結果

問題 No.248 ミラー君の宿題
ユーザー Min_25Min_25
提出日時 2015-05-21 11:53:38
言語 C++11
(gcc 11.4.0)
結果
AC  
実行時間 107 ms / 5,000 ms
コード長 4,376 bytes
コンパイル時間 713 ms
コンパイル使用メモリ 84,924 KB
実行使用メモリ 66,560 KB
最終ジャッジ日時 2024-07-06 04:20:44
合計ジャッジ時間 2,042 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 4 ms
5,248 KB
testcase_01 AC 3 ms
5,376 KB
testcase_02 AC 3 ms
5,376 KB
testcase_03 AC 5 ms
5,376 KB
testcase_04 AC 8 ms
5,376 KB
testcase_05 AC 10 ms
11,520 KB
testcase_06 AC 13 ms
11,648 KB
testcase_07 AC 17 ms
11,520 KB
testcase_08 AC 6 ms
11,520 KB
testcase_09 AC 51 ms
11,520 KB
testcase_10 AC 56 ms
11,520 KB
testcase_11 AC 68 ms
66,560 KB
testcase_12 AC 76 ms
66,432 KB
testcase_13 AC 85 ms
66,432 KB
testcase_14 AC 104 ms
66,432 KB
testcase_15 AC 107 ms
66,432 KB
testcase_16 AC 105 ms
66,432 KB
testcase_17 AC 60 ms
66,432 KB
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ソースコード

diff # 

#include <cstdio>
#include <cmath>
#include <cstring>
#include <cstdlib>
#include <ctime>
#include <cassert>

#include <iostream>
#include <utility>
#include <algorithm>
#include <queue>
#include <functional>
#include <vector>
#include <map>
#include <set>
#include <complex>

#define getchar getchar_unlocked
#define putchar putchar_unlocked

using namespace std;

typedef long long int64;
typedef long long unsigned uint64;
typedef long double float80;
typedef unsigned short uint16;
typedef unsigned uint;
typedef unsigned char uint8;

const uint N_PRIMES = 14;
const uint STATE_MAX = 1 << N_PRIMES;
const uint BITS = 65;

typedef double prob_t;

uint64 primes[N_PRIMES];

uint phi_two[STATE_MAX];
uint state_min_two[STATE_MAX];

prob_t probs_cumu[STATE_MAX][BITS];
prob_t probs_cumucumu[STATE_MAX][N_PRIMES][BITS];
prob_t probs_same[STATE_MAX];
prob_t probs_pos[STATE_MAX];
prob_t probs_neg[STATE_MAX];

prob_t state_prods[STATE_MAX];
prob_t state_phis[STATE_MAX];

prob_t pows[BITS];
prob_t dp[STATE_MAX];

inline uint ilog2(uint64 x) {
  union {
    uint64 u64;
    double d;
  } n;
  n.d = double(x) + 0.5;
  return (n.u64 >> 52) - 1023;
}

void init(uint N) {
  // O(2^N * N * log(max{E_i}))
  const uint state_max = 1 << N;

  pows[0] = 1.0;
  for (uint i = 1; i < BITS; ++i) {
    pows[i] = pows[i-1] * 0.5;
  }

  uint max_two = 0;
  for (uint i = 0; i < N; ++i) {
    uint64 phi = primes[i] - 1;
    phi_two[i] = ilog2(phi & -phi);
    max_two = max(max_two, phi_two[i]);
  }

  for (uint i = 0; i < state_max; ++i) {
    for (uint j = 0; j <= max_two; ++j) {
      probs_cumu[i][j] = 1.0;
    }
    probs_same[i] = 1.0;
    probs_pos[i] = 1.0;
    probs_neg[i] = 1.0;
    state_prods[i] = 1.0;
    state_phis[i] = 1.0;
    state_min_two[i] = 1e9;
  }

  for (uint state = 1; state < state_max; ++state) {
    uint f = state & -state;
    uint pstate = state ^ f;
    uint idx = ilog2(f);
    uint two = phi_two[idx];
    state_min_two[state] = min(state_min_two[pstate], two);
    prob_t p = primes[idx];
    probs_pos[state] = probs_pos[pstate] / p;
    probs_neg[state] = probs_neg[pstate] * (1. - 1. / p);
    state_prods[state] = state_prods[pstate] * p;
    state_phis[state]  = state_phis[pstate] * (p - 1.0);
    prob_t pw = pows[two];
    prob_t q = pw;

    probs_same[state] = probs_same[pstate] * pw;
    for (uint i = 0; i <= two; ++i) {
      probs_cumu[state][i] = probs_cumu[pstate][i] * q;
      if (i > 0) {
        pw *= 2.0;
      }
      q += pw;
    }
    for (uint i = two + 1; i <= max_two; ++i) {
      probs_cumu[state][i] = probs_cumu[pstate][i];
    }

    // x_0 y_1 + x_1 y_2 + ... 
    for (uint t = 1; t < N; ++t) {
      pw = 1.0;
      probs_cumucumu[state][t][1] = probs_cumu[state][0];
      for (uint i = 2; i <= max_two; ++i) {
        pw /= pows[t];
        probs_cumucumu[state][t][i] = probs_cumucumu[state][t][i-1] + probs_cumu[state][i-1] * pw;
      }
    }
  }
}

inline uint pop_count(uint n) {
  return __builtin_popcount(n);
}

prob_t calc(const uint N) {
  // O(3^N)
  const uint total = 1 << N;
  for (uint state = 1; state < total; ++state) {
    if ( (state & (state - 1)) == 0) {
      dp[state] = 1.0;
      continue;
    }
    prob_t Q = state_phis[state];
    prob_t P = state_prods[state];
    prob_t expected_count = 1.0;
    prob_t prob_not_repeat = 0.0;
    for (uint left_state = (state - 1) & state; left_state > 0; left_state = (left_state - 1) & state) {
      uint right_state = state ^ left_state;
      prob_t p1 = probs_pos[left_state] * probs_neg[right_state];
      prob_t p2 = probs_same[right_state]
                * probs_cumucumu[left_state][pop_count(right_state)][state_min_two[right_state]]
                * Q / P;
      prob_t p3 = p1 + p2;
      expected_count += p3 * (dp[left_state] + dp[right_state]);
      prob_not_repeat += p3;
    }
    expected_count /= prob_not_repeat;
    dp[state] = expected_count;
  }
  return dp[total - 1];
}

void solve() {
  uint T; assert(1 == scanf("%u", &T));
  assert(1 <= T && T <= 1000);
  for (; T; --T) {
    uint N; assert(1 == scanf("%u", &N));
    assert(1 <= N && N <= N_PRIMES);
    for (uint i = 0; i < N; ++i) {
      assert(1 == scanf("%llu", &primes[i]));
      assert(3 <= primes[i] && primes[i] < (1ull << 63));
    }
    init(N);
    prob_t ans = calc(N);
    printf("%.8lf\n", ans);
  }
}

int main() {
  solve();
  return 0;
}
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