图的团覆盖的Java库

有没有人知道解决小团体封面问题的库或代码（最好是Java）

我发现了一个OCaml，但我想使用一些我可以更容易集成的东西

我还找到了Java和C代码来查找图中的最大团，但我不知道如何利用这些代码来查找团覆盖（例如，迭代删除最大团，直到没有剩余节点为止，不会产生最佳解决方案）。

确定图中是否有3团的Java程序： 问题定义：

import java.util.AbstractMap.SimpleEntry;
import java.util.Map;
import java.util.AbstractMap;
import java.util.ArrayList;

public class Main{
    public static boolean three_clique(String encoding){
        if (encoding.length() == 0){
            return false;
        }
        String[] elements = encoding.substring(1, encoding.indexOf(")")).split(",");
        encoding = encoding.substring(encoding.indexOf(")")+2); 
        encoding = encoding.substring(0, encoding.length()-1);
        ArrayList<Map.Entry<Integer, Integer>> arr = new ArrayList<Map.Entry<Integer, Integer>>();
        String[] pairs = encoding.split(";");
        if (pairs.length == 1){
            return false;
        } 
        for(int x = 0; x < pairs.length; x++){
            String str = pairs[x].substring(1, pairs[x].length()-1);
            String[] items = str.split(",");
            int left = Integer.parseInt(items[0]);
            int right = Integer.parseInt(items[1]);
            arr.add(new AbstractMap.SimpleEntry(left, right));
        }
        for(int x = 0; x < elements.length; x++){
            for(int y = 0; y < elements.length; y++){
                for(int z = 0; z < elements.length; z++){
                    if (x != y && y != z && z != x){
                        int one = Integer.parseInt(elements[x]);
                        int two = Integer.parseInt(elements[y]);
                        int three = Integer.parseInt(elements[z]);
                        if (is_connected(arr, one, two) &&
                            is_connected(arr, two, three) &&
                            is_connected(arr, three, one)){
                                return true;
                        }
                    }
                }
            }
        }
        return false;
    }
    public static boolean is_connected(ArrayList<Map.Entry<Integer, Integer>> arr, int left, int right){
        for(int x = 0; x < arr.size(); x++){
            if (left == arr.get(x).getKey() && arr.get(x).getValue() == right){
                return true;
            }
            if (right == arr.get(x).getKey() && arr.get(x).getValue() == left){
                return true;
            }
        }
        return false;
    }
    public static void main(String[] args){
        tests();
    }

    public static void tests(){
        String encoding = "";
        boolean expected;
        String msg = "";

        encoding = "";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be false";
        doTest(encoding, expected, msg);

        encoding = "(1)()";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2)((1,2))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(3,1))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(3,4))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3,4)((1,2);(2,3);(3,1);(1,4))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(1,3))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);
    }
    public static void doTest(String encoding, boolean expected, String msg){
        boolean result = three_clique(encoding);
        if (result == expected){
            System.out.print(".");
        }
        else{
            System.out.println("\n" + msg);
        }
    }
}

输入格式：

import java.util.AbstractMap.SimpleEntry;
import java.util.Map;
import java.util.AbstractMap;
import java.util.ArrayList;

public class Main{
    public static boolean three_clique(String encoding){
        if (encoding.length() == 0){
            return false;
        }
        String[] elements = encoding.substring(1, encoding.indexOf(")")).split(",");
        encoding = encoding.substring(encoding.indexOf(")")+2); 
        encoding = encoding.substring(0, encoding.length()-1);
        ArrayList<Map.Entry<Integer, Integer>> arr = new ArrayList<Map.Entry<Integer, Integer>>();
        String[] pairs = encoding.split(";");
        if (pairs.length == 1){
            return false;
        } 
        for(int x = 0; x < pairs.length; x++){
            String str = pairs[x].substring(1, pairs[x].length()-1);
            String[] items = str.split(",");
            int left = Integer.parseInt(items[0]);
            int right = Integer.parseInt(items[1]);
            arr.add(new AbstractMap.SimpleEntry(left, right));
        }
        for(int x = 0; x < elements.length; x++){
            for(int y = 0; y < elements.length; y++){
                for(int z = 0; z < elements.length; z++){
                    if (x != y && y != z && z != x){
                        int one = Integer.parseInt(elements[x]);
                        int two = Integer.parseInt(elements[y]);
                        int three = Integer.parseInt(elements[z]);
                        if (is_connected(arr, one, two) &&
                            is_connected(arr, two, three) &&
                            is_connected(arr, three, one)){
                                return true;
                        }
                    }
                }
            }
        }
        return false;
    }
    public static boolean is_connected(ArrayList<Map.Entry<Integer, Integer>> arr, int left, int right){
        for(int x = 0; x < arr.size(); x++){
            if (left == arr.get(x).getKey() && arr.get(x).getValue() == right){
                return true;
            }
            if (right == arr.get(x).getKey() && arr.get(x).getValue() == left){
                return true;
            }
        }
        return false;
    }
    public static void main(String[] args){
        tests();
    }

    public static void tests(){
        String encoding = "";
        boolean expected;
        String msg = "";

        encoding = "";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be false";
        doTest(encoding, expected, msg);

        encoding = "(1)()";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2)((1,2))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(3,1))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(3,4))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3,4)((1,2);(2,3);(3,1);(1,4))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(1,3))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);
    }
    public static void doTest(String encoding, boolean expected, String msg){
        boolean result = three_clique(encoding);
        if (result == expected){
            System.out.print(".");
        }
        else{
            System.out.println("\n" + msg);
        }
    }
}

名为

three_-clique

的方法的输入是一个字符串编码，表示一个无向图，如下所示：

(1,2,3)((1,2);(2,3);(3,1))

此编码表示具有三个节点的无向图：1、2、3。在1和2、2和3以及3和1之间有边。它看起来像一个三角形。显然，这个无向图包含一个3团

无向图的这种编码不包含3-团：

(1,2,3)((1,2);(3,4))

代码：

import java.util.AbstractMap.SimpleEntry;
import java.util.Map;
import java.util.AbstractMap;
import java.util.ArrayList;

public class Main{
    public static boolean three_clique(String encoding){
        if (encoding.length() == 0){
            return false;
        }
        String[] elements = encoding.substring(1, encoding.indexOf(")")).split(",");
        encoding = encoding.substring(encoding.indexOf(")")+2); 
        encoding = encoding.substring(0, encoding.length()-1);
        ArrayList<Map.Entry<Integer, Integer>> arr = new ArrayList<Map.Entry<Integer, Integer>>();
        String[] pairs = encoding.split(";");
        if (pairs.length == 1){
            return false;
        } 
        for(int x = 0; x < pairs.length; x++){
            String str = pairs[x].substring(1, pairs[x].length()-1);
            String[] items = str.split(",");
            int left = Integer.parseInt(items[0]);
            int right = Integer.parseInt(items[1]);
            arr.add(new AbstractMap.SimpleEntry(left, right));
        }
        for(int x = 0; x < elements.length; x++){
            for(int y = 0; y < elements.length; y++){
                for(int z = 0; z < elements.length; z++){
                    if (x != y && y != z && z != x){
                        int one = Integer.parseInt(elements[x]);
                        int two = Integer.parseInt(elements[y]);
                        int three = Integer.parseInt(elements[z]);
                        if (is_connected(arr, one, two) &&
                            is_connected(arr, two, three) &&
                            is_connected(arr, three, one)){
                                return true;
                        }
                    }
                }
            }
        }
        return false;
    }
    public static boolean is_connected(ArrayList<Map.Entry<Integer, Integer>> arr, int left, int right){
        for(int x = 0; x < arr.size(); x++){
            if (left == arr.get(x).getKey() && arr.get(x).getValue() == right){
                return true;
            }
            if (right == arr.get(x).getKey() && arr.get(x).getValue() == left){
                return true;
            }
        }
        return false;
    }
    public static void main(String[] args){
        tests();
    }

    public static void tests(){
        String encoding = "";
        boolean expected;
        String msg = "";

        encoding = "";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be false";
        doTest(encoding, expected, msg);

        encoding = "(1)()";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2)((1,2))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(3,1))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(3,4))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3,4)((1,2);(2,3);(3,1);(1,4))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(1,3))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);
    }
    public static void doTest(String encoding, boolean expected, String msg){
        boolean result = three_clique(encoding);
        if (result == expected){
            System.out.print(".");
        }
        else{
            System.out.println("\n" + msg);
        }
    }
}

import java.util.AbstractMap.SimpleEntry；
导入java.util.Map；
导入java.util.AbstractMap；
导入java.util.ArrayList；
公共班机{
公共静态布尔三组（字符串编码）{
if（encoding.length（）==0）{
返回false；
}
String[]elements=encoding.substring（1，encoding.indexOf（“）”）.split（“，”）；
encoding=encoding.substring（encoding.indexOf（“）”）+2）；
encoding=encoding.substring（0，encoding.length（）-1）；
ArrayList arr=新的ArrayList（）；
String[]pairs=encoding.split（“；”）；
if（pairs.length==1）{
返回false；
} 
对于（int x=0；x

输出

程序在屏幕上输出一系列七个点，这意味着所有单元测试都通过。为了证明它是有效的，可以为像这样的大型无向图添加更多的单元测试用例：

（1,2,3,4,5）（（1,5）；（1,4）；（1,3）；（1,2）；（1,1）；）

，看看它是否返回false

运行时复杂性：

import java.util.AbstractMap.SimpleEntry;
import java.util.Map;
import java.util.AbstractMap;
import java.util.ArrayList;

public class Main{
    public static boolean three_clique(String encoding){
        if (encoding.length() == 0){
            return false;
        }
        String[] elements = encoding.substring(1, encoding.indexOf(")")).split(",");
        encoding = encoding.substring(encoding.indexOf(")")+2); 
        encoding = encoding.substring(0, encoding.length()-1);
        ArrayList<Map.Entry<Integer, Integer>> arr = new ArrayList<Map.Entry<Integer, Integer>>();
        String[] pairs = encoding.split(";");
        if (pairs.length == 1){
            return false;
        } 
        for(int x = 0; x < pairs.length; x++){
            String str = pairs[x].substring(1, pairs[x].length()-1);
            String[] items = str.split(",");
            int left = Integer.parseInt(items[0]);
            int right = Integer.parseInt(items[1]);
            arr.add(new AbstractMap.SimpleEntry(left, right));
        }
        for(int x = 0; x < elements.length; x++){
            for(int y = 0; y < elements.length; y++){
                for(int z = 0; z < elements.length; z++){
                    if (x != y && y != z && z != x){
                        int one = Integer.parseInt(elements[x]);
                        int two = Integer.parseInt(elements[y]);
                        int three = Integer.parseInt(elements[z]);
                        if (is_connected(arr, one, two) &&
                            is_connected(arr, two, three) &&
                            is_connected(arr, three, one)){
                                return true;
                        }
                    }
                }
            }
        }
        return false;
    }
    public static boolean is_connected(ArrayList<Map.Entry<Integer, Integer>> arr, int left, int right){
        for(int x = 0; x < arr.size(); x++){
            if (left == arr.get(x).getKey() && arr.get(x).getValue() == right){
                return true;
            }
            if (right == arr.get(x).getKey() && arr.get(x).getValue() == left){
                return true;
            }
        }
        return false;
    }
    public static void main(String[] args){
        tests();
    }

    public static void tests(){
        String encoding = "";
        boolean expected;
        String msg = "";

        encoding = "";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be false";
        doTest(encoding, expected, msg);

        encoding = "(1)()";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2)((1,2))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(3,1))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(3,4))";
        expected = false;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3,4)((1,2);(2,3);(3,1);(1,4))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);

        encoding = "(1,2,3)((1,2);(2,3);(1,3))";
        expected = true;
        msg = "expected '" + encoding + "' encoding to be " + expected;
        doTest(encoding, expected, msg);
    }
    public static void doTest(String encoding, boolean expected, String msg){
        boolean result = three_clique(encoding);
        if (result == expected){
            System.out.print(".");
        }
        else{
            System.out.println("\n" + msg);
        }
    }
}

---

具体来说，计算复杂性是O（n^3）。所以它的效率非常低，而且肯定不是解决这个问题的最佳算法。但它展示了如何在Java中处理和解决小团体问题的起点。

除非OCaml版本有一些优化，否则通过生成所有分区和测试，用Java编写暴力版本应该很容易。感谢您的建议，我将保留此选项作为最后的手段。是的，OCAml版本似乎有很好的运行时性能。