UVALive-6665-Dragons Cruller(Dij+Hash)

将所有的康托展开扫一遍，然后逆康托展开，以此求转移权值

然后建图，只需要建一次图，因为状态转移是固定的

然后每一次询问跑一次最短路就行

（有一部分人用的是BFS+hash，

（有一部分人用的是A*

一开始上面两种思路觉得都会TLE，但是最后大家都没有...感谢大A熊的代码

#include <iostream>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <ctime>
#define maxn 500005
#define inf 10000000

using namespace std;

int fac[12] = {1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800};
int b[12] = {0,1,2,3,4,5,6,7,8,9,10,11};
int Hash(int s[],int fac[],int len)
{
    int ktzk = 0;
    for(int i = 0;i < len;i++)
    {
        int cnt = 0;
        for(int j=i+1;j<len;j++)
            if(s[j]<s[i]) cnt++;
        ktzk+=fac[len - 1 - i]*cnt;
    }
    return ktzk;
}

void get_ans(int result[],int b[],int fac[],int len,int n)
{
    for(int i=0;i<12;i++) b[i] = i;
    for(int j=0;j<len;j++)
    {
        int temp = n/fac[len - 1 - j];
        result[j] = b[temp];
        for(int i=temp;i<len-1;i++)
            b[i] = b[i+1];
        n -= temp*fac[len - 1 - j];
    }
}

int head[maxn],next[4*maxn],node[4*maxn],val[4*maxn];
int ch,cv,start,target,Index;
int T[9];
int MaxIndex;

void Init()
{
    memset(head,0,sizeof(head));
    memset(next,0,sizeof(next));
    Index = 0;
}

void Addedge(int from,int to,int v)
{
    Index++;
    next[Index] = head[from];
    node[Index] = to;
    val[Index] = v;
    head[from] = Index;
}

struct HeapNode
{
    int d,u;
    bool operator <(const HeapNode & rhs) const
    {
        return d > rhs.d;
    }
};
bool vis[maxn];
int d[maxn];

int Dij(int s,int t)
{
    priority_queue<HeapNode> Q;
    for(int i=0;i<=MaxIndex;i++) d[i] = inf;
    d[s] = 0;
    memset(vis,false,sizeof(vis));
    Q.push((HeapNode){0,s});
    while(!Q.empty())
    {
        HeapNode x = Q.top();Q.pop();
        int u = x.u;
        if(u == t) return d[u];
        if(vis[u]) continue;
        vis[u] = true;
        for(int p = head[u];p;p=next[p])
        {
            if(d[ node[p] ]>d[u]+(val[p]==0?ch:cv))
            {
                d[node[p]] = d[u] + (val[p]==0?ch:cv);
                Q.push((HeapNode){d[node[p]],node[p]});
            }
        }
    }
}

int main()
{
    int MaxT[9] = {8,7,6,5,4,3,2,1,0};
    MaxIndex = Hash(MaxT,fac,9);
    Init();
    for(int i=0;i<=MaxIndex;i++)
    {
        int T1[12],T2[12];
        get_ans(T1,b,fac,9,i);
        int pos,to;
        for(int j=0;j<9;j++) if(T1[j] == 0) pos = j;
//Sleep(500);
        for(int j=0;j<9;j++) T2[j] = T1[j];
        swap(T2[pos],T2[(pos+1)%9]);
        to = Hash(T2,fac,9);
        Addedge(i,to,0);
//cout<<i<<' '<<to<<' '<<ch<<endl;
        for(int j=0;j<9;j++) T2[j] = T1[j];
        swap(T2[pos],T2[(pos+8)%9]);
        to = Hash(T2,fac,9);
        Addedge(i,to,0);
//cout<<i<<' '<<to<<' '<<ch<<endl;
        for(int j=0;j<9;j++) T2[j] = T1[j];
        swap(T2[pos],T2[(pos+3)%9]);
        to = Hash(T2,fac,9);
        Addedge(i,to,1);
//cout<<i<<' '<<to<<' '<<ch<<endl;
        for(int j=0;j<9;j++) T2[j] = T1[j];
        swap(T2[pos],T2[(pos+6)%9]);
        to = Hash(T2,fac,9);
        Addedge(i,to,1);
//cout<<i<<' '<<to<<' '<<ch<<endl;
    }

    while(1)
    {
        scanf("%d%d",&ch,&cv);
        if(ch == 0 && cv == 0) break;

        for(int i=0;i<9;i++) scanf("%d",&T[i]);
        start = Hash(T,fac,9);
        for(int i=0;i<9;i++) scanf("%d",&T[i]);
        target = Hash(T,fac,9);
//cout<<start<<' '<<target<<endl;
        cout<<Dij(start,target)<<endl;
    }

    return 0;
}