• HDU 1043 Eight POJ 1077 Eight (广度搜索,八数码问题,康托展开)


    HDU 1043  和  POJ 1077   两题类似。。。但是输入不同。

    HDU 上是同时多组输入,POJ是单组输入。

    两个限时不同。

    HDU 上反向搜索,把所有情况打表出来。

    POJ上正向搜索。

    这个题很经典,还需要继续做。先把第一次写的代码贴出来吧。

    继续优化中

    HDU 1043 

    Eight

    Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
    Total Submission(s): 7145    Accepted Submission(s): 1946
    Special Judge


    Problem Description
    The 15-puzzle has been around for over 100 years; even if you don't know it by that name, you've seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let's call the missing tile 'x'; the object of the puzzle is to arrange the tiles so that they are ordered as:

    1 2 3 4
    5 6 7 8
    9 10 11 12
    13 14 15 x

    where the only legal operation is to exchange 'x' with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle:

    1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
    5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8
    9 x 10 12 9 10 x 12 9 10 11 12 9 10 11 12
    13 14 11 15 13 14 11 15 13 14 x 15 13 14 15 x
    r-> d-> r->

    The letters in the previous row indicate which neighbor of the 'x' tile is swapped with the 'x' tile at each step; legal values are 'r','l','u' and 'd', for right, left, up, and down, respectively.

    Not all puzzles can be solved; in 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and
    frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing 'x' tile, of course).

    In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three
    arrangement.
     
    Input
    You will receive, several descriptions of configuration of the 8 puzzle. One description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus 'x'. For example, this puzzle

    1 2 3
    x 4 6
    7 5 8

    is described by this list:

    1 2 3 x 4 6 7 5 8
     
    Output
    You will print to standard output either the word ``unsolvable'', if the puzzle has no solution, or a string consisting entirely of the letters 'r', 'l', 'u' and 'd' that describes a series of moves that produce a solution. The string should include no spaces and start at the beginning of the line. Do not print a blank line between cases.
     
    Sample Input
    2 3 4 1 5 x 7 6 8
     
    Sample Output
    ullddrurdllurdruldr
     
    Source
     
    Recommend
    JGShining
     
     
    /*
    HDU 1043 Eight
    思路:反向搜索,从目标状态找回状态对应的路径
    用康托展开判重
    
    
    AC   G++  328ms  13924K
    
    */
    #include<stdio.h>
    #include<string.h>
    #include<iostream>
    #include<queue>
    #include<string>
    using namespace std;
    const int MAXN=1000000;//最多是9!/2
    int fac[]={1,1,2,6,24,120,720,5040,40320,362880};//康拖展开判重
    //         0!1!2!3! 4! 5!  6!  7!   8!    9!
    bool vis[MAXN];//标记
    string path[MAXN];//记录路径
    int cantor(int s[])//康拖展开求该序列的hash值
    {
        int sum=0;
        for(int i=0;i<9;i++)
        {
            int num=0;
            for(int j=i+1;j<9;j++)
              if(s[j]<s[i])num++;
            sum+=(num*fac[9-i-1]);
        }
        return sum+1;
    }
    struct Node
    {
        int s[9];
        int loc;//“0”的位置
        int status;//康拖展开的hash值
        string path;//路径
    };
    int move[4][2]={{-1,0},{1,0},{0,-1},{0,1}};//u,d,l,r
    char indexs[5]="durl";//和上面的要相反,因为是反向搜索
    int aim=46234;//123456780对应的康拖展开的hash值
    void bfs()
    {
        memset(vis,false,sizeof(vis));
        Node cur,next;
        for(int i=0;i<8;i++)cur.s[i]=i+1;
        cur.s[8]=0;
        cur.loc=8;
        cur.status=aim;
        cur.path="";
        queue<Node>q;
        q.push(cur);
        path[aim]="";
        while(!q.empty())
        {
            cur=q.front();
            q.pop();
            int x=cur.loc/3;
            int y=cur.loc%3;
            for(int i=0;i<4;i++)
            {
                int tx=x+move[i][0];
                int ty=y+move[i][1];
                if(tx<0||tx>2||ty<0||ty>2)continue;
                next=cur;
                next.loc=tx*3+ty;
                next.s[cur.loc]=next.s[next.loc];
                next.s[next.loc]=0;
                next.status=cantor(next.s);
                if(!vis[next.status])
                {
                    vis[next.status]=true;
                    next.path=indexs[i]+next.path;
                    q.push(next);
                    path[next.status]=next.path;
                }
            }
        }
    
    }
    int main()
    {
        char ch;
        Node cur;
        bfs();
        while(cin>>ch)
        {
            if(ch=='x') {cur.s[0]=0;cur.loc=0;}
            else cur.s[0]=ch-'0';
            for(int i=1;i<9;i++)
            {
                cin>>ch;
                if(ch=='x')
                {
                    cur.s[i]=0;
                    cur.loc=i;
                }
                else cur.s[i]=ch-'0';
            }
            cur.status=cantor(cur.s);
            if(vis[cur.status])
            {
                cout<<path[cur.status]<<endl;
            }
            else cout<<"unsolvable"<<endl;
        }
        return 0;
    }

    POJ  1077

    Eight
    Time Limit: 1000MS   Memory Limit: 65536K
    Total Submissions: 18379   Accepted: 8178   Special Judge

    Description

    The 15-puzzle has been around for over 100 years; even if you don't know it by that name, you've seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let's call the missing tile 'x'; the object of the puzzle is to arrange the tiles so that they are ordered as:
     1  2  3  4 
    5 6 7 8
    9 10 11 12
    13 14 15 x

    where the only legal operation is to exchange 'x' with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle:
     1  2  3  4    1  2  3  4    1  2  3  4    1  2  3  4 
    5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8
    9 x 10 12 9 10 x 12 9 10 11 12 9 10 11 12
    13 14 11 15 13 14 11 15 13 14 x 15 13 14 15 x
    r-> d-> r->

    The letters in the previous row indicate which neighbor of the 'x' tile is swapped with the 'x' tile at each step; legal values are 'r','l','u' and 'd', for right, left, up, and down, respectively.

    Not all puzzles can be solved; in 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and
    frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing 'x' tile, of course).

    In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three
    arrangement.

    Input

    You will receive a description of a configuration of the 8 puzzle. The description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus 'x'. For example, this puzzle
     1  2  3 
    x 4 6
    7 5 8

    is described by this list:

    1 2 3 x 4 6 7 5 8

    Output

    You will print to standard output either the word ``unsolvable'', if the puzzle has no solution, or a string consisting entirely of the letters 'r', 'l', 'u' and 'd' that describes a series of moves that produce a solution. The string should include no spaces and start at the beginning of the line.

    Sample Input

     2  3  4  1  5  x  7  6  8 

    Sample Output

    ullddrurdllurdruldr

    Source

     
     
     
    /*
    POJ 1077 Eight
    正向广度搜索
    把“x"当初0
    
    G++ AC 5200K 719ms
    
    
    */
    
    #include<stdio.h>
    #include<queue>
    #include<string.h>
    #include<iostream>
    #include<algorithm>
    using namespace std;
    const int MAXN=1000000;
    int fac[]={1,1,2,6,24,120,720,5040,40320,362880};//康拖展开判重
    //         0!1!2!3! 4! 5!  6!  7!   8!    9!
    bool vis[MAXN];//标记
    
    int cantor(int s[])//康拖展开求该序列的hash值
    {
        int sum=0;
        for(int i=0;i<9;i++)
        {
            int num=0;
            for(int j=i+1;j<9;j++)
              if(s[j]<s[i])num++;
            sum+=(num*fac[9-i-1]);
        }
        return sum+1;
    }
    struct Node
    {
        int s[9];
        int loc;//“0”的位置,把“x"当0
        int status;//康拖展开的hash值
        string path;//路径
    };
    string path;
    int aim=46234;//123456780对应的康拖展开的hash值
    int move[4][2]={{-1,0},{1,0},{0,-1},{0,1}};//u,d,l,r
    char indexs[5]="udlr";//正向搜索
    Node ncur;
    bool bfs()
    {
        memset(vis,false,sizeof(vis));
        Node cur,next;
        queue<Node>q;
        q.push(ncur);
        while(!q.empty())
        {
            cur=q.front();
            q.pop();
            if(cur.status==aim)
            {
                path=cur.path;
                return true;
            }
            int x=cur.loc/3;
            int y=cur.loc%3;
            for(int i=0;i<4;i++)
            {
                int tx=x+move[i][0];
                int ty=y+move[i][1];
                if(tx<0||tx>2||ty<0||ty>2)continue;
                next=cur;
                next.loc=tx*3+ty;
                next.s[cur.loc]=next.s[next.loc];
                next.s[next.loc]=0;
                next.status=cantor(next.s);
                if(!vis[next.status])
                {
                    vis[next.status]=true;
                    next.path=next.path+indexs[i];
    
                    if(next.status==aim)
                    {
                        path=next.path;
                        return true;
                    }
    
                    q.push(next);
                }
            }
        }
        return false;
    }
    int main()
    {
        char ch;
        while(cin>>ch)
        {
            if(ch=='x') {ncur.s[0]=0;ncur.loc=0;}
            else ncur.s[0]=ch-'0';
            for(int i=1;i<9;i++)
            {
                cin>>ch;
                if(ch=='x')
                {
                    ncur.s[i]=0;
                    ncur.loc=i;
                }
                else ncur.s[i]=ch-'0';
            }
            ncur.status=cantor(ncur.s);
            if(bfs())
            {
                cout<<path<<endl;
            }
            else cout<<"unsolvable"<<endl;
        }
        return 0;
    }

    这个题目我的做法是把“x"当成0的。

    网上很多当成9的话很多不一样了,特意说明下。

    康托展开很简单,百度百科上的很容易理解。

    谢谢

    ------------------------------kuangbin

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  • 原文地址:https://www.cnblogs.com/kuangbin/p/2635478.html
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