注意到答案不超过$5$,因此可以考虑BFS求出距离起始态或者终止态不超过$2$的所有状态。
设它们到起始态、终止态的距离分别为$f[S],g[S]$,则$ans=\min(5,f[S]+g[S])$。
时间复杂度$O(n^6\log(n!))$。
#include<cstdio> #include<algorithm> using namespace std; typedef unsigned long long ll; const int N=12,M=363000; int n,i,j,k,a[N],len[N],S,x,z,v[M],g[M],h,t,q[M],ans;ll f[N][M]; inline ll encode(){ ll t=0; for(int i=0;i<n;i++)t=t<<4|a[i]; return t; } inline int getid(ll x){ int l=0,r=len[n]-1; while(l<=r){ int mid=(l+r)>>1; if(f[n][mid]==x)return mid; if(f[n][mid]<x)l=mid+1;else r=mid-1; } } inline void ext(int x){ if(~v[x])return; v[q[++t]=x]=z; } int main(){ for(n=2;n<=9;n++){ for(i=0;i<n;i++)a[i]=i; do{f[n][len[n]++]=encode();}while(next_permutation(a,a+n)); sort(f[n],f[n]+len[n]); } while(~scanf("%d",&n)){ if(!n)return 0; for(i=0;i<n;i++)scanf("%d",&a[i]),a[i]--; if(n==1){puts("0");continue;} S=getid(encode()); h=1,t=0; for(i=0;i<len[n];i++)v[i]=-1; z=0; ext(S); while(h<=t){ z=v[x=q[h++]]+1; if(z>2)continue; ll O=f[n][x]; for(i=1;i<n;i++)for(j=i;j<n;j++){ ll U=(1ULL<<((j-i+2)*4))-1,F=O; int L=(j-i+1)*4; for(k=4*(i-1);k>=0;k-=4){ ll A=(F>>k)&U; F^=(A^((A>>4)|(A&15)<<L))<<k; ext(getid(F)); } } } for(i=0;i<len[n];i++)g[i]=v[i],v[i]=-1; h=1,t=z=0; ext(0); while(h<=t){ z=v[x=q[h++]]+1; if(z>2)continue; ll O=f[n][x]; for(i=1;i<n;i++)for(j=i;j<n;j++){ ll U=(1ULL<<((j-i+2)*4))-1,F=O; int L=(j-i+1)*4; for(k=4*(i-1);k>=0;k-=4){ ll A=(F>>k)&U; F^=(A^((A>>4)|(A&15)<<L))<<k; ext(getid(F)); } } } for(ans=5,i=0;i<len[n];i++)if(~v[i]&&~g[i])ans=min(ans,v[i]+g[i]); printf("%d\n",ans); } return 0; }
时间: 2024-10-10 17:44:46