递归函数问题并找到所有可能的路线

Question

我正在尝试打印地铁系统中所有可能的路径，该地铁系统的站点从 A 到 L。换句话说，目标是找出一个人可以采取多少条可能的路线来通过地铁系统而不经过不止一次的曲目。我知道有 640 条可能的路径，因为我之前使用 C 中的邻接矩阵编写了这个程序。现在我正在尝试编写相同的程序，除了使用 C++ 中的类而不使用邻接矩阵。

我遇到的问题是我似乎无法正确实现递归函数 SearchRoute，因为我需要打印路径、标记路径，然后再次取消标记路径以允许回溯。当我打印出最终结果时，我只得到了从 A 到 B 的轨迹，这显然意味着某些地方显然是错误的。

这就是我认为的问题所在：我知道在我的 SubwaySystem::SearchRoute 函数中，我使用了 if 和 else 语句，这显然不允许调用我的递归函数，但我尝试使用另一个 if 语句而不是否则，但我不太确定条件会是什么。

void SubwaySystem::SearchRoute(int Current_Station_ID)
{
    while(Current_Station_ID < 33)
    {
        cout << "In while loop\n";
        // \\ Checking progress
        if(Current_Station_ID == 0)  //Find a successful route to Station L
        {
            count_routes++; //Add 1 into the variable “count_routes”
            cout << "In if statement\n";
            // \\Checking progress
            cout << count_routes << " " << my_track[Current_Station_ID] << endl; //Print out this route
            return;
        }
        else //Get into recursive Function Body
        {
            for(int i = my_station[Current_Station_ID].track_starting_ID; i < my_station[Current_Station_ID].track_starting_ID + my_station[Current_Station_ID].track_size; i++)
            {
                if(my_track[Current_Station_ID].visited == 0)  //if this track is not visited before
                {
                    cout << "In recursive part of function\n";
                    // \\ Checking progress
                    my_track[Current_Station_ID].visited = 1; //mark this track as visited
                    my_track[Current_Station_ID].node_2 = 1; //mark its corresponding track as visited
                    cout << my_track[Current_Station_ID] << endl; //save this track
                    SearchRoute(Current_Station_ID + 1); //Recursive
                    i--; //Backtrack this track
                    my_track[Current_Station_ID].visited = 0;//mark this track as unvisited
                    my_track[Current_Station_ID].node_2 = 0;//mark its corresponding track as unvisited
                }
            }
        }
    }
}

我还尝试在整个程序中添加打印语句以跟踪整个程序的进度。由于我上面指定的原因，我的递归函数永远不会被调用（至少这就是我认为它不起作用的原因）。由于某种原因，我无法弄清楚为什么我的默认和重载轨道构造函数被多次调用。

如果您能帮我找出代码中的问题区域/告诉我正确的方法，我将不胜感激。我厌倦了思考这个问题。提前致谢。

这是一个 TU 中的其余程序：

//Function Declarations
#include <iostream>
#include <string>

using namespace std;

#ifndef SUBWAY_H
#define SUBWAY_H

class Track
{
public:
    //Default Constructor
    Track();

    //Overload Constructor
    Track(char, char);

    //Destructor
    ~Track();

    //Member variables
    char node_1;
    char node_2;
    bool visited;
};

class Station
{
public:
    //Default Constructor
    Station();

    //Destructor
    ~Station();

    //Overload Constructor
    Station(char, int, int);

    //Member variables
    char station_name;
    int track_starting_ID;
    int track_size;
};

class SubwaySystem
{
public:
    //Default Constructor
    SubwaySystem();

    //Destructor
    ~SubwaySystem();

    //Recursive function
    void SearchRoute(int);

    //Other member functions
    friend ostream& operator<<(ostream& os, const Track& my_track);
    friend ostream& operator<<(ostream& os, const Station& my_station);


    //Member variables
    Track my_track[34];
    Station my_station[12];

    int count_routes;
    int Current_Station_ID;

    //String to save found route
};

#endif

// **cpp**

//Function Definitions
#include <iostream>
#include <string>

//#include "subway.h"

using namespace std;

Track::Track()
{
    visited = 0;
    //cout << "Default Track has been called\n";
    //\\ Checking progress
}


Track::~Track()
{
}


Track::Track(char pass_track1, char pass_track2)
{
    node_1 = pass_track1;
    node_2 = pass_track2;
    visited = false;
    //cout << "Overload Track constructor has been called\n";
    // \\ Checking progress
}


Station::Station()
{
}


Station::~Station()
{
}


Station::Station(char pass_station_name, int pass_start, int pass_size)
{
    station_name = pass_station_name;
    track_starting_ID = pass_start;
    track_size = pass_size;
    //cout << "Overload station has been called\n";
    // \\ Checking progress
}


SubwaySystem::SubwaySystem()
{
    //Initialize tracks
    //node_1, node_2
    my_track[0] = Track('a', 'b');
    my_track[1] = Track('b', 'a');
    my_track[2] = Track('b', 'c');
    my_track[3] = Track('b', 'd');
    my_track[4] = Track('b', 'e');
    my_track[5] = Track('b', 'f');
    my_track[6] = Track('c', 'b');
    my_track[7] = Track('c', 'e');
    my_track[8] = Track('d', 'b');
    my_track[9] = Track('d', 'e');
    my_track[10] = Track('e', 'b');
    my_track[11] = Track('e', 'c');
    my_track[12] = Track('e', 'd');
    my_track[13] = Track('e', 'g');
    my_track[14] = Track('e', 'h');
    my_track[15] = Track('f', 'b');
    my_track[16] = Track('f', 'h');
    my_track[17] = Track('g', 'e');
    my_track[18] = Track('g', 'k');
    my_track[19] = Track('h', 'e');
    my_track[20] = Track('h', 'f');
    my_track[21] = Track('h', 'i');
    my_track[22] = Track('h', 'j');
    my_track[23] = Track('h', 'k');
    my_track[24] = Track('i', 'h');
    my_track[25] = Track('i', 'k');
    my_track[26] = Track('j', 'h');
    my_track[27] = Track('j', 'k');
    my_track[28] = Track('k', 'g');
    my_track[29] = Track('k', 'h');
    my_track[30] = Track('k', 'i');
    my_track[31] = Track('k', 'j');
    my_track[32] = Track('k', 'l');
    my_track[33] = Track('l', 'k');
    //Initialize stations
    //station_name, track_starting_ID, track_size
    my_station[0] = Station('a', 0, 1);
    my_station[1] = Station('b', 1, 5);
    my_station[2] = Station('c', 6, 2);
    my_station[3] = Station('d', 8, 2);
    my_station[4] = Station('e', 10, 5);
    my_station[5] = Station('f', 15, 2);
    my_station[6] = Station('g', 17, 2);
    my_station[7] = Station('h', 19, 5);
    my_station[8] = Station('i', 24, 2);
    my_station[9] = Station('j', 26, 2);
    my_station[10] = Station('k', 28, 5);
    my_station[11] = Station('l', 33, 1);
    //Initiaize other members
    count_routes = 0;
    Current_Station_ID = 0;
    //cout << "SubwaySystem constructor called\n";
    // \\ Checking progress
}


SubwaySystem::~SubwaySystem()
{
}

ostream& operator<<(ostream& os, const Track& my_track)
{
    os << my_track.node_1 << '.' << my_track.node_2;
    return os;
}

ostream& operator<<(ostream& os, const Station& my_station)
{
    os << my_station.station_name << '.' << my_station.track_starting_ID << '.' << my_station.track_size;
    return os;
}



// **main**

#include <iostream>
#include <string>

//#include "subway.h"

using namespace std;

int main(int argc, char **argv)
{
    SubwaySystem Test;
    Test.SearchRoute(0);
}

如果“检查进度”打印语句使代码更难阅读，我很抱歉。

Answer 1

你的第一个条件

while(Current_Station_ID < 33)
{
    cout << "In while loop\n";
    // \\ Checking progress
    if(Current_Station_ID == 0)  //Find a successful route to Station L

这将总是正确，因为这就是您在 main 中调用的内容：

int main(int argc, char **argv)
{
    SubwaySystem Test;
    Test.SearchRoute(0);
}

所以，你永远不会进入 else 分支，因为第一个总是会被占用，它会立即结束 (return)

Answer 2

使用递归算法，当您到达最终目的地时，您的 if 语句应该为真。 else 语句是当您仍在旅途中时。在这种情况下，当您访问每条轨道时，您已经“到达”。继续您的旅程由 else 语句处理。 for 循环查找所有“下一个”停止点。

我会将递归调用扩展到：

void SubwaySystem::SearchRoute(int visited_count, int current_station, string route);

如果满足visited_count，则打印路线。否则，选择下一个尚未访问过的站点。 每次递归调用时，选择下一个要访问的站点，将当前访问次数加 1，并将当前位置附加到路线字符串中。

目前你也有一个错误，如果你的 for 循环，my_station 只上升到 11，但 Current_Station_ID 可能是 33。