第二周训练 | 搜索技术 八数码问题和状态图搜索

八数码求最短步数：

#include<queue>
#include<stdio.h>
#include<iostream>
#include<string.h>
using namespace std;
const int LEN = 362880;
struct node
{
    int state[9];
    int dis;
};
int dir[4][2]={{-1,0},{0,-1},{1,0},{0,1}};
int visited[LEN]={0};
int start[9];
int goal[9];
long int factory[]={1,1,2,6,24,120,720,5040,40320,362880};
void swap(int a,int b)
{
  int c=0;
  c=a;
  a=b;
  b=c; 
}
bool Cantor(int str[],int n)
{
//    cout<<"hello"<<endl;
    long result = 0;
    for(int i=0;i<n;++i)
    {
        int counted=0;
        for(int j=i+1;j<n;j++)
        {
            if(str[i]>str[j])
            {
                ++counted;
            }
        }
        result+=counted*factory[n-i-1];
    }
    if(!visited[result])
    {
        visited[result]=1;
        return 1;
    }
    else
    {
        return 0;
    }
     
}
int bfs()
{
    node head;
    memcpy(head.state,start,sizeof(head.state));
    head.dis=0;
    queue<node> q;
    Cantor(head.state,9);
    q.push(head);
     
    while(!q.empty())
    {
        head = q.front();
        q.pop();
        int z;
        for(z = 0;z<9;z++)
        {
            if(head.state[z]==0)
            {
                break;
            }
        }
        int x = z%3;
        int y = z/3;
//        printf("head.state[%d]=%d",z,head.state[z]);
        for(int i=0;i<4;++i)
        {
            int newx = x + dir[i][0];
            int newy = y + dir[i][1];
            int nz = newx + 3*newy;
            if(newx>=0&&newx<3&&newy>=0&&newy<3)
            {
                node newnode;
                memcpy(&newnode,&head,sizeof(struct node));
                int c=newnode.state[z];
				newnode.state[z]=newnode.state[nz];
				newnode.state[nz]=c;
                newnode.dis++;
                 
                if(memcmp(newnode.state,goal,sizeof(goal))==0)
                {
                    return newnode.dis;
                }
                if(Cantor(newnode.state,9))
                {
                     
                    q.push(newnode);
                }
            }
        }
         
    }
    return -1;
}
 
int main()
{
    for(int i=0;i<9;++i)
    {
        cin>>start[i];
//      cout<< start[i];
    }
    cout<<"输入的棋盘："<<endl;
    for(int i=1;i<=9;++i)
    {
        cout<<start[i-1]<<" ";
        if(i%3==0)cout<<endl;
    }
     
    for(int i=0;i<9;++i) cin>>goal[i];
    cout<<"目标的棋盘："<<endl;
    for(int i=1;i<=9;++i)
    {
        cout<<goal[i-1]<<" ";
        if(i%3==0)cout<<endl;
    }
    int num = bfs();
    if(num!=-1)
    {
        cout<<num<<endl;
    }
    else
    {
        cout<<"Impossible"<<endl;
    }
    return 0;
}

八数码求最短路径：

/*

2 3 4 1 5 x 7 6 8
1 2 3 4 6 7 5 8 x

2 3 4 1 5 0 7 6 8
1 2 3 4 5 6 7 8 0
ullddrurdllurdruldr
*/
#include<map>
#include<queue>
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
using namespace std;
const int LEN = 362880;
typedef struct node
{
	int state[9];
	int dis;
	char road;
}node;
int dir[4][2]={{-1,0},{0,-1},{1,0},{0,1}};
char dir_mark[4]={'l','u','r','d'};
int visited[LEN]={0};
int start[9];
int goal[9];
long int factory[]={1,1,2,6,24,120,720,5040,40320,362880};
int flag=1;
string bigparent="";
bool Cantor(int str[],int n)
{
	long result = 0;
	for(int i=0;i<n;++i)
	{
		int counted=0;
		for(int j=i+1;j<n;j++)
		{
			if(str[i]>str[j])
			{
				++counted;
			}
		}
		result+=counted*factory[n-i-1];
	}
	if(!visited[result])
	{
		visited[result]=1;
		return 1;
	}
	else
	{
		return 0;
	}
	
}
int bfs()
{
	node head;
	memcpy(head.state,start,sizeof(head.state));
	head.dis=0;
	head.road='0';
	queue<node> q;
	Cantor(head.state,9);
	q.push(head);
	map<string,map<string,char> >parent;
	
	string str1="";
	for(int i=0;i<9;++i)
	{
		str1+=head.state[i]+'0'; 
	}
	parent[str1]["bigparent"]='0';
				
	while(!q.empty())
	{
		head = q.front();
		q.pop();
		int z;
		for(z = 0;z<9;z++)
		{
			if(head.state[z]==0)
			{
				break;
			}
		}
		int x = z%3;
		int y = z/3;
		for(int i=0;i<4;++i)
		{
			int newx = x + dir[i][0];
			int newy = y + dir[i][1];
			int nz = newx + 3*newy;
			if(newx>=0&&newx<3&&newy>=0&&newy<3)
			{
				node newnode;
				
				memcpy(&newnode,&head,sizeof(struct node));
				int c=newnode.state[z];
				newnode.state[z]=newnode.state[nz];
				newnode.state[nz]=c;
				
				//创建一个parent数组记录个节点的父节点 
				string str1="";
				string str2="";
				for(int i=0;i<9;++i)
				{
					str1+=newnode.state[i]+'0';
					str2+=head.state[i]+'0'; 
				}
				parent[str1][str2]=dir_mark[i];
//				cout<<"	parent["<<str1<<"]["<<str2<<"]="<<parent[str1][str2]<<endl; 


				newnode.dis++;
				if(memcmp(newnode.state,goal,sizeof(goal))==0)
				{
					string rest="",child="",littleparent="";
					for(int i=0;i<9;++i)
					{
						child+=newnode.state[i]+'0'; 
					}
				    while(1)
				    {
				    	cout<<"parent["<<child<<"]["<<littleparent<<"]="<<parent[child][littleparent]<<endl;
				    	rest+=parent[child];
				    	child=littleparent;
				    	if(littleparent==bigparent)break;
					}
					cout<<rest;
					flag=0;
					return newnode.dis;
				}
				if(Cantor(newnode.state,9))
				{		
				  
					q.push(newnode);
					
				}
			}
		}
		
	}
	return -1;
}

int main()
{
	
	for(int i=0;i<9;++i) 
	{
		char temp;
		cin>>temp;
		bigparent+=temp;
		if(temp=='x')
		{
			start[i]=0;
		}
		else
		{
			start[i]=temp-'0';
		}
//		cout<< start[i];
	}
	cout<<"输入的棋盘："<<endl;
	for(int i=1;i<=9;++i) 
	{
		cout<<start[i-1]<<" ";
		if(i%3==0)cout<<endl;
	}
	
	for(int i=0;i<9;++i)
	{
		char temp;
		 cin>>temp;
		 if(temp=='x')
		{
			goal[i]=0;
		}
		else
		{
			goal[i]=temp-'0';
		}
	}
	
	cout<<"目标的棋盘："<<endl;
	for(int i=1;i<=9;++i) 
	{
		cout<<goal[i-1]<<" ";
		if(i%3==0)cout<<endl;
	}
	
	bfs();
	if(flag)
	{
		cout<<"unsolvable"<<endl;
	}

	return 0;
 }