POJ 1077 Eight （正向BFS + 康托展开）

题意不说了 八数码问题：

和上篇博客 HDU 1043  题目是一样的！

但是做法上有些出入。

HDU 时间限制比较长，而且是多组输入，所以要逆向bfs 进行打表处理。

而POJ 1077 这个题目，时间是1S ，单组输入。

因此输入一组 搜索一组即可。

9个数的排列  判重用康托展开来做。

但是这个队列要自己写，STL的queue 会超时。

自己写的队列，在输出时 能很方便的用la[]数组来记录上一个 位置。  dfs 逆向输出即可！（用String 还是会超时！= =）

#include <cstdio>#include <cstring>#include <algorithm>#include <queue>#include <string>using namespace std;char cmd[2];int jie[10];int q[400000];int l = 0,r = 0;bool vis[370000];const int dx[] = {-1,1,0,0}; ///const int dy[] = {0,0,-1,1};const char *flag = "udlr";void init(){    jie[0] = jie[1] = 1;    for (int i = 2; i < 9; ++i){        jie[i] = jie[i-1] * i;    }}char hs[10];int Hash(int v){    for (int i = 0; i < 9; ++i){        hs[8-i] = v % 10 + 48;        v/=10;    }    int sum = 0;    for (int i = 0; i < 9; ++i){        int t = 0;        for (int j = i+1; j < 9; ++j){            if (hs[j] < hs[i])++t;        }        sum += jie[8-i]*t;    }    return sum;}int goal;int la[370000];char al[370000];char s[10];char tab[5][5];void bfs(int v){    q[r++] = v;    vis[Hash(v)] = 1;    while(l < r){        int u = q[l++];        int idu = Hash(u);        if (idu == goal) return;        int uu = u;        for (int i = 0; i < 9; ++i){            s[8-i] = uu % 10 + 48;            uu /= 10;        }        int p;        for (int i = 0; i < 9; ++i){            if (s[i] == 48)p = i;            tab[i / 3][i % 3] = s[i];        }        int x = p/3; int y = p % 3;        for (int i = 0; i < 4; ++i){            int xx = x + dx[i];            int yy = y + dy[i];            if (xx >= 0 && xx <= 2 && yy >= 0 && yy < 3){                swap(tab[xx][yy],tab[x][y]);                int v2 = 0;                for (int j = 0; j < 9; ++j){                    v2 = v2 * 10 + tab[j/3][j%3] - 48;                }                int idv2 = Hash(v2);                if (!vis[idv2]){                    vis[idv2] = 1;                    q[r++] = v2;                    al[r-1] = flag[i];                    la[r-1] = l-1;//                    state[idv2] = state[idu] + flag[i];                }                swap(tab[xx][yy],tab[x][y]);            }        }    }}void dfs(int cc){    if (cc){//        printf("c\n");        dfs(la[cc]);        putchar(al[cc]);    }    else return;}int main(){    int v = 0;//    memset(la,-1,sizeof la);    init();    goal = Hash(123456780);    for (int i = 0; i < 9; ++i){        scanf("%s",cmd);        if (cmd[0] == 'x')cmd[0] = '0';        v = v * 10 + cmd[0] - 48;    }    bfs(v);    if (!vis[goal])puts("unsolvable");    else {        l--;        dfs(l);        puts("");    }    return 0;}

Eight

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 31422 Accepted: 13685 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

South Central USA 1998