 最后修改于: 2023-12-03 15:32:05.630000 🧑 作者: Mango
在交通规划中，需要考虑到车站的数量，以保证公共交通系统覆盖面广，同时又能够高效地运转。本文将介绍一个用Java程序解决车站数量问题的方法。
某城市规划部门需要对该市的公共交通系统进行改善，提高其覆盖面和运转效率。其首要任务是确定足够的车站数量，以便乘客可以在附近轻松地访问公共交通站点。
规划部门想要计算几个因素：
本问题可以通过使用Java中的图形算法来解决。
Dijkstra算法是一个用于搜寻和查找图中最短路径的算法。它以一个起始点作为出发点，在新的点被找到的时候进行扩展，并对路径进行优化。
下面是使用Dijkstra算法计算两车站之间最短路线长度的Java代码：
import java.util.*;
public class DijkstraAlgorithm{
private static final Graph graph = new Graph();
public static void main(String... args) {
Vertex start = graph.getVertex("起始点");
Vertex end = graph.getVertex("结束点");
DijkstraAlgorithm.findShortestPath(start);
LinkedList<Vertex> path = DijkstraAlgorithm.getPath(end);
System.out.println("从起始点到结束点的最短路线长度为：" + path.size());
}
public static void findShortestPath(Vertex start) {
start.setDistance(0);
PriorityQueue<Vertex> priorityQueue = new PriorityQueue<>();
priorityQueue.add(start);
while (!priorityQueue.isEmpty()) {
Vertex vertex = priorityQueue.poll();
for (Edge edge : vertex.getEdges()) {
Vertex u = edge.getStart();
Vertex v = edge.getEnd();
double weight = edge.getWeight();
double distanceFromStart = u.getDistance() + weight;
if (distanceFromStart < v.getDistance()) {
priorityQueue.remove(v);
v.setDistance(distanceFromStart);
v.setPrevious(u);
priorityQueue.add(v);
}
}
}
}
public static LinkedList<Vertex> getPath(Vertex end) {
LinkedList<Vertex> path = new LinkedList<>();
for (Vertex vertex = end; vertex != null; vertex = vertex.getPrevious()) {
path.add(vertex);
}
Collections.reverse(path);
return path;
}
}
class Graph {
private Set<Vertex> vertices = new HashSet<>();
public void addVertex(Vertex vertex) {
vertices.add(vertex);
}
public Vertex getVertex(String name) {
for (Vertex vertex : vertices) {
if (vertex.getName().equals(name)) {
return vertex;
}
}
return null;
}
}
class Edge {
private Vertex start;
private Vertex end;
private double weight;
public Edge(Vertex start, Vertex end, double weight) {
this.start = start;
this.end = end;
this.weight = weight;
}
public Vertex getStart() {
return start;
}
public Vertex getEnd() {
return end;
}
public double getWeight() {
return weight;
}
}
class Vertex implements Comparable<Vertex> {
private String name;
private List<Edge> edges = new ArrayList<>();
private double distance = Double.MAX_VALUE;
private Vertex previous;
public Vertex(String name) {
this.name = name;
}
public void addEdge(Edge edge) {
edges.add(edge);
}
@Override
public int compareTo(Vertex otherVertex) {
return Double.compare(distance, otherVertex.distance);
}
@Override
public String toString() {
return name;
}
public String getName() {
return name;
}
public List<Edge> getEdges() {
return edges;
}
public double getDistance() {
return distance;
}
public void setDistance(double distance) {
this.distance = distance;
}
public Vertex getPrevious() {
return previous;
}
public void setPrevious(Vertex previous) {
this.previous = previous;
}
}
Floyd算法是一种用于搜索图中最短路径的算法，同时还可以计算出从一个节点到其他节点的最短路径。
下面是使用Floyd算法计算两车站之间最短路线长度的Java代码：
import java.util.*;
public class FloydAlgorithm {
private int[][] distances;
public static void main(String args[]) {
FloydAlgorithm floyd = new FloydAlgorithm();
int[][] graph = {
{0, 3, 6, 15, 0, 0},
{3, 0, 2, 0, 11, 0},
{6, 2, 0, 1, 6, 8},
{15, 0, 1, 0, 2, 5},
{0, 11, 6, 2, 0, 3},
{0, 0, 8, 5, 3, 0},
};
floyd.calculateDistances(graph);
System.out.println(floyd.getShortestDistance(0, 5));
}
public void calculateDistances(int[][] matrix) {
int n = matrix.length;
distances = matrix.clone();
for (int k = 0; k < n; k++) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (distances[i][k] + distances[k][j] < distances[i][j]) {
distances[i][j] = distances[i][k] + distances[k][j];
}
}
}
}
}
private int getShortestDistance(int i, int j) {
return distances[i][j];
}
}
K-Means算法是一种聚类算法，它将给定的数据集分成k个不同的组或簇。
下面是使用K-Means算法计算车站数量的Java代码：
import java.util.*;
public class KMeans {
private static final int MAX_ITERATIONS = 100;
private static final Map<Integer, Cluster> clusterMap = new HashMap<>();
public static void main(String[] args) {
List<Double[]> dataList = new ArrayList<>();
for (int i = 0; i < 10; i++) {
double[] coordinates = new double[2];
coordinates[0] = Math.random();
coordinates[1] = Math.random();
dataList.add(coordinates);
}
List<Cluster> clusters = initialCluster(dataList, 3);
assignDataToCluster(dataList, clusters);
for (int i = 0; i < MAX_ITERATIONS; i++) {
for (Cluster cluster : clusters) {
double[] means = new double[2];
for (Double[] data : cluster.getData()) {
means[0] += data[0];
means[1] += data[1];
}
means[0] /= cluster.getData().size();
means[1] /= cluster.getData().size();
cluster.setCentroid(means);
}
boolean isConverged = true;
for (Double[] data : dataList) {
int clusterNumber = getClosestClusterNumber(data, clusters);
Cluster oldCluster = clusterMap.get(data.hashCode());
if (clusterNumber != oldCluster.getNumber()) {
oldCluster.getData().remove(data);
clusters.get(clusterNumber).getData().add(data);
clusterMap.put(data.hashCode(), clusters.get(clusterNumber));
isConverged = false;
}
}
if (isConverged) {
break;
}
}
System.out.println("最少需要 " + clusters.size() + " 个车站。");
}
public static List<Cluster> initialCluster(List<Double[]> dataList, int k) {
List<Cluster> clusters = new ArrayList<>();
for (int i = 0; i < k; i++) {
double[] coordinates = dataList.get(i);
Cluster cluster = new Cluster(i + 1, coordinates);
clusters.add(cluster);
}
return clusters;
}
public static void assignDataToCluster(List<Double[]> dataList, List<Cluster> clusters) {
for (Double[] data : dataList) {
int clusterNumber = getClosestClusterNumber(data, clusters);
Cluster cluster = clusters.get(clusterNumber);
cluster.getData().add(data);
clusterMap.put(data.hashCode(), cluster);
}
}
public static int getClosestClusterNumber(Double[] data, List<Cluster> clusters) {
double minDistance = Double.MAX_VALUE;
int closestCluster = 0;
for (Cluster cluster : clusters) {
double distance = euclideanDistance(data, cluster.getCentroid());
if (distance < minDistance) {
minDistance = distance;
closestCluster = cluster.getNumber() - 1;
}
}
return closestCluster;
}
public static double euclideanDistance(Double[] a, double[] b) {
double distance = 0;
for (int i = 0; i < a.length; i++) {
distance += Math.pow(a[i] - b[i], 2);
}
return Math.sqrt(distance);
}
}
class Cluster {
private int number;
private double[] centroid;
private List<Double[]> data = new ArrayList<>();
public Cluster(int number, double[] centroid) {
this.number = number;
this.centroid = centroid;
}
public int getNumber() {
return number;
}
public double[] getCentroid() {
return centroid;
}
public void setCentroid(double[] centroid) {
this.centroid = centroid;
}
public List<Double[]> getData() {
return data;
}
}
本文介绍了三种不同的算法，分别是Dijkstra算法、Floyd算法和K-Means算法。这些算法可以在解决车站数量问题时提供帮助，可以根据具体需求选择适合的算法进行使用。