迷宫路径&广度优先求解&深度优先求解&迷宫游戏
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求解迷宫的通道是数据结构中一个很经典的问题,解决这个问题大概有两种思路,一
种是深度优先,一种是广度优先。深度优先是只要找到一条通道就可以了,而广度优先
则是寻找最短的路径。下面我们来对这两种思想做一个剖析。
深度优先:
如果要用一句俗语来解释深度优先的话,那么一定是“不撞南墙不回头”。深度优先的重点于“深”,找到一条路就一头扎下去,直到走不通才回头。由于这里有了回退的要求,所以就要借用栈来实现。
用深度优先来求解迷宫路径的算法:
#define _CRT_SECURE_NO_WARNINGS#include<iostream>#include<cassert>using namespace std;typedef struct NodePos{ int x; int y; NodePos(int row=0, int col=0) :x(row) , y(col){}}Node;//因为迷宫用的栈 是我自己的,为了方便验证,我将栈也给出template<typename T>class Stack{public: Stack() :_capacity(0) , _size(0) , _ptr(NULL) {} ~Stack() { delete[] _ptr; _size = 0; _capacity = 0; _ptr = NULL; } void Push(const T& data); void Pop(); T Top(); int Size(); bool Empty();private: void CheckCapacity() { if (_size >= _capacity) { int NewCapacity = _capacity * 2 + 1; T* tmp = new T[NewCapacity]; for (int i = 0; i < _size; i++) { tmp[i] = _ptr[i]; } delete[] _ptr; _ptr = tmp; _capacity = NewCapacity; } }private: T* _ptr; int _capacity; int _size;};template<typename T>bool Stack<T>::Empty(){ if (_size == 0) return true; else return false;}template<typename T>void Stack<T>::Push(const T& data){ CheckCapacity(); _ptr[_size++] = data;}template<typename T>void Stack<T>::Pop(){ assert(_size>0); --_size;}template<typename T>T Stack<T>::Top(){ return _ptr[_size - 1];}template<typename T>int Stack<T>::Size(){ return _size;}//下面用到的栈是自己实现的栈template<typename T>class Maze{ typedef Node Pos;public: Maze() :_row(0) , _col(0) , _start(0,0) , _map(NULL) {} ~Maze() { for (int i = 0; i < _row; i++) { delete[] _map[i]; } delete[] _map; } bool SearchPath(); //查找迷宫路径 void PrintMap(); //输出迷宫地图 void PrintPath(); //打印路径的坐标 void SetMap(); //设置地图private: bool CheckNextAccess(Pos coor); //判断该坐标能否通过private: int _row; int _col; T **_map; Stack<Pos> _s; Pos _start;};template<typename T>bool Maze<T>::CheckNextAccess(Pos coor) //判断该坐标能否通过{ if (coor.x >= 0 && coor.x < _row &&coor.y >= 0 && coor.y < _col &&_map[coor.x][coor.y] == 0) //判断是否越界 { return true; } else { return false; }}template<typename T>void Maze<T>::SetMap(){ char c; FILE *fp = fopen("MazeMap.txt", "r"); //打开文件读取地图 assert(fp); //读取行 while ((c = getc(fp))!= ' '&&c != '\n') { _row=_row*10+(c-'0'); } //读取迷宫列 while ((c = getc(fp)) != ' '&&c != '\n') { _col=_col*10+(c - '0'); } //读取迷宫入口横坐标 while ((c = getc(fp)) != ' '&&c != '\n') { _start.x = _start.x*10+(c - '0'); } //读取迷宫入口纵坐标 while ((c = getc(fp)) != ' '&&c != '\n') { _start.y = _start.y*10+(c - '0'); } //开辟迷宫数组 _map = new T*[_row]; for (int i = 0; i < _row; i++) { _map[i] = new T[_col]; } //读取迷宫地图 for (int i = 0; i < _row; i++) { for (int j = 0; j < _col;) { c = getc(fp); if (c == '1' || c == '0') { _map[i][j] = c - '0'; j++; } } } fclose(fp); //关闭文件}template<typename T>bool Maze<T>::SearchPath(){ Pos cur = _start; _s.Push(_start); //将起点坐标压入栈 _map[_start.x][_start.y] = 2; //走过的路径设置为2 while (!_s.Empty()) //如果栈以空,则说明又回到入口,则迷宫无解 { Pos next=_s.Top(); cur = next; _map[cur.x][cur.y] = 2; //将坐标设置为已走过 if (next.x==_row-1||next.y==_col-1) //判断是否走到出口 { return true; } //上 next.x--; if (CheckNextAccess(next)) //如果当前坐标能够通过,则加入坐标 { _s.Push(next); continue; } next.x++; //下 next.x++; if (CheckNextAccess(next)) { _s.Push(next); continue; } next.x--; //左 next.y--; if (CheckNextAccess(next)) { _s.Push(next); continue; } next.y++; //右 next.y++; if (CheckNextAccess(next)) { _s.Push(next); continue; } _s.Pop(); //如果当前坐标不通,则退栈 _map[next.x][next.y]= 3; //并将这个坐标标记为不通 } return false;}template<typename T>void Maze<T>::PrintMap() //打印迷宫地图,但是必须先设置迷宫地图{ for (int i = 0; i < _row; i++) { for (int j = 0; j < _col; j++) { cout << _map[i][j] <<" "; } cout << endl; }}template<typename T>void Maze<T>::PrintPath() //打印迷宫路径{ Stack<Pos> coor; while (!_s.Empty()) { coor.Push(_s.Top()); _s.Pop(); } while (!coor.Empty()) { cout << "(" << coor.Top().x << "," << coor.Top().y << ")" << endl; coor.Pop(); }}void test(){ Maze<int> m; m.SetMap(); //先设置地图 m.PrintMap(); cout << (m.SearchPath() == 1 ? "Yes":"NO") << endl; m.PrintMap(); m.PrintPath();}int main(){ test(); system("pause"); return 0;}
广度优先:
如果要用一个成语来描述广度优先的话,那么这个成语就是“层层递进”。广度优先的重点再于“广”,从一点开始辐射状的遍历周围所有可能到达的点。广度优先通常都要借助队列来实现。
广度优先求解迷宫最短路径算法:
#define _CRT_SECURE_NO_WARNINGS#include<iostream>#include<cassert>#include<queue>using namespace std;typedef struct NodePos{ int x; int y; NodePos(int row = 0, int col = 0) :x(row) , y(col){}}Node;//因为迷宫用的栈 是我自己的,为了方便验证,我将栈也给出template<typename T>class Stack{public: Stack() :_capacity(0) , _size(0) , _ptr(NULL) {} ~Stack() { delete[] _ptr; _size = 0; _capacity = 0; _ptr = NULL; } void Push(const T& data); void Pop(); T Top(); int Size(); bool Empty();private: void CheckCapacity() { if (_size >= _capacity) { int NewCapacity = _capacity * 2 + 1; T* tmp = new T[NewCapacity]; for (int i = 0; i < _size; i++) { tmp[i] = _ptr[i]; } delete[] _ptr; _ptr = tmp; _capacity = NewCapacity; } }private: T* _ptr; int _capacity; int _size;};template<typename T>bool Stack<T>::Empty(){ if (_size == 0) return true; else return false;}template<typename T>void Stack<T>::Push(const T& data){ CheckCapacity(); _ptr[_size++] = data;}template<typename T>void Stack<T>::Pop(){ assert(_size>0); --_size;}template<typename T>T Stack<T>::Top(){ return _ptr[_size - 1];}template<typename T>int Stack<T>::Size(){ return _size;}//下面用到的栈是自己实现的栈template<typename T>class Maze{ typedef Node Pos;public: Maze() :_row(0) , _col(0) , _start(0, 0) , _map(NULL) ,_book(NULL) {} ~Maze() { for (int i = 0; i < _row; i++) { delete[] _map[i]; delete[] _book[i]; } delete[] _map; delete[] _book; } bool SearchPath(); //查找迷宫路径 void PrintMap(); //输出迷宫地图 void PrintPath(); //打印路径的坐标 void SetMap(); //设置地图private: bool CheckNextAccess(Pos coor); //判断下一个坐标能否通过 bool CheckPrevAccess(Pos coor); //判断前一个坐标能否通过private: int _row; int _col; T **_map; //地图数组 T **_book; //辅助数组 Stack<Pos> _s; Pos _start;};template<typename T>bool Maze<T>::CheckNextAccess(Pos coor) //判断该坐标能否通过{ if (coor.x >= 0 && coor.x < _row &&coor.y >= 0 && coor.y < _col &&_map[coor.x][coor.y] == 0) //判断是否越界 { return true; } else { return false; }}template<typename T>bool Maze<T>::CheckPrevAccess(Pos coor) //判断该坐标能否通过{ if (coor.x >= 0 && coor.x < _row &&coor.y >= 0 && coor.y < _col &&(_book[coor.x][coor.y] == (_book[_s.Top().x][_s.Top().y] - 1))) //判断是否越界 { return true; } else { return false; }}template<typename T>bool Maze<T>::SearchPath(){ queue<Node> q; q.push(_start); //起点入队 Pos cur = _start; int step = 1; _book[cur.x][cur.y] = 0; //将起点标记为0 while (!q.empty()) //如果队列不空,广度优先查找 { Pos next = q.front(); cur = next; _map[cur.x][cur.y] = 2; //将走过的路径标记位2 step = _book[q.front().x][q.front().y] + 1; //在辅助数组中标记处当前结点的层数 if (((cur.x == _row - 1)&&cur.x!=_row-1) || ((cur.y == _col- 1)&&cur.y != _col- 1) || (cur.x == 0 && _start.x != 0) || (cur.y == 0 && _start.y != 0)) //如果找到出口则跳出循环,出口与入口不再同一侧 { break; } //上 next.x--; if (CheckNextAccess(next)) //如果当前坐标能够通过,则加入坐标 { q.push(next); _book[next.x][next.y] = step; } next.x++; //下 next.x++; if (CheckNextAccess(next)) { q.push(next); _book[next.x][next.y] = step; } next.x--; //左 next.y--; if (CheckNextAccess(next)) { q.push(next); _book[next.x][next.y] = step; } next.y++; //右 next.y++; if (CheckNextAccess(next)) { q.push(next); _book[next.x][next.y] = step; } next.y--; q.pop(); //如果都不能通,则将这点出队 } if (!q.empty()) //如果队列不空,则将终点压入栈中 { _s.Push(cur); } //倒着寻找路径 while (!_s.Empty()) //倒着将从终点到起点的坐标压入 { Pos next = _s.Top(); //上 if (_book[next.x][next.y] == 0) //如果找到起点 { return true; } next.x--; if (CheckPrevAccess(next)) //如果当前坐标能够通过,则加入坐标 { _s.Push(next); continue; } next.x++; //下 next.x++; if (CheckPrevAccess(next)) { _s.Push(next); continue; } next.x--; //左 next.y--; if (CheckPrevAccess(next)) { _s.Push(next); continue; } next.y++; //右 next.y++; if (CheckPrevAccess(next)) { _s.Push(next); continue; } next.y--; } return false;}template<typename T>void Maze<T>::SetMap(){ char c; FILE *fp = fopen("MazeMap.txt", "r"); //打开文件读取地图 assert(fp); //读取行 while ((c = getc(fp)) != ' '&&c != '\n') { _row = _row * 10 + (c - '0'); } //读取迷宫列 while ((c = getc(fp)) != ' '&&c != '\n') { _col = _col * 10 + (c - '0'); } //读取迷宫入口横坐标 while ((c = getc(fp)) != ' '&&c != '\n') { _start.x = _start.x * 10 + (c - '0'); } //读取迷宫入口纵坐标 while ((c = getc(fp)) != ' '&&c != '\n') { _start.y = _start.y * 10 + (c - '0'); } //开辟迷宫数组 _map = new T*[_row]; for (int i = 0; i < _row; i++) { _map[i] = new T[_col]; } //开辟辅助数组 _book = new T*[_row]; for (int i = 0; i < _row; i++) { _book[i] = new T[_col]; } //初始化辅助数组 for (int i = 0; i < _row; i++) { for (int j = 0; j < _col; j++) { _book[i][j] = -1; } } //读取迷宫地图 for (int i = 0; i < _row; i++) { for (int j = 0; j < _col;) { c = getc(fp); if (c == '1' || c == '0') { _map[i][j] = c - '0'; j++; } } } fclose(fp); //关闭文件}template<typename T>void Maze<T>::PrintMap() //打印迷宫地图,但是必须先设置迷宫地图{ cout << "迷宫地图中所走过的路径" << endl; for (int i = 0; i < _row; i++) { for (int j = 0; j < _col; j++) { cout << _map[i][j] << " "; } cout << endl; } cout << endl << endl; //打印辅助数组 cout << "辅助数组中所有入队的坐标" << endl; for (int i = 0; i < _row; i++) { for (int j = 0; j < _col; j++) { printf("%2d ",_book[i][j]); } cout << endl; }}template<typename T>void Maze<T>::PrintPath() //打印迷宫路径{ while (!_s.Empty()) { cout << "(" << _s.Top().x << "," << _s.Top().y << ")" << endl; _s.Pop(); }}void test(){ Maze<int> m; m.SetMap(); cout << (m.SearchPath() != 0 ? "YES":"NO")<< endl; m.PrintMap(); m.PrintPath();}int main(){ test(); system("pause"); return 0;}
下面为大家在介绍一下简单迷宫游戏的简单实现:
要实现迷宫游戏需要具备一下条件:
1、地图
可以开辟一个二维数组,然后用随机数生成地图,为了保证地图的起点和终点不被用,
所以在随机生成的地图后再将起点和终点单独拿出来设置。
2、控制键
通过方向键来获得小人下一步要走的位置,然后拿到这个位置,判断是否越界和是
否能够通过。获得位置的函数如下:
//分别按上下左右时,a2的值分别是72 80 75 77 a1的值都是224
#include<conio.h>
int a1 = _getch();
int a2 = _getch();
3、重绘
为了使得小人能够动起来,我们在得到小人下一步的坐标时,就要先将当前位置的
小人先擦除掉,然后再在下个坐标将小人重新绘制出。
获得光标位置的函数如下:
//调用move函数,给move传一个坐标,则光标就跳转到坐标处
//对于光标来说,他在显示屏上的坐标是,以左上角为原点,横坐标为x,向右增长
//纵坐标为y向下增长
#include<Windows.h>
void move(int x, int y)
{
COORD cd;
cd.X = x;
cd.Y = y;
HANDLE handle = GetStdHandle(STD_OUTPUT_HANDLE);
SetConsoleCursorPosition(handle, cd);
}
#include<iostream>#include<cassert>#include<conio.h>#include<Windows.h>#include<time.h>using namespace std;void move(int x, int y){COORD cd;cd.X = x;cd.Y = y;HANDLE handle = GetStdHandle(STD_OUTPUT_HANDLE);SetConsoleCursorPosition(handle, cd);}//声明一个坐标类型typedef struct{int x;int y;}Coor;void InitMap(char **map,int line, int row){Coor start, end; //start是起点坐标 end是终点坐标start.x = 1;start.y = 0;end.x = line - 2;end.y = row - 1;//初始化地图for (int i = 0; i < line; i++){for (int j = 0; j < row; j++){map[i][j] = ' ';}}//打印边框墙for (int i = 0; i < line; i++){map[i][0] = '#';map[i][row-1] = '#';}for (int i = 0; i <row; i++){map[0][i] = '#';map[line-1][i] = '#';}//产生随机障碍物int count = (line*row)/3;srand((unsigned)time(NULL));while (--count){int i = 0;int j = 0;i = rand() % (line-3) + 1;j= rand() % (row-3) + 1;map[i][j] = '#';}//保证起点和终点不被占用map[start.x][start.y] = ' ';map[end.x][end.y] =' ';map[start.x][start.y+1] = ' ';map[start.x][start.y +2] = ' ';map[end.x][end.y-1] = ' ';//打印地图move(0,0);for (int i = 0; i < line; i++){for (int j = 0; j <row; j++){cout << map[i][j];}cout << endl;}}void PlayGame(char **map,int line,int row){Coor start, end; //start是起点坐标 end是终点坐标start.x =0;start.y =1;end.x = row-1;end.y =line-2;InitMap(map,line,row); //初始化地图//初始化猪脚int x = start.x;int y = start.y;move(x, y);cout << 'T';//开始玩游戏while (1){int a1 = _getch();if (a1 == 48){return;}int a2 = _getch();move(x,y);cout << ' ';switch (a2){case 72:y--;if (y < 1 || map[y][x] == '#'){y++;}break;case 80:y++;if ((y>line - 2) || map[y][x] == '#'){y--;}break;case 75:x--;if (x < 1 || map[y][x] == '#'){x++;}break;case 77:x++;if (map[y][x] == '#'){x--;}break;default:break;}if ((end.x == x) && (end.y == y)){break;}move(x, y);cout << 'T';}move(row, line);cout << "you are Win!!!" << endl;Sleep(1000);}void menu(){cout << "******************************" << endl;cout << "***Welecom to labyrinth maze**" << endl;cout << "说明:" << endl;cout << "移动:上下左右"<<endl;cout << "#:墙壁,猪脚无法穿墙"<<endl;cout << "若迷宫无法通过" << endl;cout << "按0重新生成地图" << endl;cout << "处于菜单选项时按0退出" << endl;Sleep(1000);cout << " Please choose model" << endl << endl;cout << " -->1、classic model" << endl;cout << " -->2、difficulty model" << endl;}char** Capacity(int line,int row){char **map = (char**)malloc(line*sizeof(char*));for (int i = 0; i <line; i++){map[i] = (char *)malloc(row*sizeof(char));}return map;}void DesMap(char** map,int line,int row){move(0,0);for (int i = 0; i < line; i++){for (int j = 0; j <row; j++){cout<<" ";}cout << endl;}free(map);}void test(){int line = 0;int row = 0;char** map =NULL;int n = 1;while (1){menu();cin >> n;switch (n){case 0:exit(1);break;case 1:line = 20;row = 40;map = Capacity(line,row);break;case 2:line =40;row = 60;map = Capacity(line,row);break;default:line = 40;row = 60;map = Capacity(line, row);break;}PlayGame(map,line,row);Sleep(1000);DesMap(map,line,row);}}int main(){test();system("pause");return 0;}
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