基于动态规划的TSP问题的实现算法

import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.HashMap;

public class FiveFour {

    private double[][] dArray; //距离矩阵
    private int length; //距离矩阵的长度
    private int lengthOfLength; //距离矩阵长度字符串的长度
    private String allzero = ""; //0组成的字符串  最大值是length个(length - 1)连接起来的字符串，同样最小值是length个0连接起来
    private String biggest ="";
    private List<String> list = new ArrayList<String>();  //城市流列表
    private Map<String, Double> store;   //存储中间数据
    private String notExist = "不存在";
    private String firnalRoad = notExist; //最终的路径，即距离矩阵的列号取值
    private String firnalCityFlow = ""; //最终形成的城市流
    private String min = notExist; //最终求得的最小值
    private String allFlowTime = notExist; //求解所有城市流的时间
    private String guihuaTime = notExist; //动态规划的时间

    /** Creates a new instance of TwentyTwo */
    public FiveFour(double[][] dArray) {
        if (this.check(dArray)) {
            this.dArray = dArray;
            this.length = dArray.length;
            this.lengthOfLength = (length - 1 + "").length();
            for (int zeroLength = 0; zeroLength < (length * lengthOfLength);) {
                allzero += 0;
                zeroLength = allzero.length();
            }
            for(int i = this.length; i > 0; i--){
                this.biggest += this.toLengthOfLength(i - 1);
            }
            long start = System.currentTimeMillis();
            this.allFlow();
            long end = System.currentTimeMillis();
            this.allFlowTime = end - start + "毫秒";
            start = System.currentTimeMillis();
            this.initstoreMap();
            this.guihua(this.length - 2);
            end = System.currentTimeMillis();
            this.guihuaTime = end - start + "毫秒";
        }
    }

    public String getFirnalRoad() {
        return this.firnalRoad;
    }

    public String getFirnalCityFlow() {
        if ("".equals(this.firnalCityFlow)) {
            return this.notExist;
        }
        return this.firnalCityFlow;
    }

    public String getMin() {
        return this.min;
    }

    public String getAllFlowTime() {
        return this.allFlowTime;
    }

    public String getGuihuaTime() {
        return this.guihuaTime;
    }
    //输入距离矩阵的有效性判读

    private boolean check(double[][] dArray) {
        if (dArray.length < 3) {
            System.out.println("错误信息：距离矩阵长度过小");
            return false;
        }
        for (int i = 0; i < dArray.length; i++) {  // 每个double[]的长度都进行判断
            if (dArray.length != dArray[i].length) {
                System.out.println("错误信息：距离数组长度不合法");
                return false;
            }
        }
        for (int i = 0; i < dArray.length; i++) {
            if (!oneZero(dArray[i], i)) {
                System.out.println("错误信息：距离数组顺序或元素值设置不合法");
                return false;
            }
        }
        return true;
    }
    //对于一个doulbe类型的数组，只有第i个元素为0的判断

    private boolean oneZero(double[] dArray, int i) {
        int numOfZero = 0;
        for (double d : dArray) {
            if (d == 0.0) {
                numOfZero++;
            }
        }
        if (numOfZero == 1 && (dArray[i] == 0)) {
            return true;
        } else {
            return false;
        }
    }
    //判断一个城市流是否合法

    private boolean oneFlow(String str) {
        //将一个字符串更改为一个字符链表
        List<String> listString = new ArrayList<String>();
        for (int i = 0; i < (this.length * this.lengthOfLength);) {
            listString.add(str.substring(i, i + this.lengthOfLength));
            i += this.lengthOfLength;
        }
        //如果有相同的元素，则false
        for (int i = 0; i < (this.length - 1); i++) {
            for (int j = i + 1; j < this.length; j++) {
                if (listString.get(i * this.lengthOfLength).equals(listString.get(j * this.lengthOfLength))) {
                    return false;
                }
            }
        }
        //如果有距离矩阵全0对角线上的元素，则false
        for (int i = 0; i < listString.size(); i++) {
            if (Integer.parseInt(listString.get(i)) == i) {
                return false;
            }
        }
        //排除没有遍历所有城市的情况（从0点出发到达0点）
        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < this.length;) {
            map.put(i, Integer.parseInt(str.substring(i, i + this.lengthOfLength)));
            i += this.lengthOfLength;
        }
        int allcity = 0;
        for (int i = 0;;) {
            i = map.get(i);
            allcity++;
            if (i == 0) {
                break;
            }
        }
        if (allcity < this.length) {
            return false;
        }
        return true;
    }
    //初始化存储map

    private void initstoreMap() {
        this.store = new HashMap<String, Double>();
        //存距离矩阵最后一行可能的列号
        for (int i = 0; i < this.length - 1; i++) {
            this.store.put(this.toLengthOfLength(i), this.dArray[this.length - 1][i]);
        }
        //存距离矩阵倒数两行可能的列号
        for (int i = 0; i < this.length; i++) {
            if(i == this.length -2)
                continue;
            for (int j = 0; j < this.length - 1; j++) {
                if (i == j) {
                    continue;
                }
                store.put(this.toLengthOfLength(i) + this.toLengthOfLength(j), this.dArray[this.length - 2][i] + store.get(this.toLengthOfLength(j)));
            }
        }
    }

    //两个相近的城市流，前length - 2 - temp个数相同，后面不同，用动态规划实现
    private void guihua(int temp) {
        if (list.size() == 1) {
            this.firnalRoad = list.get(0);
            this.thePrint(list.get(0));
            this.min = this.store.get(list.get(0)) + "";
            return;
        }
        for (int i = 0; i < (list.size() - 1); i++) {
            int next = (i + 1);
            if (list.get(i).substring(0, temp * this.lengthOfLength).equals(list.get(next).substring(0, temp * this.lengthOfLength))) {
                double iValue = 0;
                double nextValue = 0;

                iValue = this.dArray[temp][Integer.parseInt(list.get(i).substring(temp, temp + this.lengthOfLength))] +
                        store.get(list.get(i).substring((temp + 1) * this.lengthOfLength));
                nextValue = this.dArray[temp][Integer.parseInt(list.get(next).substring(temp, temp + this.lengthOfLength))] +
                        store.get(list.get(next).substring((temp + 1) * this.lengthOfLength));

                this.store.put(list.get(i).substring(temp * this.lengthOfLength), iValue);
                this.store.put(list.get(next).substring(temp * this.lengthOfLength), nextValue);

                if (iValue >= nextValue) {
                    list.remove(i);
                } else {
                    list.remove(next);
                }
                i--;
            }
        }
        this.guihua(temp - 1);
    }
    //组成所有的城市流

    private void allFlow() {
        while (!this.biggest.equals(this.allzero)) {
            this.allzero = this.addone(this.allzero);
            if (this.oneFlow(this.allzero)) {
                this.list.add(this.allzero);
            }
        }
    }
    //将length进制的字符串加1操作

    private String addone(String str) {
        List<String> listString = new ArrayList<String>();
        for (int i = 0; i < (this.length * this.lengthOfLength);) {
            listString.add(str.substring(i, i + this.lengthOfLength));
            i += this.lengthOfLength;
        }
        for (int i = (length - 1); i > -1; i--) {
            int last = Integer.parseInt(listString.get(i));
            if (last == (length - 1)) {
                last = 0;
                String strLast = this.toLengthOfLength(last);
                listString.set(i, strLast);
            } else {
                last++;
                String strLast = this.toLengthOfLength(last);
                listString.set(i, strLast);
                break;
            }
        }
        String ret = "";
        for (String s : listString) {
            ret += s;
        }
        return ret;
    }
    //如果一个int字符串长度不够lengthOfLength 则补足

    private String toLengthOfLength(Object i) {
        String returnString = i.toString();
        while (returnString.length() < this.lengthOfLength) {
            returnString = (0 + returnString);
        }
        return returnString;
    }
    //将一个字符串键值映射，并标准输出

    private void thePrint(String str) {
        Map<Integer, Integer> map = new HashMap<Integer, Integer>();
        for (int i = 0; i < this.length;) {
            map.put(i, Integer.parseInt(str.substring(i, i + this.lengthOfLength)));
            i += this.lengthOfLength;
        }
        String cityFlow = this.toLengthOfLength(0);
        for (int i = 0;;) {
            i = map.get(i);
            cityFlow += this.toLengthOfLength(i);
            if (i == 0) {
                break;
            }
        }
        for (int i = 0; i < this.length + 1;) {
            if (i < (this.length)) {
                this.firnalCityFlow += Integer.parseInt(cityFlow.substring(i, i + this.lengthOfLength)) + "->";
            } else {
                this.firnalCityFlow += Integer.parseInt(cityFlow.substring(i, i + this.lengthOfLength));
            }
            i += this.lengthOfLength;
        }
    }

    public static void main(String[] args) {
        double[][] first = {
            {0, 2, 1, 3, 4, 5, 5, 6},
            {1, 0, 4, 4, 2, 5, 5, 6},
            {5, 4, 0, 2, 2, 6, 5, 6},
            {5, 2, 2, 0, 3, 2, 5, 6},
            {4, 2, 4, 2, 0, 3, 5, 6},
            {4, 2, 4, 2, 3, 0, 5, 6},
            {4, 2, 4, 2, 4, 3, 0, 6},
            {4, 2, 4, 2, 8, 3, 5, 0}};
        long start = System.currentTimeMillis();
        FiveFour ff = new FiveFour(first);
        System.out.println("路径是：" + ff.getFirnalRoad());
        System.out.println("城市顺序：" + ff.getFirnalCityFlow());
        System.out.println("最小值：" + ff.getMin());
        System.out.println("生成所有合法城市流用时：" + ff.getAllFlowTime());
        System.out.println("动态规划求解过程用时：" + ff.getGuihuaTime());
    }
}

详细的说明和完整的代码，谢啦！

上学时候做的，现在想想觉得还有些问题呢...
PS:JE的回复引用不好使了？

虽然说明已经很多了，但是还是希望可以在更多的地方加上注释。不过很感谢楼主的分享，刚学习这方面内容，很需要啊。