用邻接矩阵算最小生成树的总个数java代码

以下是使用邻接矩阵计算最小生成树总个数的Java代码示例：

import java.util.*;

public class MinimumSpanningTreeCount {
    private int V; // 图的顶点数
    private int[][] graph; // 图的邻接矩阵

    public MinimumSpanningTreeCount(int[][] graph) {
        this.graph = graph;
        this.V = graph.length;
    }

    // 计算最小生成树的总个数
    public int countMinimumSpanningTrees() {
        int[][] laplacian = calculateLaplacianMatrix(); // 计算拉普拉斯矩阵
        int[][] reducedLaplacian = reduceMatrix(laplacian); // 缩减矩阵
        return calculateDeterminant(reducedLaplacian); // 计算行列式，即最小生成树的总个数
    }

    // 计算拉普拉斯矩阵
    private int[][] calculateLaplacianMatrix() {
        int[][] laplacian = new int[V][V];

        // 初始化对角线元素为度数之和，非对角线元素为负的边权重
        for (int i = 0; i < V; i++) {
            for (int j = 0; j < V; j++) {
                if (i == j) {
                    laplacian[i][j] = calculateDegree(i);
                } else {
                    laplacian[i][j] = -graph[i][j];
                }
            }
        }

        return laplacian;
    }

    // 计算顶点的度数之和
    private int calculateDegree(int v) {
        int degree = 0;
        for (int i = 0; i < V; i++) {
            degree += graph[v][i];
        }
        return degree;
    }

    // 缩减矩阵
    private int[][] reduceMatrix(int[][] matrix) {
        int[][] reducedMatrix = new int[V - 1][V - 1];

        for (int i = 1; i < V; i++) {
 for (int j = 1; j < V; j++) {
                reducedMatrix[i - 1][j - 1] = matrix[i][j];
            }
        }

        return reducedMatrix;
    }

    // 计算矩阵的行列式
    private int calculateDeterminant(int[][] matrix) {
        int n = matrix.length;
        int[][] temp = Arrays.copyOf(matrix, n);

        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                int factor = temp[j][i] / temp[i][i];
                for (int k = i; k < n; k++) {
                    temp[j][k] -= factor * temp[i][k];
                }
            }
        }

        int determinant = 1;
        for (int i = 0; i < n; i++) {
            determinant *= temp[i][i];
        }

        return determinant;
    }

    public static void main(String[] args) {
        int[][] graph = {
            {0, 2, 0, 6, 0},
            {2, 0, 3, 8, 5},
            {0, 3, 0, 0, 7},
            {6, 8, 0, 0, 9},
            {0, 5, 7, 9, 0}
        };

        MinimumSpanningTreeCount mstCount = new MinimumSpanningTreeCount(graph);
        int count = mstCount.countMinimumSpanningTrees();
        System.out.println("Minimum Spanning Tree Count: " + count);
    }
}

以上代码中，我们使用了邻接矩阵来表示图，并实现了计算最小生成树总个数的方法。在`main`方法中，我们创建了一个示例图的邻接矩阵，并计算最小生成树的总个数并输出结果。请注意，这只是一个简单的示例，你可以根据自己的需求修改代码来适应不同的图结构。