QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#73669 | #3537. The only winner | sinbad# | AC ✓ | 245ms | 4572kb | C++ | 7.5kb | 2023-01-27 15:31:33 | 2023-01-27 15:31:34 |
Judging History
answer
// #define LOCAL
#define _USE_MATH_DEFINES
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>
using namespace std;
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
out << "(" << a.first << "," << a.second << ")";
return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
out << "["; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
out << "["; bool first = true;
for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const multiset<T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
const char* comma = strchr(names + 1, ',');
cerr.write(names, comma - names) << ": " << arg1 << " |";
__f(comma + 1, args...);
}
template <class T> auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D> auto vect(const T& v, int n, D... m) {
return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}
using int64 = long long;
using int128 = __int128_t;
using ii = pair<int, int>;
#define SZ(x) (int)((x).size())
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
const int MOD = 1e9 + 7;
// const int MOD = 998244353;
mt19937_64 mrand(random_device{}());
int64 rnd(int64 x) { return mrand() % x; }
constexpr inline int lg2(int64 x) { return x == 0 ? -1 : sizeof(int64) * 8 - 1 - __builtin_clzll(x); }
constexpr inline int p2ceil(int64 x) { return 1 << (lg2(x - 1) + 1); }
template <class T> void out(const vector<T>& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; }
template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template <class T> void dedup(vector<T>& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); }
inline void add_mod(int& x, int y) { x += y; if (x >= MOD) x -= MOD; }
inline void sub_mod(int& x, int y) { x += MOD - y; if (x >= MOD) x -= MOD; }
inline int mod(int x) { return x >= MOD ? x - MOD : x; }
struct fast_ios {
fast_ios() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
};
} fast_ios_;
template <int MOD_> struct modnum {
static constexpr int MOD = MOD_;
static_assert(MOD_ > 0, "MOD must be positive");
private:
int v;
static int minv(int a, int m) {
a %= m; assert(a);
return a == 1 ? 1 : int(m - int64(minv(m, a)) * int64(m) / a);
}
public:
modnum() : v(0) {}
modnum(int64 v_) : v(int(v_ % MOD)) { if (v < 0) v += MOD; }
explicit operator int() const { return v; }
friend std::ostream& operator << (std::ostream& out, const modnum& n) { return out << int(n); }
friend std::istream& operator >> (std::istream& in, modnum& n) { int64 v_; in >> v_; n = modnum(v_); return in; }
friend bool operator == (const modnum& a, const modnum& b) { return a.v == b.v; }
friend bool operator != (const modnum& a, const modnum& b) { return a.v != b.v; }
modnum inv() const { modnum res; res.v = minv(v, MOD); return res; }
friend modnum inv(const modnum& m) { return m.inv(); }
modnum neg() const { modnum res; res.v = v ? MOD-v : 0; return res; }
friend modnum neg(const modnum& m) { return m.neg(); }
modnum operator- () const { return neg(); }
modnum operator+ () const { return modnum(*this); }
modnum& operator ++ () { ++v; if (v == MOD) v = 0; return *this; }
modnum& operator -- () { if (v == 0) v = MOD; --v; return *this; }
modnum& operator += (const modnum& o) { v += o.v; if (v >= MOD) v -= MOD; return *this; }
modnum& operator -= (const modnum& o) { v -= o.v; if (v < 0) v += MOD; return *this; }
modnum& operator *= (const modnum& o) { v = int(int64(v) * int64(o.v) % MOD); return *this; }
modnum& operator /= (const modnum& o) { return *this *= o.inv(); }
friend modnum operator ++ (modnum& a, int) { modnum r = a; ++a; return r; }
friend modnum operator -- (modnum& a, int) { modnum r = a; --a; return r; }
friend modnum operator + (const modnum& a, const modnum& b) { return modnum(a) += b; }
friend modnum operator - (const modnum& a, const modnum& b) { return modnum(a) -= b; }
friend modnum operator * (const modnum& a, const modnum& b) { return modnum(a) *= b; }
friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= b; }
friend modnum power(modnum a, int64 n) {
modnum ret = 1;
for (; n; n >>= 1) {
if (n & 1) ret *= a;
a *= a;
}
return ret;
}
};
using mint = modnum<MOD>;
int main() {
int n;
cin >> n;
if (n == 1) {
cout << 1 << '\n';
return 0;
}
// vector<int> p(n * 2);
// iota(p.begin(), p.end(), 1);
// int ans = 0, tot = 0;
// map<int, int> ans2;
// do {
// bool ok = 1;
// for (int i = 0; i < n * 2; i += 2) {
// if (p[i + 1] < p[i]) ok = 0;
// }
// if (!ok) continue;
// map<int, int> A;
// for (int i = 0; i < n * 2; i += 2) {
// A[p[i] + p[i + 1]]++;
// }
// int mx = A.rbegin()->first;
// if (A[mx] == 1) {
// ++ans;
// ans2[mx]++;
// }
// ++tot;
// } while (next_permutation(p.begin(), p.end()));
// trace(ans, tot);
// trace(ans, ans2, tot);
vector<mint> fact(2 * n + 1);
for (int i = 0; i <= 2 * n; ++i) fact[i] = i == 0 ? 1 : fact[i - 1] * i;
vector<mint> p2(2 * n + 1);
for (int i = 0; i <= 2 * n; ++i) p2[i] = i == 0 ? 1 : p2[i - 1] * 2;
mint ret = 0;
for (int k = 2; k < n * 2; ++k) {
mint cur = (2 * n - k + 1) / 2;
int D = 2 * n - (2 * n + k + 1) / 2;
// trace(n, k, cur, D);
cur *= power(mint(k - 1), D) * fact[D + 1];
int m = 2 * n - 2 * (D + 1);
// trace(m, cur);
cur *= fact[m] / p2[m / 2];
cur *= fact[1 + D + m / 2] / fact[1 + D] / fact[m / 2];
// trace(k, D, m, cur);
ret += cur;
}
trace(ret, fact[2 * n] / p2[n]);
ret /= fact[2 * n] / p2[n];
cout << ret << '\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3380kb
input:
2
output:
666666672
result:
ok 1 number(s): "666666672"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3360kb
input:
1
output:
1
result:
ok 1 number(s): "1"
Test #3:
score: 0
Accepted
time: 0ms
memory: 3388kb
input:
5
output:
647619053
result:
ok 1 number(s): "647619053"
Test #4:
score: 0
Accepted
time: 2ms
memory: 3376kb
input:
3
output:
600000005
result:
ok 1 number(s): "600000005"
Test #5:
score: 0
Accepted
time: 2ms
memory: 3356kb
input:
7
output:
365567769
result:
ok 1 number(s): "365567769"
Test #6:
score: 0
Accepted
time: 2ms
memory: 3344kb
input:
10
output:
458729432
result:
ok 1 number(s): "458729432"
Test #7:
score: 0
Accepted
time: 2ms
memory: 3340kb
input:
42
output:
643505700
result:
ok 1 number(s): "643505700"
Test #8:
score: 0
Accepted
time: 1ms
memory: 3444kb
input:
228
output:
125716107
result:
ok 1 number(s): "125716107"
Test #9:
score: 0
Accepted
time: 5ms
memory: 3364kb
input:
1225
output:
497563335
result:
ok 1 number(s): "497563335"
Test #10:
score: 0
Accepted
time: 24ms
memory: 3512kb
input:
8888
output:
372234803
result:
ok 1 number(s): "372234803"
Test #11:
score: 0
Accepted
time: 27ms
memory: 3484kb
input:
10500
output:
553242929
result:
ok 1 number(s): "553242929"
Test #12:
score: 0
Accepted
time: 42ms
memory: 3340kb
input:
16384
output:
235400649
result:
ok 1 number(s): "235400649"
Test #13:
score: 0
Accepted
time: 72ms
memory: 3444kb
input:
30000
output:
348712971
result:
ok 1 number(s): "348712971"
Test #14:
score: 0
Accepted
time: 164ms
memory: 4032kb
input:
65535
output:
304508463
result:
ok 1 number(s): "304508463"
Test #15:
score: 0
Accepted
time: 224ms
memory: 4512kb
input:
89898
output:
178782007
result:
ok 1 number(s): "178782007"
Test #16:
score: 0
Accepted
time: 241ms
memory: 4472kb
input:
100000
output:
600566479
result:
ok 1 number(s): "600566479"
Test #17:
score: 0
Accepted
time: 242ms
memory: 4572kb
input:
99999
output:
933686708
result:
ok 1 number(s): "933686708"
Test #18:
score: 0
Accepted
time: 245ms
memory: 4472kb
input:
99998
output:
113943006
result:
ok 1 number(s): "113943006"
Test #19:
score: 0
Accepted
time: 2ms
memory: 3372kb
input:
4
output:
228571431
result:
ok 1 number(s): "228571431"
Test #20:
score: 0
Accepted
time: 2ms
memory: 3348kb
input:
16
output:
646577665
result:
ok 1 number(s): "646577665"
Test #21:
score: 0
Accepted
time: 2ms
memory: 3420kb
input:
1024
output:
489408992
result:
ok 1 number(s): "489408992"
Test #22:
score: 0
Accepted
time: 3ms
memory: 3380kb
input:
2048
output:
390257222
result:
ok 1 number(s): "390257222"