该程序的目标是枚举一个人可以通过地铁系统从 A 站到达 L 站的所有可能路径，而无需多次经过轨道。我知道教练告诉我们有 640 条可能的路径，我们使用邻接矩阵在 C 语言中编写了这个程序作为早期作业。现在的目标是做同样的事情，即枚举所有可能的路线并打印出每条路线，除了使用类（特别是 3 个：SubwaySystem、Station 和 Track），这次不使用矩阵。这是地铁系统本身的示意图。
我和我的助教讨论了这个项目以及如何处理它。他给了我一些想法，例如使用数组来表示车站和轨道，我决定使用我在帖子底部的整个代码中展示的方法。
让我向您展示我的代码中我无法解决的问题区域（递归对我来说是新的）。
void SubwaySystem::SearchRoute(int Current_Station_ID)
{
if(my_station[Current_Station_ID].track_starting_ID == 33) // Find a successful route to Station L.
//The condition is set to check for 33 because a track_starting_ID of 33 would correspond to station L.
{
count_routes++; //Add 1 into the variable “count_routes”
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
{
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].node_1; //save this track
SearchRoute(Current_Station_ID++); //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
}
}
}
}
}
让我解释一下变量代表什么：
Current_Station_ID基本上是一个类似 i 的计数器。
my_station是一个大小为 12 的数组，包含所有 12 个站点。
my_track是一个大小为 34 的数组，其中包含每个站点之间所有可能的轨道组合。
track_starting_ID表示某个站点的可能轨道在 my_track 数组中开始的位置。抱歉，我不知道如何以更好的方式表达这一点。例如，如果您在帖子底部的整个代码部分中引用我在 SubwaySystem 构造函数中初始化的车站数组和轨道数组。你可以看到track_starting_ID指某个车站的轨道开始的起始位置。即，starting_ID 为 0 对应于 my_track[0]，my_track[0] 是从站“A”引导的轨道的开始，starting_ID 为 1 是指 my_track(1)，它是从站“B”引导的轨道的开始。并且起始 ID 为 6 对应于位置 [6] 的 my_track 数组中从站“C”开始的轨道。等等。（希望这使它更清晰而不是更混乱）。
track_size表示您可以从图片中看到的每个站点的轨道数量。例如，站 B 的轨道大小将为 5，因为有 5 条轨道从 B 站发芽
。visited和node_1和node_2是不言自明的。visited 是一个布尔变量，用于检查是否已访问过一个站点，并且节点分别是当前轨道每一侧的站点。
问题是我不知道如何修复递归函数。几天前我和我的助教讨论了这个问题，我告诉他我想用我的功能完成什么。我们一起编写了一些伪代码，以便更清楚地了解我尝试编写的函数的目标是什么：
SearchRoute(int Current_Station_ID)
{
if ( ) //Find a successful route to Station L
{
… //Add 1 into the variable “count_routes”
… //Print out this route
return;
}
else //Get into recursive Function Body
{
//Use the track array to get all of its connected stations
for(int i = starting_ID; i < starting_ID + current size; i++)
{
if() // if this track is not visited before
{
… //mark this track as visited
… //mark its corresponding track as visited
… //save this track
SearchRoute( nextStaton_ID); // Recursive
… //Backtrack this track
… //mark this track as unvisited
… //mark its corresponding track as unvisited
}
}
}
}
这就是我理解的问题所在：我似乎无法正确实现我的递归函数 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，我要么陷入无限循环，要么得到一个单一的轨道，例如 A 到 B，这取决于我尝试放入递归调用本身的内容。
为了清楚起见，这是整个程序，不包括我在上面发布的递归部分：
//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; // node_1 and node_2 represent stations (for example
char node_2; // node_1 would be station A and node_2 would be station B)
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;
}
Track::~Track()
{
}
Track::Track(char pass_track1, char pass_track2)
{
node_1 = pass_track1;
node_2 = pass_track2;
visited = false;
}
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;
}
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;
}
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;
}
//This is where the above recursive function SearchRoute goes. I posted it separately so it's easier to read.
// **main**
#include <iostream>
#include <string>
//#include "subway.h"
using namespace std;
int main()
{
SubwaySystem findPaths;
findPaths.SearchRoute(0);
}