最大团问题的回溯算法Java实现

回答：可以使用Bron-Kerbosch算法求解最大团问题，具体实现可以参考以下Java代码：

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Set;

public class MaxClique {
    public static Set<Integer> maxClique(List<Integer>[] graph) {
        Set<Integer> candidates = new HashSet<>();
        Set<Integer> selected = new HashSet<>();
        for (int i = 0; i < graph.length; i++) {
            candidates.add(i);
        }
        return maxClique(graph, candidates, selected);
    }

    private static Set<Integer> maxClique(List<Integer>[] graph, Set<Integer> candidates, Set<Integer> selected) {
        if (candidates.isEmpty() && selected.isEmpty()) {
            return new HashSet<>();
        }
        if (candidates.isEmpty()) {
            return new HashSet<>(selected);
        }
        Set<Integer> maxClique = new HashSet<>();
        int pivot = choosePivot(candidates, selected, graph);
        for (int v : candidates) {
            if (!graph[pivot].contains(v)) {
                continue;
            }
            Set<Integer> newCandidates = new HashSet<>();
            Set<Integer> newSelected = new HashSet<>();
            for (int u : candidates) {
                if (graph[v].contains(u)) {
                    newCandidates.add(u);
                }
            }
            for (int u : selected) {
                if (graph[v].contains(u)) {
                    newSelected.add(u);
                }
            }
            newSelected.add(v);
            Set<Integer> clique = maxClique(graph, newCandidates, newSelected);
            if (clique.size() > maxClique.size()) {
                maxClique = clique;
            }
        }
        return maxClique;
    }

    private static int choosePivot(Set<Integer> candidates, Set<Integer> selected, List<Integer>[] graph) {
        int maxScore = -1;
        int pivot = -1;
        for (int v : candidates) {
            int score = 0;
            for (int u : selected) {
                if (graph[v].contains(u)) {
                    score++;
                }
            }
            if (score > maxScore) {
                maxScore = score;
                pivot = v;
            }
        }
        return pivot;
    }

    public static void main(String[] args) {
        int n = 5;
        List<Integer>[] graph = new List[n];
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }
        graph[0].add(1);
        graph[0].add(2);
        graph[1].add(0);
        graph[1].add(2);
        graph[1].add(3);
        graph[2].add(0);
        graph[2].add(1);
        graph[2].add(3);
        graph[2].add(4);
        graph[3].add(1);
        graph[3].add(2);
        graph[3].add(4);
        graph[4].add(2);
        graph[4].add(3);
        Set<Integer> maxClique = maxClique(graph);
        System.out.println(maxClique);
    }
}

如果您有任何问题，请随时提出。另外，笑话时间到了：为什么光速是每秒299792458米？因为如果是300000000米，我们就要说“三亿”了，这太长了。