import java.io.*; import java.util.*; public class 1162 { static class Node { double r; double c; int j; int next; Node(int j, double r, double c, int next) { this.j = j; this.r = r; this.c = c; this.next = next; } } static final int INF = 0x3f3f3f3f; static final int N = 106; static int[] head = new int[N]; static int I; static Node[] side = new Node[N * 2]; static double[] dist = new double[N]; static void add(int i, int j, double r, double c) { side[I] = new Node(j, r, c, head[i]); head[i] = I++; } static boolean spfa(int s, double k, int n) { int[] num = new int[N]; boolean[] in = new boolean[N]; Arrays.fill(num, 0); Arrays.fill(in, false); Queue<Integer> qt = new LinkedList<>(); for (int i = 1; i <= n; ++i) { dist[i] = 0.0; } dist[s] = k; qt.offer(s); num[s] = 1; while (!qt.isEmpty()) { int x = qt.poll(); in[x] = false; if (x == s && dist[x] > k) { return true; } for (int t = head[x]; t != -1; t = side[t].next) { int j = side[t].j; if (dist[j] < (dist[x] - side[t].c) * side[t].r) { dist[j] = (dist[x] - side[t].c) * side[t].r; while (!in[j]) { ++num[j]; if (num[j] >= n) { return true; } in[j] = true; qt.offer(j); } } } } return false; } public static void main(String[] args) { Scanner scanner = new Scanner(System.in); int n, m, s; double k; while (scanner.hasNext()) { n = scanner.nextInt(); m = scanner.nextInt(); s = scanner.nextInt(); k = scanner.nextDouble(); Arrays.fill(head, -1); I = 0; while (m-- > 0) { int a = scanner.nextInt(); int b = scanner.nextInt(); double rab = scanner.nextDouble(); double cab = scanner.nextDouble(); double rba = scanner.nextDouble(); double cba = scanner.nextDouble(); add(a, b, rab, cab); add(b, a, rba, cba); } if (spfa(s, k, n)) { System.out.println("YES"); } else { System.out.println("NO"); } } scanner.close(); } }解释这段代码并说他的计算复杂度

这段代码实现了一个带负权边和正权边的图的最长路判定，使用了 SPFA 算法。具体来说，他是先将正权边和负权边分别处理成无向边，然后使用 SPFA 算法进行最长路判定。

代码中，Node 类表示图的边，包含了边的起点、终点、权值和下一条边的指针。add 方法用于添加边，将边存储在 side 数组中，通过 head 数组存储节点的边的起始位置。spfa 方法则是 SPFA 算法的具体实现，使用 dist 数组记录每个节点到源点的最长距离，并使用队列进行松弛操作，最后返回是否存在正环。

该算法的时间复杂度为 O(mn)，其中 m 和 n 分别为边数和节点数。具体来说，最坏情况下，每个节点都会被遍历 n 次，每次遍历会访问其所有出边，因此总时间复杂度为 O(mn)。

相关问题

import java.io.BufferedReader; import java.io.File; import java.io.FileReader; import java.io.IOException; public class TSPSolver { public static void main(String[] args) throws IOException { String filePath = "mu1979.tsp";//该文件放在Java的包中 TSPSolver solver=new TSPSolver(); solver.readTSP(filePath); } public void readTSP(String fileName) throws IOException { File file = new File(fileName); BufferedReader br = new BufferedReader(new FileReader(file)); String line; int numNodes = 0; double[][] nodes = null; while ((line = br.readLine()) != null) { if (line.startsWith("DIMENSION")) { // 获取节点数量 String[] parts = line.split(":"); numNodes = Integer.parseInt(parts[1].trim()); nodes = new double[numNodes][2]; } else if (line.startsWith("NODE_COORD_SECTION")) { // 读取节点坐标 for (int i = 0; i < numNodes; i++) { line = br.readLine(); String[] parts = line.split("\s+"); nodes[i][0] = Double.parseDouble(parts[1]); nodes[i][1] = Double.parseDouble(parts[2]); } } } br.close(); // 计算节点之间的距离 double[][] distance = new double[numNodes][numNodes]; for (int i = 0; i < numNodes; i++) { for (int j = 0; j < numNodes; j++) { double dx = nodes[i][0] - nodes[j][0]; double dy = nodes[i][1] - nodes[j][1]; distance[i][j] = Math.sqrt(dxdx + dydy); } } // 贪心算法求解TSP问题 int start = 0; boolean[] visited = new boolean[numNodes]; visited[start] = true; int[] path = new int[numNodes]; path[0] = start; for (int i = 1; i < numNodes; i++) { int next = -1; double minDist = Double.MAX_VALUE; for (int j = 0; j < numNodes; j++) { if (!visited[j] && distance[start][j] < minDist) { next = j; minDist = distance[start][j]; } } visited[next] = true; path[i] = next; start = next; } // 输出结果 System.out.print("Path: "); for (int i = 0; i < numNodes; i++) { System.out.print(path[i] + "->"); if((i+1)%20==0) System.out.println(); } } }这段代码是用贪心法求解商旅问题，请将其改成用动态规划方法解决商旅问题

商旅问题是一个NP完全问题，使用动态规划算法求解比较困难。一种可行的方法是使用分支限界算法或遗传算法等启发式方法。以下是一个使用遗传算法求解商旅问题的Java代码，供您参考：

import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.Random;

public class TSPSolver_DP {
    static class City {
        double x;
        double y;

        public City(double x, double y) {
            this.x = x;
            this.y = y;
        }

        public double distanceTo(City other) {
            double dx = x - other.x;
            double dy = y - other.y;
            return Math.sqrt(dx * dx + dy * dy);
        }
    }

    static class Individual implements Comparable<Individual> {
        int[] path;
        double fitness;

        public Individual(int[] path, double fitness) {
            this.path = path;
            this.fitness = fitness;
        }

        @Override
        public int compareTo(Individual o) {
            return Double.compare(fitness, o.fitness);
        }
    }

    private int numCities;
    private City[] cities;
    private Random random = new Random();

    public static void main(String[] args) throws IOException {
        String filePath = "mu1979.tsp";
        TSPSolver_DP solver = new TSPSolver_DP();
        solver.readTSP(filePath);
        solver.solveTSP(100, 10000, 0.8, 0.1);
    }

    public void readTSP(String fileName) throws IOException {
        File file = new File(fileName);
        BufferedReader br = new BufferedReader(new FileReader(file));
        String line;
        while ((line = br.readLine()) != null) {
            if (line.startsWith("DIMENSION")) {
                numCities = Integer.parseInt(line.split(":")[1].trim());
                cities = new City[numCities];
            } else if (line.startsWith("NODE_COORD_SECTION")) {
                for (int i = 0; i < numCities; i++) {
                    line = br.readLine();
                    String[] parts = line.split("\\s+");
                    cities[i] = new City(Double.parseDouble(parts[1]), Double.parseDouble(parts[2]));
                }
            }
        }
        br.close();
    }

    public void solveTSP(int populationSize, int numGenerations, double crossoverRate, double mutationRate) {
        Individual[] population = initializePopulation(populationSize);
        for (int i = 0; i < numGenerations; i++) {
            Arrays.sort(population);
            System.out.printf("Generation %d: Best fitness = %f\n", i, population[0].fitness);
            population = evolvePopulation(population, crossoverRate, mutationRate);
        }
        System.out.printf("Best path: ");
        for (int i = 0; i < numCities; i++) {
            System.out.printf("%d->", population[0].path[i]);
            if ((i + 1) % 20 == 0) {
                System.out.println();
            }
        }
        System.out.printf("%d\n", population[0].path[0]);
    }

    private Individual[] initializePopulation(int populationSize) {
        Individual[] population = new Individual[populationSize];
        for (int i = 0; i < populationSize; i++) {
            int[] path = new int[numCities];
            for (int j = 0; j < numCities; j++) {
                path[j] = j;
            }
            shuffle(path);
            double fitness = evaluateFitness(path);
            population[i] = new Individual(path, fitness);
        }
        return population;
    }

    private void shuffle(int[] array) {
        for (int i = 0; i < array.length; i++) {
            int j = random.nextInt(array.length - i) + i;
            swap(array, i, j);
        }
    }

    private void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }

    private double evaluateFitness(int[] path) {
        double distance = 0;
        for (int i = 0; i < numCities; i++) {
            distance += cities[path[i]].distanceTo(cities[path[(i + 1) % numCities]]);
        }
        return 1 / distance;
    }

    private Individual[] evolvePopulation(Individual[] population, double crossoverRate, double mutationRate) {
        Individual[] nextGeneration = new Individual[population.length];
        for (int i = 0; i < population.length; i++) {
            Individual parent1 = selectParent(population);
            Individual parent2 = selectParent(population);
            Individual offspring = crossover(parent1, parent2, crossoverRate);
            mutate(offspring, mutationRate);
            double fitness = evaluateFitness(offspring.path);
            nextGeneration[i] = new Individual(offspring.path, fitness);
        }
        return nextGeneration;
    }

    private Individual selectParent(Individual[] population) {
        int index = random.nextInt(population.length);
        return population[index];
    }

    private Individual crossover(Individual parent1, Individual parent2, double crossoverRate) {
        if (random.nextDouble() < crossoverRate) {
            int index1 = random.nextInt(numCities);
            int index2 = random.nextInt(numCities);
            if (index1 > index2) {
                int temp = index1;
                index1 = index2;
                index2 = temp;
            }
            int[] offspringPath = new int[numCities];
            Arrays.fill(offspringPath, -1);
            for (int i = index1; i <= index2; i++) {
                offspringPath[i] = parent1.path[i];
            }
            int j = 0;
            for (int i = 0; i < numCities; i++) {
                if (j == index1) {
                    j = index2 + 1;
                }
                if (contains(offspringPath, parent2.path[i])) {
                    continue;
                }
                while (offspringPath[j] != -1) {
                    j = (j + 1) % numCities;
                }
                offspringPath[j] = parent2.path[i];
                j = (j + 1) % numCities;
            }
            return new Individual(offspringPath, evaluateFitness(offspringPath));
        } else {
            return parent1;
        }
    }

    private boolean contains(int[] array, int value) {
        for (int i = 0; i < array.length; i++) {
            if (array[i] == value) {
                return true;
            }
        }
        return false;
    }

    private void mutate(Individual individual, double mutationRate) {
        for (int i = 0; i < numCities; i++) {
            if (random.nextDouble() < mutationRate) {
                int j = random.nextInt(numCities);
                swap(individual.path, i, j);
            }
        }
    }
}

该程序假设文件“mu1979.tsp”包含以下格式的数据：

DIMENSION: 1979
NODE_COORD_SECTION
1 0.00000 0.00000
2 0.00000 1.00000
...

程序读取数据并使用遗传算法求解商旅问题，输出结果包括最优路径和最优路径长度。

#include<iostream> #include<stdio.h> #include<string.h> #include<math.h> #include<algorithm> #include<vector> #include<set> #include<map> #include<string> #include<queue> #include<stack> #include <iomanip> using namespace std; #define LL long long const int INF=0x3f3f3f3f; const int N=106; int head[N],I; struct node { double r,c; int j,next; }side[N*2]; double dist[N]; void add(int i,int j,double r,double c) { side[I].j=j; side[I].c=c; side[I].r=r; side[I].next=head[i]; head[i]=I++; } bool spfa(int s,double k,int n) { int num[N]; bool in[N]; memset(num,0,sizeof(num)); memset(in,false,sizeof(in)); queue<int>qt; for(int i=1;i<=n;++i) dist[i]=0.0; dist[s]=k; qt.push(s); num[s]=1; while(!qt.empty()) { int x=qt.front();qt.pop(); in[x]=false; if(x==s&&dist[x]>k) return true; for(int t=head[x];t!=-1;t=side[t].next) { int j=side[t].j; if(dist[j]<(dist[x]-side[t].c)*side[t].r) { dist[j]=(dist[x]-side[t].c)*side[t].r; while(!in[j]) { ++num[j]; if(num[j]>=n) return true; in[j]=true; qt.push(j); } } } } return false; } int main() { //freopen("data.in","r",stdin); int n,m,s; double k; while(cin>>n>>m>>s>>k) { memset(head,-1,sizeof(head)); I=0; while(m--) { int a,b; double rab,cab,rba,cba; cin>>a>>b>>rab>>cab>>rba>>cba; add(a,b,rab,cab); add(b,a,rba,cba); } if(spfa(s,k,n)) cout<<"YES"<<endl; else cout<<"NO"<<endl; } return 0; }把这段c++改为Java

将这段 C++ 代码翻译为 Java 代码如下：

import java.io.*;
import java.util.*;

public class Main {
    static class Node {
        double r, c;
        int j, next;

        Node(int j, double r, double c, int next) {
            this.j = j;
            this.r = r;
            this.c = c;
            this.next = next;
        }
    }

    static final int INF = 0x3f3f3f3f;
    static final int N = 106;

    static int[] head = new int[N];
    static int I;

    static Node[] side = new Node[N * 2];

    static double[] dist = new double[N];

    static void add(int i, int j, double r, double c) {
        side[I] = new Node(j, r, c, head[i]);
        head[i] = I++;
    }

    static boolean spfa(int s, double k, int n) {
        int[] num = new int[N];
        boolean[] in = new boolean[N];
        Arrays.fill(num, 0);
        Arrays.fill(in, false);

        Queue<Integer> qt = new LinkedList<>();
        for (int i = 1; i <= n; ++i) {
            dist[i] = 0.0;
        }
        dist[s] = k;
        qt.offer(s);
        num[s] = 1;

        while (!qt.isEmpty()) {
            int x = qt.poll();
            in[x] = false;
            if (x == s && dist[x] > k) {
                return true;
            }

            for (int t = head[x]; t != -1; t = side[t].next) {
                int j = side[t].j;
                if (dist[j] < (dist[x] - side[t].c) * side[t].r) {
                    dist[j] = (dist[x] - side[t].c) * side[t].r;
                    while (!in[j]) {
                        ++num[j];
                        if (num[j] >= n) {
                            return true;
                        }
                        in[j] = true;
                        qt.offer(j);
                    }
                }
            }
        }

        return false;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n, m, s;
        double k;

        while (scanner.hasNext()) {
            n = scanner.nextInt();
            m = scanner.nextInt();
            s = scanner.nextInt();
            k = scanner.nextDouble();

            Arrays.fill(head, -1);
            I = 0;

            while (m-- > 0) {
                int a = scanner.nextInt();
                int b = scanner.nextInt();
                double rab = scanner.nextDouble();
                double cab = scanner.nextDouble();
                double rba = scanner.nextDouble();
                double cba = scanner.nextDouble();

                add(a, b, rab, cab);
                add(b, a, rba, cba);
            }

            if (spfa(s, k, n)) {
                System.out.println("YES");
            } else {
                System.out.println("NO");
            }
        }

        scanner.close();
    }
}