USACO Magic Squares

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/*
 ID: wcr19961
 PROG: msquare
 LANG: C++11
*/
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long LL;
const int maxn = 10;
const int maxm = 100330;
const int A[maxn] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
int len[maxm], fa[maxm];
char p[maxm], s[maxm];
bool vis[maxm];
struct node {
  int a[8], st;
  
  node trans(int t) {
    node k = *this;
    if (t == 0) {
      for (int i = 0; i < 4; ++i) {
        swap(k.a[i], k.a[8 - i - 1]);
      }
    } else if (t == 1) {
      for (int i = 3; i > 0; --i) {
        swap(k.a[i], k.a[i - 1]);
        swap(k.a[8 - i - 1], k.a[8 - i]);
      }
    } else {
      swap(k.a[5], k.a[6]);
      swap(k.a[2], k.a[5]);
      swap(k.a[1], k.a[2]);
    }
    k.cantor();
    return k;
  }
  
  int cantor() {
    st = 0;
    for (int i = 0; i < 8; ++i) {
      int cnt = 0;
      for (int j = i + 1; j < 8; ++j) {
        if (a[i] > a[j]) {
          ++cnt;
        }
      }
      st += cnt * A[7 - i];
    }
    return st;
  }
} a;
int main() {
  freopen("msquare.in", "r", stdin);
  freopen("msquare.out", "w", stdout);
  for (int i = 0; i < 8; ++i) {
    scanf("%d", &a.a[i]);
  }
  int aim = a.cantor();
  for (int i = 0; i < 8; ++i) {
    a.a[i] = i + 1;
  }
  vis[a.cantor()] = true;
  fa[a.st] = -1, len[a.st] = 0;
  queue<node> q;
  q.push(a);
  while (!q.empty()) {
    node k = q.front();
    q.pop();
    if (k.st == aim) {
      printf("%d\n", len[aim]);
      int cnt = 0;
      while (fa[aim] != -1) {
        s[cnt++] = p[aim];
        aim = fa[aim];
      }
      for (int i = 0; i < cnt; ++i) {
        putchar(s[cnt - i - 1]);
        if (i % 60 == 59) {
          puts("");
        }
      }
      if (cnt == 0 || cnt % 60 != 0) {
        puts("");
      }
      return 0;
    }
    for (int i = 0; i < 3; ++i) {
      node x = k.trans(i);
      if (!vis[x.st]) {
        vis[x.st] = true;
        len[x.st] = len[k.st] + 1;
        fa[x.st] = k.st;
        p[x.st] = i + 'A';
        q.push(x);
      }
    }
  }
  return 0;
}

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