HDU 1430 魔板

思路：

初态a和末态b经过相同的一系列操作，使初态a变成12345678，同时得到新的末态c，然后只需要求12345678到末态c的变换步骤即为初态a到末态b的变换步骤。所以，只要把12345678的所有可达状态遍历一次并记录下变换步骤即可。

#include <cstdio>
#include <string.h>
#include <stack>
using namespace std;
const int MAX = 40500, fact[] = {1, 1, 2, 6, 24, 120, 720, 5040}, Move[3][8] = {{7, 6, 5, 4, 3, 2, 1, 0}, {3, 0, 1, 2, 5, 6, 7, 4}, {0, 6, 1, 3, 4, 2, 5, 7}};
bool vis[MAX] = {0};
int LOG[MAX][8] = {1, 2, 3, 4, 5, 6, 7, 8};
struct node
{
    char MOVE;
    int father;
}path[MAX];
bool TryToInsert(int Front, int Rear, int MOVE)
{
    int Fcode = 0, Rcode = 0, i, j, cnt;
    for(i=0; i<7; ++i)
    {
        cnt = 0;
        for(j=i+1; j<8; ++j)
            if(LOG[Rear][i] > LOG[Rear][j])
                ++cnt;
        Rcode += cnt * fact[7-i];
    }
    if(vis[Rcode])
        return false;
    else
    {
        for(i=0; i<7; ++i)
        {
            cnt = 0;
            for(j=i+1; j<8; ++j)
                if(LOG[Front][i] > LOG[Front][j])
                    ++cnt;
            Fcode += cnt * fact[7-i];
        }
        path[Rcode].father = Fcode;
        path[Rcode].MOVE = 'A' + MOVE;
        return vis[Rcode] = true;
    }
}
void BFS(void)
{
    vis[0] = true;
    int Front = 0, Rear = 1, i, j;
    do
    {
        for(i=0; i<3; ++i)
        {
            for(j=0; j<8; ++j)
                LOG[Rear][j] = LOG[Front][ Move[i][j] ];
            if(TryToInsert(Front, Rear, i))
                ++Rear;
        }
        ++Front;
    } while (Front < Rear);
}
int main(void)
{
    BFS();
    stack<char> s;
    int Start[8], End[8], Aim[8], AimCode, i, j, cnt;
    char StartStr[10], EndStr[10];
    while(~scanf("%s%s", StartStr, EndStr))
    {
        for(i=0; i<8; ++i)
        {
            Start[i] = StartStr[i] - '0';
            End[i] = EndStr[i] - '0';
        }
        for(i=0; i<8; ++i)
        {
            for(j=0; End[i] != Start[j]; ++j);
            Aim[i] = j+1;
        }
        AimCode = 0;
        for(i=0; i<7; ++i)
        {
            cnt = 0;
            for(j=i+1; j<8; ++j)
                if(Aim[i] > Aim[j])
                    ++cnt;
            AimCode += cnt * fact[7-i];
        }
        while(AimCode)
        {
            s.push(path[AimCode].MOVE);
            AimCode = path[AimCode].father;
        }
        while(!s.empty())
        {
            printf("%c", s.top());
            s.pop();
        }
        printf("
");
    }
}