UVALive 6665 Dragon’s Cruller --BFS，类八数码问题

题意大概就是八数码问题，只不过把空格的移动方式改变了：空格能够向前或向后移动一格或三格（循环的）。

分析：其实跟八数码问题差不多，用康托展开记录状态，bfs即可。

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <cstdlib>
#define Mod 1000000007
#define SMod 10007
#define INint 2147483647
#define LL (0x3f3f3f3f3f3f3f3f)*2
#define ll long long
using namespace std;
#define N 500007

struct node
{
    ll cantor,cost;
    int pos;
    bool operator <(const node& a)const
    {
        return cost > a.cost;
    }
}S,E;

priority_queue<node> que;
ll fact[11] = {1,1,2,6,24,120,720,5040,40320,362880,3628800};
int dx[4] = {1,-1,3,-3};
int a[11],b[11],Can[N][11],vis[N];
ll ans,ch,cv;

ll Cantor(int *a)
{
    int i,j;
    ll cnt;
    ll res = 0;
    for(i=0;i<9;i++)
    {
        cnt = 0;
        for(j=i+1;j<9;j++)
            if(a[i] > a[j])
                cnt++;
        res += cnt*fact[8-i];
    }
    return res;
}

void getcantor(ll cantor,int *a)
{
    for(int i=0;i<9;i++)
        Can[cantor][i] = a[i];
}

void geta(ll cantor)
{
    for(int i=0;i<9;i++)
        a[i] = Can[cantor][i];
}

void bfs()
{
    while(!que.empty())
        que.pop();
    memset(vis,0,sizeof(vis));
    int i,j;
    que.push(S);
    //vis[S.cantor] = 1;
    while(!que.empty())
    {
        node tmp = que.top();
        que.pop();
        ll cantor = tmp.cantor;
        ll cost = tmp.cost;
        int pos = tmp.pos;
        if(vis[cantor])
            continue;
        vis[cantor] = 1;
        if(cost >= ans)
            continue;
        if(cantor == E.cantor)
        {
            ans = min(ans,cost);
            break;
        }
        geta(cantor);
        for(int k=0;k<4;k++)
        {
            int v = (pos+dx[k]+9)%9;
            swap(a[v],a[pos]);
            ll newcantor = Cantor(a);
            if(vis[newcantor])
            {
                swap(a[v],a[pos]);
                continue;
            }
            getcantor(newcantor,a);
            swap(a[v],a[pos]);
            node now;
            now.cantor = newcantor;
            now.pos = v;
            if(k < 2)
                now.cost = cost + ch;
            else
                now.cost = cost + cv;
            if(now.cost >= ans)
                continue;
            //vis[newcantor] = 1;
            que.push(now);
        }
    }
}

int main()
{
    int i,j;
    while(scanf("%lld%lld",&ch,&cv) && (ch||cv))
    {
        for(i=0;i<9;i++)
        {
            scanf("%d",&a[i]);
            if(a[i] == 0)
                S.pos = i;
        }
        S.cantor = Cantor(a);
        S.cost = 0;
        for(i=0;i<9;i++)
            scanf("%d",&b[i]);
        E.cantor = Cantor(b);
        getcantor(S.cantor,a);
        getcantor(E.cantor,b);
        ans = (1LL<<62);
        bfs();
        printf("%lld
",ans);
    }
    return 0;
}