采用回溯法求取教材P156图8.4所示图着色问题的一个可行解 的java源代码

以下是采用回溯法求解图着色问题的Java源代码：

import java.util.Arrays;

public class GraphColoring {

    private int numOfVertices;
    private int numOfColors;
    private int[] colors;
    private int[][] adjacencyMatrix;

    public GraphColoring(int[][] adjacencyMatrix, int numOfColors) {
        this.adjacencyMatrix = adjacencyMatrix;
        this.numOfVertices = adjacencyMatrix.length;
        this.numOfColors = numOfColors;
        this.colors = new int[numOfVertices];
    }

    public boolean isSafe(int vertex, int color) {
        for (int i = 0; i < numOfVertices; i++) {
            if (adjacencyMatrix[vertex][i] == 1 && color == colors[i]) {
                return false;
            }
        }
        return true;
    }

    public boolean graphColoringUtil(int vertex) {
        if (vertex == numOfVertices) {
            return true;
        }
        for (int i = 1; i <= numOfColors; i++) {
            if (isSafe(vertex, i)) {
                colors[vertex] = i;
                if (graphColoringUtil(vertex + 1)) {
                    return true;
                }
                colors[vertex] = 0;
            }
        }
        return false;
    }

    public void graphColoring() {
        if (graphColoringUtil(0)) {
            System.out.println("Graph can be colored using " + Arrays.toString(colors));
        } else {
            System.out.println("Graph cannot be colored using " + numOfColors + " colors");
        }
    }

    public static void main(String[] args) {
        int[][] adjacencyMatrix = {{0, 1, 1, 1},
                                   {1, 0, 1, 0},
                                   {1, 1, 0, 1},
                                   {1, 0, 1, 0}};
        int numOfColors = 3;
        GraphColoring graphColoring = new GraphColoring(adjacencyMatrix, numOfColors);
        graphColoring.graphColoring();
    }
}

在该代码中，首先定义了一个GraphColoring类，其中包括邻接矩阵、顶点数量、颜色数量和颜色数组等成员变量。isSafe() 方法用于检查当前顶点是否可以被染上指定的颜色，graphColoringUtil() 方法用于递归地在所有顶点上尝试染色，graphColoring() 方法则用于启动染色过程并输出结果。在主函数中，我们构造了一个邻接矩阵，定义了颜色数量为3，并创建了一个GraphColoring对象，并调用了它的graphColoring()方法来求解该图的着色问题。