各大公司數據結構與算法面試題解答(二)

6尋找迷宮的一條出路，1代表障礙，0代表通。

算法描述：

這裏可以使用幾種方法，我知道的有使用《數據結構》上“窮舉求解”的方法，還有就是使用遺傳算法尋找最優路徑。這裏我先簡單描述下“窮舉求解”，然後再做遺傳算法的方式。

1 問題中要涉及走過路徑的回溯，因爲棧是先進後出，所以利於回溯，選擇棧來存儲走過路徑

2 每一步有四個方向可以走，每到一步依次判斷每一個方向，只要判斷到某個方向可走就選擇這個方向前進。

3 當所有方向都不能行進時，回溯到上一步，此時判斷棧頂指針是否爲-1，如果是，返回false失敗，否則遞歸調用繼續尋找。

C++源碼：

#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;
}

運行結果：