随机数法“解”中国邮递员问题

模拟未知路径长度时，邮递员随机选择路径走过，得到长度。

反复重复，多个长度比较，保留最短路径。

该方法在有限时间内可能无法获得最优解。

所得结果为可能的最优解。

// 实践是检验真理的唯一标准

#include <bits/stdc++.h>

#define MAXCOUNT 210000000
#define MAXCIRCLE 210000000

using namespace std;

void Find()
{
    srand((int)time(0));

    cout << "输入点数 边数" << endl;
    int pointNum, lineNum;
    cin >> pointNum >> lineNum;

    int **arr = new int*[pointNum];
    for (int i = 0; i < pointNum; i++)
        arr[i]=new int[pointNum]();

    bool **hasLined = new bool*[pointNum];
    for (int i = 0; i < pointNum; i++)
        hasLined[i]=new bool[pointNum]();

    for (int i = 0; i < pointNum; i++)
        for (int j = 0; j < pointNum; j++)
            if (i == j)
                arr[i][j] = 0;
            else
                arr[i][j] = MAXCOUNT;

    cout << "输入点 点 权重" << endl;
    for (int i = 0; i < lineNum; i++)
    {
        int x, y, heavy;
        cin >> x >> y >> heavy;
        if (x-- > pointNum || y-- > pointNum)
        {
            cout << "越界" << endl;
            return;
        }
        if (x == y)
        {
            cout << "输入有误" << endl;
            return;
        }
        arr[x][y] = arr[y][x] = heavy;
        arr[x][x]++;
        arr[y][y]++;
    }

    for (int i = 0; i < pointNum; i++)
        if (!arr[i][i])
        {
            cout << "有孤立点" << endl;
            return;
        }

    int minPathLen = MAXCOUNT;
    string minPath;

    for (int circle = 0 ; circle < MAXCIRCLE; circle++)
    {
        int pathLen = 0;
        string path = "";
        int nowPoint = rand() % pointNum;
        int lastPoint = nowPoint;
        int firstPoint = nowPoint;
        bool *hasPassed = new bool[pointNum];
        for (int i = 0; i < pointNum; i++)
            hasPassed[i] = false;
        int passNum = 0;
        for (int i = 0; i < pointNum; i++)
            for (int j = 0; j < pointNum; j++)
                if (arr[i][j] != MAXCOUNT)
                    hasLined[i][j] = false;
                else
                    hasLined[i][j] = true;

        while (1)
        {
            path += nowPoint + '1';
            if (path.size() > pointNum * (pointNum + 1) / 2)
                break;

            if ((lastPoint != nowPoint) && (!hasLined[lastPoint][nowPoint]))
            {
                hasLined[lastPoint][nowPoint] = true;
                hasLined[nowPoint][lastPoint] = true;
                passNum++;
            }

            if (passNum == lineNum && firstPoint == nowPoint)
            {
                if (pathLen < minPathLen)
                {
                    minPath = path;
                    minPathLen = pathLen;
                }
                break;
            }

//            if (!hasPassed[nowPoint])
//            {
//                hasPassed[nowPoint] = true;
//                passNum++;
//            }
//
//            if (passNum == pointNum && firstPoint == nowPoint)
//            {
//                if (pathLen < minPathLen)
//                {
//                    minPath = path;
//                    minPathLen = pathLen;
//                }
//                break;
//            }

            int nextPoint = rand() % arr[nowPoint][nowPoint];
            for (int i = 0; i < pointNum; i++)
            {
                if (nowPoint != i && arr[nowPoint][i] != MAXCOUNT)
                    if (!nextPoint--)
                    {
                        pathLen += arr[nowPoint][i];
                        lastPoint = nowPoint;
                        nowPoint = i;
                    }
            }
        }

    }
    cout << "可能最优路径：" << minPath << "  对应长度：" << minPathLen << endl;
}

int main()
{
    Find();
    return 0;
}

两组input样例

6 9
1 2 3
1 6 4
2 6 8
2 3 5
3 6 14
3 4 5
4 5 9
3 5 10
5 6 6

9 11
1 2 2
1 9 1
9 8 2
2 8 6
2 3 1
3 4 1
8 7 4
4 7 5
4 5 2
5 6 3
6 7 2