地图着色问题 --- java(BFS)

Posted 2022-01-01 So istes immer

 已知中国地图，对各省进行着色，要求相邻省所使用的颜色不同，并保证使用的颜色总数最少。

public class Map 
	
	private static final int BOARD_NUMBER = 31;
    private String[] board = new String[BOARD_NUMBER];
    private int[][] edge = new int[BOARD_NUMBER][BOARD_NUMBER];
    //初始化所有顶点均涂色0
    private int[] color = new int[BOARD_NUMBER];
    
    public Map(String[] board, int[][] edge) 
        this.board = board;
        this.edge = edge;
    
    
    public boolean colour(int colorKind) 
    	int vertex = 0;    //从图中的一个顶点开始
    	//vertex从0~BOARD_NUMBER-1表示所有顶点
    	while(vertex < BOARD_NUMBER) 
    		int flag = 1;
    		//如果发现colorKind种颜色不能满足，返回false
    		if(vertex == -1) 
    			return false;
    		
    		color[vertex]++;
    		//当涂色超过colorKind种，回溯
    		if(color[vertex] > colorKind) 
    			color[vertex] = 0;
    			vertex--;
    			continue;
    		
    		for(int i = 0; i < vertex; ++i) 
    			//发现邻接点涂相同颜色
    			if (edge[vertex][i] == 1 && color[vertex] == color[i]) 
                    flag = 0;
                    break;
                
    		
    		//发现邻接点涂相同颜色,该结点重涂
    		if(flag == 0) continue;
    		vertex++;
    	
    	for(int i = 0; i < BOARD_NUMBER; ++i) 
    		System.out.println(board[i] + "涂色为：" + color[i]);
    	
    	return true;
    
	
	public static void main(String[] args) 
		String board[]="广西","广东","云南","贵州","湖南","江西","福建","浙江","安徽","湖北","重庆","四川","西藏","青海",
	     "新疆","甘肃","陕西","宁夏","内蒙","北京","黑龙江","吉林","辽宁","天津","河北","山西","河南","江苏","山东","上海","海南","台湾","香港","澳门";
		// 1、广西; 2、广东; 3、云南; 4、贵州; 5、湖南; 6、江西; 7、福建; 8、浙江; 9、安徽;10、湖北;11、重庆;12、四川;13、西藏;14、青海;15、新疆;16、甘肃;
		// 17、陕西;18、宁夏;19、内蒙;20、北京;21、黑龙江;22、吉林;23、辽宁;24、天津;25、河北;26、山西;27、河南;28、江苏;29、山东;30、上海;31、海南;
		// 用邻接矩阵建立图结构
		int edge[][]=
		 0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//1
		 1,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//2
		 1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//3
		 1,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//4
		 1,1,0,1,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//5
		 0,1,0,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//6
		 0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//7
		 0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,//8
		 0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,//9
		 0,0,0,0,1,1,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,//10
		 0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//11
		 0,0,1,1,0,0,0,0,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//12
		 0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//13
		 0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//14
		 0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,//15
		 0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,//16
		 0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,//17
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,//18
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,//19
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,//20
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,//21
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,//22
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,//23
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,//24
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,0,1,0,0,//25
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,//26
		 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,0,//27
		 0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,//28
		 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,//29
		 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,//30
		 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0//31
		;
        Map p = new Map(board, edge);
        int colorKind = 1;
        while(!p.colour(colorKind)) 
        	colorKind++;
        
        System.out.println("最少要涂" + colorKind + "种颜色");
    

输出 

广西涂色为：1
广东涂色为：2
云南涂色为：2
贵州涂色为：3
湖南涂色为：4
江西涂色为：1
福建涂色为：3
浙江涂色为：2
安徽涂色为：3
湖北涂色为：2
重庆涂色为：1
四川涂色为：4
西藏涂色为：1
青海涂色为：2
新疆涂色为：3
甘肃涂色为：1
陕西涂色为：3
宁夏涂色为：2
内蒙涂色为：4
北京涂色为：1
黑龙江涂色为：1
吉林涂色为：2
辽宁涂色为：1
天津涂色为：2
河北涂色为：3
山西涂色为：1
河南涂色为：4
江苏涂色为：1
山东涂色为：2
上海涂色为：3
海南涂色为：1
最少要涂4种颜色