HDU 5836 Rubik's Cube

发表于 分类于 Disqus：

链接

传送门

题意

给出一个黑白色魔方，最多有五个黑块，求最多有几种不同形态。

思路

场上感觉这道能搞，搞了搞就出来了。枚举移动，用最小表示判重就好了。

代码

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#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <set>

using namespace std;
typedef long long LL;
const int rf[][16] = {
  { 0,  1,  2,  5,  8,  7,  6,  3,  0,  1,  2,  5,  8,  7,  6,  3},
  { 9, 10, 11, 14, 17, 16, 15, 12,  9, 10, 11, 14, 17, 16, 15, 12},
  {18, 19, 20, 23, 26, 25, 24, 21, 18, 19, 20, 23, 26, 25, 24, 21},
  {27, 28, 29, 32, 35, 34, 33, 30, 27, 28, 29, 32, 35, 34, 33, 30},
  {36, 37, 38, 41, 44, 43, 42, 39, 36, 37, 38, 41, 44, 43, 42, 39},
  {45, 46, 47, 50, 53, 52, 51, 48, 45, 46, 47, 50, 53, 52, 51, 48},
};
const int re[][24] = {
  {38, 37, 36, 29, 28, 27, 20, 19, 18, 11, 10,  9, 38, 37, 36, 29, 28, 27, 20, 19, 18, 11, 10,  9},
  { 0,  3,  6, 18, 21, 24, 45, 48, 51, 44, 41, 38,  0,  3,  6, 18, 21, 24, 45, 48, 51, 44, 41, 38},
  { 6,  7,  8, 27, 30, 33, 47, 46, 45, 17, 14, 11,  6,  7,  8, 27, 30, 33, 47, 46, 45, 17, 14, 11},
  {36, 39, 42, 53, 50, 47, 26, 23, 20,  8,  5,  2, 36, 39, 42, 53, 50, 47, 26, 23, 20,  8,  5,  2},
  { 2,  1,  0,  9, 12, 15, 51, 52, 53, 35, 32, 29,  2,  1,  0,  9, 12, 15, 51, 52, 53, 35, 32, 29},
  {15, 16, 17, 24, 25, 26, 33, 34, 35, 42, 43, 44, 15, 16, 17, 24, 25, 26, 33, 34, 35, 42, 43, 44},
  { 1,  4,  7, 19, 22, 25, 46, 49, 52, 43, 40, 37,  1,  4,  7, 19, 22, 25, 46, 49, 52, 43, 40, 37},
  {12, 13, 14, 21, 22, 23, 30, 31, 32, 39, 40, 41, 12, 13, 14, 21, 22, 23, 30, 31, 32, 39, 40, 41},
  { 3,  4,  5, 28, 31, 34, 50, 49, 48, 16, 13, 10,  3,  4,  5, 28, 31, 34, 50, 49, 48, 16, 13, 10},
};
const LL Mask[] = {-481977700336, -2588525269081674, -246300532427201, -10278919686062373, -15796654028395016, -17447110756761601, -5146951406846099, -3855821598721, -1970344432837689};
set<LL> s;
queue<LL> q;

LL Rotate(LL k, int x, int d1, int d2) {
  LL res = k & Mask[x];
  for (int i = 0; i < 8; ++i) {
    if (k & (1LL << rf[x][i])) {
      res |= 1LL << rf[x][i + d1];
    }
  }
  for (int i = 0; i < 12; ++i) {
    if (k & (1LL << re[x][i])) {
      res |= 1LL << re[x][i + d2];
    }
  }
  return res;
}

LL Rotate2(LL k, int x, int d) {
  LL res = k & Mask[x];
  for (int i = 0; i < 12; ++i) {
    if (k & (1LL << re[x][i])) {
      res |= 1LL << re[x][i + d];
    }
  }
  return res;
}

LL trans(LL k) {
  LL res = k, x = k;
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  x = Rotate(k, 0, 2, 3);
  x = Rotate(x, 5, 6, 9);
  x = Rotate2(x, 7, 9);
  if (x < res) {
    res = x;
  }
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  x = Rotate(k, 0, 4, 6);
  x = Rotate(x, 5, 4, 6);
  x = Rotate2(x, 7, 6);
  if (x < res) {
    res = x;
  }
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  x = Rotate(k, 0, 6, 9);
  x = Rotate(x, 5, 2, 3);
  x = Rotate2(x, 7, 3);
  if (x < res) {
    res = x;
  }
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  x = Rotate(k, 1, 2, 3);
  x = Rotate(x, 3, 6, 9);
  x = Rotate2(x, 6, 3);
  if (x < res) {
    res = x;
  }
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  x = Rotate(k, 1, 6, 9);
  x = Rotate(x, 3, 2, 3);
  x = Rotate2(x, 6, 9);
  if (x < res) {
    res = x;
  }
  for (int i = 1; i < 4; ++i) {
    x = Rotate(x, 2, 2, 3);
    x = Rotate(x, 4, 6, 9);
    x = Rotate2(x, 8, 3);
    if (x < res) {
      res = x;
    }
  }
  return res;
}

int main() {
  int t, tt = 0;
  scanf("%d", &t);
  while (t--) {
    int n;
    scanf("%d", &n);
    LL st = 0;
    for (int i = 0; i < n; ++i) {
      int x;
      scanf("%d", &x);
      st |= 1LL << x;
    }
    st = trans(st);
    q = queue<LL>();
    s.clear();
    q.push(st);
    s.insert(st);
    while (!q.empty()) {
      LL k = q.front();
      q.pop();
      for (int i = 0; i < 6; ++i) {
        LL a = trans(Rotate(k, i, 2, 3));
        if (!s.count(a)) {
          s.insert(a);
          q.push(a);
        }
        LL b = trans(Rotate(k, i, 6, 9));
        if (!s.count(b)) {
          s.insert(b);
          q.push(b);
        }
      }
    }
    printf("Case #%d: %d\n", ++tt, int(s.size()));
  }
  return 0;
}
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