各大公司数据结构与算法面试题解答(二)

6寻找迷宫的一条出路，1代表障碍，0代表通。
算法描述：这里可以使用几种方法，我知道的有使用《数据结构》上“穷举求解”的方法，还有就是使用遗传算法寻找最优路径。这里我先简单描述下“穷举求解”，然后再做遗传算法的方式。1 问题中要涉及走过路径的回溯，因为栈是先进后出，所以利于回溯，选择栈来存储走过路径2 每一步有四个方向可以走，每到一步依次判断每一个方向，只要判断到某个方向可走就选择这个方向前进。3 当所有方向都不能行进时，回溯到上一步，此时判断栈顶指针是否为-1，如果是，返回false失败，否则递归调用继续寻找。C++源码：

#include "stdafx.h"
#include <stdio.h>
#include <iostream>
using namespace std;
#define MAX_SIZE 10

int maze[MAX_SIZE][MAX_SIZE]=
{	{1,1,1,1,1,1,1,1,1,1},
{1,0,0,1,0,0,0,1,0,1},
{1,0,0,1,0,0,0,1,0,1},
{1,0,0,0,0,1,1,0,0,1},
{1,0,1,1,1,0,0,0,0,1},
{1,0,0,0,1,0,0,0,0,1},
{1,0,1,0,0,0,1,0,0,1},
{1,0,1,1,1,0,1,1,0,1},
{1,1,0,0,0,0,0,0,0,1},
{1,1,1,1,1,1,1,1,1,1}
};
typedef struct
{
int x;
int y;
}POINT;

typedef struct
{
POINT data[MAX_SIZE*MAX_SIZE];
int top;
}STACK;

bool operator != (POINT& point1,POINT& point2)
{
if(point1.x!=point2.x||point1.y!=point2.y)
return true;
else
return false;
}
bool operator == (POINT& point1,POINT& point2)
{
if(point1.x==point2.x&&point1.y==point2.y)
return true;
else
return false;
}

bool FindWay(int maze[][MAX_SIZE],POINT start,POINT end,STACK& way)
{

POINT step;
step.x = start.x;
step.y = start.y;
if(way.data[way.top]!=end)
{
/************first,make sure the direction**********/
if(maze[step.y][step.x+1]==0)	//east
{
maze[step.y][step.x] = 1;
way.top++;
way.data[way.top] = step;
step.x++;
FindWay(maze,step,end,way);
}
else if(maze[step.y+1][step.x]==0)	//south
{
maze[step.y][step.x] = 1;
way.top++;
way.data[way.top] = step;
step.y++;
FindWay(maze,step,end,way);
}
else if(maze[step.y][step.x-1]==0)	//west
{
maze[step.y][step.x] = 1;
way.top++;
way.data[way.top] = step;
step.x--;
FindWay(maze,step,end,way);
}
else if(maze[step.y-1][step.x]==0)	//north
{
maze[step.y][step.x] = 1;
way.top++;
way.data[way.top] = step;
step.y--;
FindWay(maze,step,end,way);
}
else	//There is no direction available
{
if(way.top<0)
return false;
else
{
maze[step.y][step.x] = 1;
step = way.data[way.top];
way.top--;
FindWay(maze,step,end,way);
}
}//end else
}//end if
else
return true;
}

int main(int argc, char* argv[])
{
POINT start,end;
start.x = 1;
start.y = 1;
end.x = 8;
end.y = 8;
STACK way;
way.top = -1;
if(FindWay(maze,start,end,way))
{
cout<<"Have found the way!"<<endl;
for(int i=0;i<=way.top;i++)
printf("(%d,%d)  ",way.data[i].x,way.data[i].y);
}
else
cout<<"Don't find the way!"<<endl;
return 1;
}

运行结果：