汉密尔顿最短路径用java语言编写

下面是一个用Java语言编写的解决汉密尔顿最短路径的算法示例：

import java.util.Arrays;

public class HamiltonianPath {

    private int[][] graph;
    private int[] path;
    private boolean[] visited;
    private int n;
    private int minDist;

    public HamiltonianPath(int[][] graph) {
        this.graph = graph;
        this.n = graph.length;
        this.path = new int[n];
        this.visited = new boolean[n];
        Arrays.fill(visited, false);
        this.minDist = Integer.MAX_VALUE;
    }

    public int findMinDist() {
        visited[0] = true;
        path[0] = 0;
        dfs(1, 0);
        return minDist;
    }

    private void dfs(int depth, int dist) {
        if (depth == n) {
            minDist = Math.min(minDist, dist + graph[path[n - 1]][0]);
            return;
        }
        for (int i = 1; i < n; i++) {
            if (!visited[i]) {
                visited[i] = true;
                path[depth] = i;
                dfs(depth + 1, dist + graph[path[depth - 1]][i]);
                visited[i] = false;
            }
        }
    }

    public static void main(String[] args) {
        int[][] graph = {
            {0, 2, 9, 10},
            {1, 0, 6, 4},
            {15, 7, 0, 8},
            {6, 3, 12, 0}
        };
        HamiltonianPath hp = new HamiltonianPath(graph);
        System.out.println("The minimum distance is: " + hp.findMinDist());
    }
}

在这个示例中，我们使用了深度优先搜索算法来遍历所有可能的路径，并计算出每条路径的长度。对于每个节点，我们遍历未访问的节点，并将其添加到路径中，然后递归地继续搜索下一个节点。最终，我们找到一条包含所有节点的路径，并计算出其长度，然后将其与当前的最小路径长度进行比较，更新最小路径长度。