【USACO 3.2】Magic Squares

/*
USER:19flipp1
TASK:msquare
LANG:C++
*/
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define ll long long
#define in(s) freopen(#s".in","r",stdin);freopen(#s".out","w",stdout);
#define N 10
using namespace std;
int a[N],fac[N];
struct node{
    int a[N];
    int d;
    char s[25];
}nd;
bool vis[320000];
int cantor(int a[N]){
    int ans=0,c;
    for(int i=1;i<8;i++){
        c=0;
        for(int j=i;j<=8;j++)if(a[i]>a[j])c++;
        ans+=fac[8-i]*c;
    }
    return ans;
}
void work(int a[],int i){
    if(i==0){
        for(int j=1;j<=4;j++)swap(a[j],a[9-j]);
    }else if(i==1){
        int t=a[1];
        a[1]=a[4],a[4]=a[3],a[3]=a[2],a[2]=t;
        t=a[5];
        a[5]=a[6],a[6]=a[7],a[7]=a[8],a[8]=t;
    }else if(i==2){
        int t=a[2];
        a[2]=a[7];a[7]=a[6];a[6]=a[3];a[3]=t;
    }
}
void bfs(){
    queue<node> q;
    node p;
    for(int i=1;i<=8;i++)p.a[i]=i;
    p.d=0;
    q.push(p);
    while(!q.empty()){
        node p=q.front();
        q.pop();
        int ok=1;
        for(int i=1;i<=8;i++)if(p.a[i]!=nd.a[i]){ok=0;break;}
        if(ok){
            printf("%d\n",p.d);
            for(int i=1;i<=p.d;i++)
                printf("%c",p.s[i]);
            puts("");
            break;
        }
        for(int i=0;i<3;i++){
            node np=p;
            work(np.a,i);
            int num=cantor(np.a);
            if(!vis[num]){
                vis[num]=1;
                np.d++;
                np.s[np.d]='A'+i;
                q.push(np);
            }
        }
    }
}
int main(){
    in(msquare);
    fac[0]=1;
    for(int i=1;i<=8;i++){
        scanf("%d",&nd.a[i]);
        fac[i]=fac[i-1]*i;
    }
    bfs();
    return 0;
}

/*
USER:19flipp1
TASK:msquare
LANG:C++
*/
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#define ll long long
#define in(s) freopen(#s".in","r",stdin);freopen(#s".out","w",stdout);
#define N 10
using namespace std;
int a[N],fac[N];
struct node{
    int a[N];
    int d;
    char s[25];
}nd;
bool vis[8][8][8][8][8][8][8];
void work(int a[],int i){
    if(i==0){
        for(int j=1;j<=4;j++)swap(a[j],a[9-j]);
    }else if(i==1){
        int t=a[1];
        a[1]=a[4],a[4]=a[3],a[3]=a[2],a[2]=t;
        t=a[5];
        a[5]=a[6],a[6]=a[7],a[7]=a[8],a[8]=t;
    }else if(i==2){
        int t=a[2];
        a[2]=a[7];a[7]=a[6];a[6]=a[3];a[3]=t;
    }
}
bool Vis(int a[]){
    bool &t=vis[a[1]-1][a[2]-1][a[3]-1][a[4]-1][a[5]-1][a[6]-1][a[7]-1];
    if(t)return 1;
    t=1;
    return 0;
}
void bfs(){
    queue<node> q;
    node p;
    for(int i=1;i<=8;i++)p.a[i]=i;
    p.d=0;
    q.push(p);
    while(!q.empty()){
        node p=q.front();
        q.pop();
        int ok=1;
        for(int i=1;i<=8;i++)if(p.a[i]!=nd.a[i]){ok=0;break;}
        if(ok){
            printf("%d\n",p.d);
            for(int i=1;i<=p.d;i++)
                printf("%c",p.s[i]);
            puts("");
            break;
        }
        for(int i=0;i<3;i++){
            node np=p;
            work(np.a,i);
            if(!Vis(np.a)){
                np.d++;
                np.s[np.d]='A'+i;
                q.push(np);
            }
        }
    }
}
int main(){
    in(msquare);
    fac[0]=1;
    for(int i=1;i<=8;i++){
        scanf("%d",&nd.a[i]);
        fac[i]=fac[i-1]*i;
    }
    bfs();
    return 0;
}