HDU 1043 Eight (BFS·八数码·康托展开)

时间：2015-07-05 18:36:06 阅读：136 评论：0 收藏：0 [点我收藏+]

标签：acm hdu

题意输出八数码问题从给定状态到12345678x的路径

用康托展开将排列对应为整数即这个排列在所有排列中的字典序然后就是基础的BFS了

#include <bits/stdc++.h>
using namespace std;
const int N = 5e5, M = 9;
int x[4] = { -1, 1, 0, 0};
int y[4] = {0, 0, -1, 1};
int fac[] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320};
int sta[N][M], nex[N], dir[N], vis[N], q[N];

int getCantor(int a[])  //康托展开  将排列转化为整数
{
    int ret = 0;
    for(int i = 0; i < M; ++i)
    {
        for(int j = i + 1; j < M; ++j)
            if(a[j] < a[i]) ret += fac[M - i - 1];
    }
    return ret;
}

void bfs()
{
    int t[M] = {1, 2, 3, 4, 5, 6, 7, 8, 0};
    int id = getCantor(t);
    printf("%d\n",id);
    nex[id] = -1;
    memcpy(sta[id], t, sizeof(t));

    int r, c, k, nr, nc, nk, nid;
    int front = 0, rear = 0;
    q[rear++] = id;
    vis[id] = 1;

    while(front < rear)
    {
        int id = q[front++];
        memcpy(t, sta[id], sizeof(sta));
        for(k = 0; t[k]; ++k); //0的位置
        r = k / 3, c = k % 3;  //一维转二维

        for(int i = 0; i < 4; ++i)
        {
            nr = r + x[i], nc = c + y[i], nk = nr * 3 + nc;
            if(nr < 0 || nr > 2 || nc < 0 || nc > 2) continue;
            swap(t[k], t[nk]);
            nid = getCantor(t);
            memcpy(sta[nid], t, sizeof(t));
            swap(t[k], t[nk]);

            if(vis[nid]) continue;
            vis[nid] = 1;
            q[rear++] = nid;
            nex[nid] = id;
            dir[nid] = i;
        }
    }
}

int main()
{
    char t[5];
    int s[M], id;
    bfs();
    while(~scanf("%s", t))
    {
        s[0] = t[0] == 'x' ? 0 : t[0] - '0';
        for(int i = 1; i < M; ++i)
        {
            scanf("%s", t);
            s[i] = t[0] == 'x' ? 0 : t[0] - '0';
        }

        id = getCantor(s);
        if(!vis[id]) puts("unsolvable");
        else
        {
            while(nex[id] >= 0)
                printf("%d", nex[id]);
            puts("");
        }
    }
    return 0;
}
//Last modified :   2015-07-05 11:15

Eight

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

HDU 1043 Eight (BFS·八数码·康托展开)

标签：acm hdu

原文地址：http://blog.csdn.net/acvay/article/details/46764025

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