实现函数的麻烦（递归）
该计划的目的是列举一个人可以通过地铁系统从车站A到车站L的所有可能路径，而不会超过轨道多次。我知道教师告诉我们有640条可能的路径，我们使用邻接矩阵将该程序编写为C中的早期赋值。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，除非使用类（特别是3：SubwaySystem，Station和Track）这样做，这次没有使用矩阵。这是地铁系统本身的示意图。
我和我的TA讨论了这个程序以及如何处理它。他给了我一些想法，例如使用数组来表示电台和曲目，我决定使用我在帖子底部的整个代码中显示的方法。
让我向您展示我无法解决的代码中有问题的区域（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
}
}
}
}
}
让我解释变量代表什么：
Current_Station_ID 基本上是一个像i的计数器
my_station 是一个大小为12的数组，可容纳所有12个站点
my_track 是一个大小为34的数组，它包含每个相应电台之间所有可能的音轨组合。
track_starting_ID 表示某个电台的可能音轨在my_track数组中开始的位置。抱歉，我不确定如何以更好的方式表达这一点。例如，如果您引用在岗位底部的整个代码部分中在SubwaySystem构造函数中初始化的工作站数组和轨道数组。您可以看到 track_starting_ID 指的是某个电台的音轨开始的起始位置。即，starting_ID为0对应于my_track [0]，它是从电台引出的轨道的开始＆＃34; A＆＃34;并且starting_ID为1指的是my_track（1），它是从车站＆＃34; B＆＃34;开始的轨道的开始。而start_ID为6对应于从车站前进的轨道＆＃34; C＆＃34;在位置[6]的my_track数组中。等等。 （希望这会使它更清晰，而不是更令人困惑）
track_size 表示从图片中可以看到的每个电台的曲目数量。例如，由于有5个轨道从站B发出，因此站B的轨道大小将是5
访问和 node_1 和 node_2 是不言自明的。 visit是一个布尔变量，它检查是否已访问过一个站点，并且节点分别是当前轨道两侧的站点。
问题是我不知道如何修复递归发生的功能。几天前我和我的TA讨论了这个问题，我告诉他我的功能是什么。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：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，要么得到单个轨道，例如A到B，这取决于我试图放入递归调用本身。
这是整个程序，不包括我为了清楚起见而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);
}
3 个答案:
答案 0 :(得分：2)
好的，这是一个有效的解决方案，它提供了605个解决方案，我认为是正确的
// RandomTest.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include <iostream>
#include <string>
using namespace std;
class Track
{
public:
//Default Constructor
Track();
//Overload Constructor
Track(char, char, int station, int opposite);
//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;
int connected_station;
int opposite_track;
};
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
void SearchRoute(int Current_Station_ID, int from_track_id, Track **currentPath, int pathCount);
};
// **cpp**
//#include "subway.h"
using namespace std;
Track::Track()
{
visited = 0;
}
Track::~Track()
{
}
Track::Track(char pass_track1, char pass_track2, int station, int opposite)
{
node_1 = pass_track1;
node_2 = pass_track2;
connected_station = station;
opposite_track = opposite;
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', 1, 1);
my_track[1] = Track('b', 'a', 0, 0);
my_track[2] = Track('b', 'c', 2, 6);
my_track[3] = Track('b', 'd', 3, 8);
my_track[4] = Track('b', 'e', 4, 10);
my_track[5] = Track('b', 'f', 5, 15);
my_track[6] = Track('c', 'b', 1, 2);
my_track[7] = Track('c', 'e', 4, 11);
my_track[8] = Track('d', 'b', 1, 3);
my_track[9] = Track('d', 'e', 4, 12);
my_track[10] = Track('e', 'b', 1, 4);
my_track[11] = Track('e', 'c', 2, 7);
my_track[12] = Track('e', 'd', 3, 9);
my_track[13] = Track('e', 'g', 6, 17);
my_track[14] = Track('e', 'h', 7, 19);
my_track[15] = Track('f', 'b', 1, 5);
my_track[16] = Track('f', 'h', 7, 20);
my_track[17] = Track('g', 'e', 4, 13);
my_track[18] = Track('g', 'k', 10, 28);
my_track[19] = Track('h', 'e', 4, 14);
my_track[20] = Track('h', 'f', 5, 16);
my_track[21] = Track('h', 'i', 8, 24);
my_track[22] = Track('h', 'j', 9, 26);
my_track[23] = Track('h', 'k', 10, 29);
my_track[24] = Track('i', 'h', 7, 21);
my_track[25] = Track('i', 'k', 10, 30);
my_track[26] = Track('j', 'h', 7, 22);
my_track[27] = Track('j', 'k', 10, 30);
my_track[28] = Track('k', 'g', 6, 18);
my_track[29] = Track('k', 'h', 7, 23);
my_track[30] = Track('k', 'i', 8, 25);
my_track[31] = Track('k', 'j', 9, 27);
my_track[32] = Track('k', 'l', 11, 33);
my_track[33] = Track('l', 'k', 10, 32);
//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()
{
}
void SubwaySystem::SearchRoute(int Current_Station_ID, int from_track_id, Track **currentPath, int pathCount)
{
if(my_station[Current_Station_ID].track_starting_ID == 33)
{
count_routes++; //Add 1 into the variable “count_routes”
cout << count_routes << " ";
for(int i= 0; i < pathCount; i++)
{
cout << *currentPath[i];
}
cout << endl;
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++)
{
//check all the tracks that we have visited before
bool visited = false;
for(int n = 0; n < pathCount; n++)
{
if(currentPath[n] == &my_track[i] || i == currentPath[n]->opposite_track) visited = true;
}
if(!visited)
{
int nextStation = my_track[i].connected_station;
currentPath[pathCount] = &my_track[i];
SearchRoute(nextStation, i, currentPath, pathCount + 1);
}
}
}
}
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 "subway.h"
int _tmain(int argc, _TCHAR* argv[])
{
Track *tempTracks[34];
SubwaySystem findPaths;
findPaths.SearchRoute(0, -1, tempTracks, 0);
getchar();
return 0;
}
答案 1 :(得分：1)
我认为你的主要问题在于：
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++); <<<<<<<< PROBLEM
i--; //Backtrack this track <<<<<<< Also this will do nothing
my_track[Current_Station_ID].visited = 0; <<<<<<< Now Current_Station_ID is 1 more than you are expecting it to be.
my_track[Current_Station_ID].node_2 = 0;//mark its corresponding track as unvisited
你在块的中间执行Current_Station_ID ++，然后再次使用它，好像它与之前的值相同，++运算符实际上是将Current_Station_ID的值增加1。
您也不需要在for循环中锁定此项。所以它应该是这样的：
void SubwaySystem::SearchRoute(int Current_Station_ID, int from_track_id, Track *currentPath, int pathCount)
{
if(my_station[Current_Station_ID].track_starting_ID == 33)
{
count_routes++; //Add 1 into the variable “count_routes”
cout << count_routes << " ";
for(int i= 0; i < pathCount; i++)
{
cout << my_track[i];
}
cout << endl;
return;
}
else //Get into recursive Function Body
{
if(from_track_id >= 0) my_track[from_track_id].visited = 1;
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++)
{
int nextStation = my_track[i].node_2; ///<<<<<<< But you will need to change node_2 to be an int, and use the station number, not letter when you set them up
if(my_track[i].visited == 0)
{
currentPath[pathCount] = my_track[i];
SearchRoute(nextStation, i, currentPath, pathCount + 1);
}
}
if(from_track_id >= 0) my_track[from_track_id].visited = 0;
}
}
然后在你的主要功能中执行以下操作：
int main()
{
Track tempTracks[34];
SubwaySystem findPaths;
findPaths.SearchRoute(0, -1, tempTracks, 0);
}
答案 2 :(得分：1)
我找到了640条路线：
#include <stdio.h>
const char *connectom[] = {
"B", // A
"ACDEF", // B
"BE", // C
"BE", // D
"CDBGH", // E
"BH", // F
"EK", // G
"EFJKI", // H
"HK", // I
"HK", // J
"HIJGL", // K
"K" // L
};
char tracks[0x100];
char strout[0x100];
void path(char x, char *s) {
*s++ = x;
if(x == 'L') {
*s = 0;
printf("path=%s\n", strout);
} else {
for(const char *p = connectom[x - 'A']; *p; p++) {
unsigned char track_ndx = x > *p? (x << 4) ^ *p : (*p << 4) ^ x;
if(tracks[track_ndx] == 0) {
tracks[track_ndx] = 1;
path(*p, s);
tracks[track_ndx] = 0;
} // if
} // for
} // else
} // path
int main(int argc, char **argv) {
path('A', strout);
} // main
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