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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#449134#8526. Polygon IIucup-team3215AC ✓1737ms12640kbC++204.0kb2024-06-20 18:33:072024-06-20 18:33:08

Judging History

你现在查看的是最新测评结果

  • [2024-06-20 18:33:08]
  • 评测
  • 测评结果:AC
  • 用时:1737ms
  • 内存:12640kb
  • [2024-06-20 18:33:07]
  • 提交

answer

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>

using namespace std;

constexpr int mod = 1e9 + 7, C = 51, N = 1e3 + 1;

using poly = vector<int>;

auto& mul(auto&& a, auto... b) { return ((a = a * (uint64_t)b % mod), ...); }
auto& add(auto&& a, auto... b) { return ((a -= (a += b) >= mod? mod: 0), ...); }
auto& adp(auto&& a, auto b, auto c) { return (a = (a + (uint64_t)b * c) % mod); }
auto& mad(auto&& a, auto b, auto c) { return (a = (a * (uint64_t)b + c) % mod); }
int inv_(int a) { for (int r = 1, b = mod - 2; ; mul(a, a), b /= 2) if (b % 2) mul(r, a); else if (!b) return r; }
poly dif(poly p, poly q) { if (p.size() < q.size()) p.resize(q.size()); for (int i = 0; i < q.size(); ++i) add(p[i], mod - q[i]); return p; }

int eval(const poly& p, int x) {
  int res = 0;
  for (int i = p.size(); i--; ) mad(res, x, p[i]);
  return res;
}

int inv[N];

poly ade(poly p) {
  for (int i = 0; i < p.size(); ++i) mul(p[i], inv[i + 1]);
  p.insert(p.begin(), 0);
  return p;
}

poly ksb(poly a, poly b) {
  poly res(a.size() + b.size() - 1);
  if (min(a.size(), b.size()) < 64) {
    for (int i = 0; i < a.size(); ++i)
    for (int j = 0; j < b.size(); ++j) adp(res[i + j], a[i], b[j]);
    return res;
  }
  int s = (max(a.size(), b.size()) + 1) / 2;
//  if (s == 58) cout << a.size() << ' ' << b.size() << ' ' << s << '\n';
  a.resize(s * 2);
  b.resize(s * 2);
  poly l = ksb({a.begin(), a.begin() + s}, {b.begin(), b.begin() + s});
  poly r = ksb({a.begin() + s, a.end()}, {b.begin() + s, b.end()});
  for (int i = 0; i < s; ++i) add(a[i], a[i + s]);
  for (int i = 0; i < s; ++i) add(b[i], b[i + s]);
  poly m = ksb({a.begin(), a.begin() + s}, {b.begin(), b.begin() + s});
  copy(l.begin(), l.end(), res.begin());
  copy_n(r.begin(), res.size() - s * 2, res.begin() + s * 2);
  for (int i = 0; i < min(m.size(), res.size() - s); ++i) res[i + s] = (res[i + s] + m[i] + 2ull * mod - l[i] - r[i]) % mod;
  return res;
}

int main() {
  cin.tie(0)->sync_with_stdio(0);
  for (int i = 1; i < N; ++i) inv[i] = inv_(i);
  int n; cin >> n;
  int c0[C]{}, cnt[C]{};
  for (int i = 0, x; i < n; ++i) cin >> x, ++c0[x], cnt[x - !!x] += !!x;
  for (int i = C; --i; ) cnt[i - 1] += cnt[i];
  vector<poly> cont{{1}, {0}}, nx;
  for (int i = 1; i < n; ++i) {
    poly pp;
    for (int i = 0; auto& p: cont) {
      p = ade(p);
      uint64_t s = 0;
      for (auto& x: pp) s += x;
      pp.resize(max(pp.size(), p.size()));
      for (int i = 0; i < p.size(); ++i) pp[i] = add(+p[i], mod - pp[i]);
      for (int i = p.size(); i < pp.size(); ++i) pp[i] = mod - pp[i];
      add(pp[0], s % mod);
      nx.push_back(move(pp));
      swap(pp, p);
    }
    nx.push_back({0});
    swap(cont = {}, nx);
  }
  vector<int> e(n);
  for (int i = 0; i < n; ++i) e[i] = add(eval(ade(cont[i]), 1), e[i - !!i]);
  int ans = 0;
  vector<poly> coef;
  for (int c = 0; c < C; ++c) if (cnt[c]) {
    poly cur{1};
    for (int j = cnt[c]; j--; ) {
      cur.push_back(0);
      for (int i = 0, p = 0, t; i < cur.size(); ++i) t = p, p = cur[i], cur[i] = mul(t + p, mod / 2 + 1);
    }
    coef.push_back(cur);
  }
  for (int c = C; c--; ) if (c0[c]) {
    vector<int> dens{{1}}, ndens;
    int64_t mins = 1 - (1ll << c), maxs = n - 2 + mins, L = 0;
    for (int i = C; i--; ) maxs += 1ll * cnt[i] << i;
    int cans = 0;
    for (int i = C; i--; ) if (cnt[i]) {
      for (auto& x: dens) ndens.push_back(x), ndens.push_back(0);
      swap(dens = {}, ndens);
      dens.pop_back();
      L *= 2;
      dens = ksb(dens, coef[i]);
      maxs -= 0ll + cnt[i] - (i < c) << i;
      mins += 0ll + (i < c) << i;
      L -= i < c;
      int d = 0;
      while (-L > maxs >> i) add(cans, dens[d++]), ++L;
      dens.erase(dens.begin(), dens.begin() + d);
      while ((int)dens.size() + L - 1 > -mins >> i) dens.pop_back();
    }
    for (int i = 0; L <= 0; ++i) add(cans, mul(+dens[i], e[-L++]));
    add(ans, mul(cans, c0[c]));
  }
  cout << add(1, mod - ans) << '\n';
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3820kb

input:

3
0 2 0

output:

166666668

result:

ok 1 number(s): "166666668"

Test #2:

score: 0
Accepted
time: 1ms
memory: 3668kb

input:

3
0 0 0

output:

500000004

result:

ok 1 number(s): "500000004"

Test #3:

score: 0
Accepted
time: 1ms
memory: 3632kb

input:

3
5 6 7

output:

208333335

result:

ok 1 number(s): "208333335"

Test #4:

score: 0
Accepted
time: 1ms
memory: 3632kb

input:

3
0 25 50

output:

889268532

result:

ok 1 number(s): "889268532"

Test #5:

score: 0
Accepted
time: 1ms
memory: 3576kb

input:

10
39 11 25 1 12 44 10 46 27 15

output:

913863330

result:

ok 1 number(s): "913863330"

Test #6:

score: 0
Accepted
time: 4ms
memory: 3732kb

input:

57
43 22 3 16 7 5 24 32 25 16 41 28 24 30 28 10 32 48 41 43 34 37 48 34 3 9 21 41 49 25 2 0 36 45 34 33 45 9 42 29 43 9 38 34 44 33 44 6 46 39 22 36 40 37 19 34 3

output:

400729664

result:

ok 1 number(s): "400729664"

Test #7:

score: 0
Accepted
time: 4ms
memory: 3816kb

input:

100
44 32 6 6 6 44 12 32 6 9 23 12 14 23 12 14 23 49 6 14 32 23 49 9 32 24 23 6 32 6 49 23 12 44 24 9 14 6 24 44 24 23 44 44 49 32 49 12 49 49 24 49 12 23 3 14 6 3 3 6 12 3 49 24 49 24 24 32 23 32 49 14 3 24 49 3 32 14 44 24 49 3 32 23 49 44 44 9 23 14 49 9 3 6 44 24 3 3 12 44

output:

32585394

result:

ok 1 number(s): "32585394"

Test #8:

score: 0
Accepted
time: 890ms
memory: 12500kb

input:

1000
2 27 0 0 27 0 2 0 27 0 27 27 0 0 0 0 0 2 0 27 0 2 2 0 27 27 0 0 0 27 2 2 2 27 0 2 27 2 0 2 27 0 0 27 0 27 0 0 27 2 27 2 2 27 2 27 0 0 27 0 27 0 2 27 2 2 0 27 27 27 27 0 27 0 27 0 2 2 0 2 2 27 0 0 27 0 0 27 0 2 27 27 2 27 2 0 0 2 27 27 27 27 27 27 2 2 0 2 2 0 2 2 0 27 0 27 2 2 0 27 27 0 0 27 2 2...

output:

94588769

result:

ok 1 number(s): "94588769"

Test #9:

score: 0
Accepted
time: 1087ms
memory: 12636kb

input:

1000
40 14 47 3 32 18 3 49 22 23 32 18 23 24 18 32 23 39 32 27 49 49 22 50 50 22 23 47 14 47 50 32 22 24 49 49 18 22 18 22 50 3 32 47 40 3 39 22 24 47 32 49 49 22 32 39 14 49 39 3 32 22 24 18 39 49 24 18 40 23 23 49 39 39 18 39 27 49 14 27 27 14 18 24 39 22 40 50 18 18 18 39 39 18 23 23 22 3 49 47 2...

output:

626481946

result:

ok 1 number(s): "626481946"

Test #10:

score: 0
Accepted
time: 1127ms
memory: 12640kb

input:

1000
28 32 35 9 21 11 43 23 45 15 23 2 8 3 39 41 31 9 45 35 27 14 40 28 31 9 31 9 9 40 8 6 27 43 3 27 23 49 27 6 28 25 11 9 15 27 38 27 12 28 25 2 15 27 45 6 27 1 21 38 1 25 27 21 49 31 31 14 39 39 8 39 40 28 15 31 21 14 43 38 11 8 8 23 9 11 15 2 11 39 32 14 28 15 40 49 27 9 23 9 9 6 21 2 2 1 14 11 ...

output:

644443122

result:

ok 1 number(s): "644443122"

Test #11:

score: 0
Accepted
time: 1330ms
memory: 11848kb

input:

972
39 15 23 0 40 29 43 47 6 9 30 9 2 8 19 9 45 25 26 38 33 18 6 33 44 48 24 8 4 16 33 42 33 31 36 33 13 16 3 12 21 19 1 30 24 23 43 35 0 33 31 32 23 31 36 12 26 0 29 48 28 33 28 28 3 49 9 5 29 8 29 28 49 41 33 49 5 49 6 9 50 25 39 11 1 36 6 44 10 34 32 31 25 31 36 36 3 9 50 35 47 43 25 46 30 18 5 2...

output:

684920840

result:

ok 1 number(s): "684920840"

Test #12:

score: 0
Accepted
time: 34ms
memory: 4204kb

input:

147
34 47 42 23 46 3 41 9 15 42 21 32 24 1 19 46 29 35 38 20 2 43 36 47 19 23 20 9 6 28 48 46 45 21 19 41 31 36 50 7 11 25 0 43 38 46 21 2 26 40 32 14 45 35 47 21 13 26 26 30 3 36 35 45 36 21 21 25 2 40 35 50 23 3 16 44 40 42 6 37 36 19 20 14 30 47 13 49 47 45 26 12 15 21 42 30 19 5 21 9 28 8 3 34 4...

output:

972735235

result:

ok 1 number(s): "972735235"

Test #13:

score: 0
Accepted
time: 1424ms
memory: 12456kb

input:

1000
36 15 9 5 35 37 17 30 24 13 18 32 14 35 36 26 23 7 21 15 43 15 21 11 33 33 9 16 5 26 1 45 48 27 20 20 20 48 42 27 22 7 39 35 11 38 33 47 22 34 43 4 32 0 47 35 48 8 9 3 40 3 27 22 20 43 12 37 30 18 2 37 37 35 44 3 42 14 20 24 44 5 17 38 46 41 28 23 21 7 13 15 35 38 21 14 6 37 37 6 13 34 32 13 23...

output:

179933029

result:

ok 1 number(s): "179933029"

Test #14:

score: 0
Accepted
time: 1413ms
memory: 12460kb

input:

1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7...

output:

540327646

result:

ok 1 number(s): "540327646"

Test #15:

score: 0
Accepted
time: 1413ms
memory: 12616kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 46 46 46 46 46 46 46 46 46 46 46 46 46 4...

output:

169647494

result:

ok 1 number(s): "169647494"

Test #16:

score: 0
Accepted
time: 1737ms
memory: 12504kb

input:

1000
11 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 40 50 50 50 50 50 21 50 12 50 50 50 50 50 0 50 50 50 38 50 50 50 50 50 50 25 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 7 50 50 50 50 50 50 50 50 ...

output:

862643524

result:

ok 1 number(s): "862643524"

Test #17:

score: 0
Accepted
time: 943ms
memory: 12456kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 5...

output:

819612372

result:

ok 1 number(s): "819612372"

Test #18:

score: 0
Accepted
time: 951ms
memory: 12640kb

input:

1000
50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 5...

output:

18215579

result:

ok 1 number(s): "18215579"

Test #19:

score: 0
Accepted
time: 1ms
memory: 3580kb

input:

16
0 2 24 1 23 9 14 17 28 29 25 27 15 19 11 20

output:

115090079

result:

ok 1 number(s): "115090079"

Test #20:

score: 0
Accepted
time: 883ms
memory: 12408kb

input:

1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0...

output:

819612372

result:

ok 1 number(s): "819612372"

Test #21:

score: 0
Accepted
time: 1ms
memory: 3644kb

input:

18
9 4 21 5 22 6 9 16 3 14 11 2 0 12 6 3 7 21

output:

0

result:

ok 1 number(s): "0"

Extra Test:

score: 0
Extra Test Passed