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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#463871 | #7308. Permutation and noitatumreP | hos_lyric | AC ✓ | 75ms | 3800kb | C++14 | 7.5kb | 2024-07-05 15:23:48 | 2024-07-05 15:23:48 |
Judging History
answer
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 1000000007;
using Mint = ModInt<MO>;
vector<Mint> findLinearRecurrence(const vector<Mint> &as) {
const int n = as.size();
int d = 0, m = 0;
vector<Mint> cs(n + 1, 0), bs(n + 1, 0);
cs[0] = bs[0] = 1;
Mint invBef = 1;
for (int i = 0; i < n; ++i) {
++m;
Mint dif = as[i];
for (int j = 1; j < d + 1; ++j) dif += cs[j] * as[i - j];
if (dif.x != 0) {
auto csDup = cs;
const Mint r = dif * invBef;
for (int j = m; j < n; ++j) cs[j] -= r * bs[j - m];
if (2 * d <= i) {
d = i + 1 - d;
m = 0;
bs = csDup;
invBef = dif.inv();
}
}
}
cs.resize(d + 1);
return cs;
}
// x^e mod rev(cs)
vector<Mint> powerRev(const vector<Mint> &cs, Int e) {
assert(!cs.empty());
assert(cs[0] == 1);
const int d = (int)cs.size() - 1;
if (d == 0) {
return {};
} else if (d == 1) {
return {(-cs[1]).pow(e)};
}
auto mul = [&](const vector<Mint> &fs, const vector<Mint> &gs) {
vector<Mint> hs(d + d - 1, 0);
for (int i = 0; i < d; ++i) for (int j = 0; j < d; ++j) {
hs[i + j] += fs[i] * gs[j];
}
for (int i = d + d - 1; --i >= d; ) {
for (int j = 1; j <= d; ++j) {
hs[i - j] -= cs[j] * hs[i];
}
}
hs.resize(d);
return hs;
};
vector<Mint> xs(d, 0), ys(d, 0);
xs[1] = 1;
ys[0] = 1;
for (; ; xs = mul(xs, xs)) {
if (e & 1) ys = mul(ys, xs);
if (!(e >>= 1)) break;
}
return ys;
}
Mint linearRecurrenceAt(const vector<Mint> &as, const vector<Mint> &cs, Int e) {
assert(!cs.empty());
assert(cs[0] == 1);
const int d = (int)cs.size() - 1;
assert((int)as.size() >= d);
const auto fs = powerRev(cs, e);
Mint ans = 0;
for (int i = 0; i < d; ++i) {
ans += fs[i] * as[i];
}
return ans;
}
void exper() {
for (int N = 1; N <= 8; ++N) {
int all = 0;
vector<int> ps(N);
for (int i = 0; i < N; ++i) ps[i] = i + 1;
do {
vector<int> qs(N+N);
for (int i = 0; i < N; ++i) qs[i] = qs[N+N - 1 - i] = ps[i];
bool ok = true;
for (int a = 0; a < N+N; ++a) for (int b = a + 1; b < N+N; ++b) for (int c = b + 1; c < N+N; ++c) for (int d = c + 1; d < N+N; ++d) {
ok = ok && !(qs[a] < qs[c] && qs[c] < qs[d] && qs[d] < qs[b]);
}
if (ok) {
++all;
cout << ps << endl;
}
} while (next_permutation(ps.begin(), ps.end()));
cerr << "N = " << N << ": " << all << endl;
}
}
/*
N = 1: 1
N = 2: 2
N = 3: 6
N = 4: 16
N = 5: 36
N = 6: 80
N = 7: 178
N = 8: 394
*/
int main() {
// exper();
constexpr int M = 100;
vector<Mint> dp(M);
dp[0] = 1;
dp[1] = 1;
dp[2] = 2;
dp[3] = 6;
for (int n = 4; n < M; ++n) {
/*
insert n
- left side: empty
n, [1, n-1]
- left side: min = x, max = y
conditions about n
x, n, ?, ?': right side has (<= 1) value in [x+1, n-1]
x, n, ?', ?': right side has no value in [x+1, y-1]
1, n', ?, ?: left side is incr. in [2, n-1]
- y = n-2
2,...,n-2, n, n-1; insert 1 into left side
2,...,n-2, n, 1, n-1
x,...,n-2, n, n-1, [1, x-1] (2 <= x <= n-2)
- y = n-1
2,...,n-1, n; insert 1 into left side
x,...,n-1, n, [1, x-1] (2 <= x <= n-1)
*/
dp[n] += dp[n-1];
dp[n] += (n-2);
dp[n] += 1;
for (int x = 2; x <= n-2; ++x) dp[n] += dp[x-1];
dp[n] += (n-1);
for (int x = 2; x <= n-1; ++x) dp[n] += dp[x-1];
}
cerr<<"dp = "<<dp<<endl;
const auto cs = findLinearRecurrence(dp);
cerr<<"cs = "<<cs<<endl;
Int N;
for (; ~scanf("%lld", &N); ) {
const Mint ans = linearRecurrenceAt(dp, cs, N);
printf("%u\n", ans.x);
}
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
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Test #1:
score: 100
Accepted
time: 1ms
memory: 3776kb
input:
4 1000000000
output:
16 861159011
result:
ok 2 number(s): "16 861159011"
Test #2:
score: 0
Accepted
time: 75ms
memory: 3800kb
input:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 ...
output:
1 2 6 16 36 80 178 394 870 1920 4236 9344 20610 45458 100262 221136 487732 1075728 2372594 5232922 11541574 25455744 56144412 123830400 273116546 602377506 328585407 930287362 462952218 254489838 439267033 341486279 937462398 314191817 969869915 877202216 68596237 107062384 91326979 251250197 609562...
result:
ok 20000 numbers
Extra Test:
score: 0
Extra Test Passed