/*
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,fma,bmi,bmi2,sse4.2,popcnt,lzcnt")
*/
#include <bits/stdc++.h>
#define taskname ""
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define i64 long long
#define pb push_back
#define ff first
#define ss second
#define isz(x) (int)x.size()
using namespace std;
const int mxN = 2e5 + 5;
// const int mod = 1e9 + 7;
const i64 oo = 1e18;
using uint = unsigned int;
template<uint _mod>
struct modular_fixed_base{
static constexpr uint mod(){
return _mod;
}
template<class T>
static vector<modular_fixed_base> precalc_power(T base, int SZ){
vector<modular_fixed_base> res(SZ + 1, 1);
for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
return res;
}
static vector<modular_fixed_base> _INV;
static void precalc_inverse(int SZ){
if(_INV.empty()) _INV.assign(2, 1);
for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
}
// _mod must be a prime
static modular_fixed_base _primitive_root;
static modular_fixed_base primitive_root(){
if(_primitive_root) return _primitive_root;
if(_mod == 2) return _primitive_root = 1;
if(_mod == 998244353) return _primitive_root = 3;
uint divs[20] = {};
divs[0] = 2;
int cnt = 1;
uint x = (_mod - 1) / 2;
while(x % 2 == 0) x /= 2;
for(auto i = 3; 1LL * i * i <= x; i += 2){
if(x % i == 0){
divs[cnt ++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt ++] = x;
for(auto g = 2; ; ++ g){
bool ok = true;
for(auto i = 0; i < cnt; ++ i){
if((modular_fixed_base(g).power((_mod - 1) / divs[i])) == 1){
ok = false;
break;
}
}
if(ok) return _primitive_root = g;
}
}
constexpr modular_fixed_base(): data(){ }
modular_fixed_base(const double &x){ data = normalize(llround(x)); }
modular_fixed_base(const long double &x){ data = normalize(llround(x)); }
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base(const T &x){ data = normalize(x); }
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> static uint normalize(const T &x){
int sign = x >= 0 ? 1 : -1;
uint v = _mod <= sign * x ? sign * x % _mod : sign * x;
if(sign == -1 && v) v = _mod - v;
return v;
}
const uint &operator()() const{ return data; }
template<class T> operator T() const{ return data; }
modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
modular_fixed_base &operator++(){ return *this += 1; }
modular_fixed_base &operator--(){ return *this += _mod - 1; }
modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
modular_fixed_base &operator*=(const modular_fixed_base &rhs){
data = (unsigned long long)data * rhs.data % _mod;
return *this;
}
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>
modular_fixed_base &inplace_power(T e){
if(e < 0) *this = 1 / *this, e = -e;
modular_fixed_base res = 1;
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class T, typename enable_if<is_integral<T>::value>::type* = nullptr>
modular_fixed_base power(T e) const{
return modular_fixed_base(*this).inplace_power(e);
}
modular_fixed_base &operator/=(const modular_fixed_base &otr){
int a = otr.data, m = _mod, u = 0, v = 1;
if(a < _INV.size()) return *this *= _INV[a];
while(a){
int t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return *this *= u;
}
uint data;
};
template<uint _mod> vector<modular_fixed_base<_mod>> modular_fixed_base<_mod>::_INV;
template<uint _mod> modular_fixed_base<_mod> modular_fixed_base<_mod>::_primitive_root;
template<uint _mod> bool operator==(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data == rhs.data; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(const modular_fixed_base<_mod> &lhs, T rhs){ return lhs == modular_fixed_base<_mod>(rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator==(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) == rhs; }
template<uint _mod> bool operator!=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return !(lhs == rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(const modular_fixed_base<_mod> &lhs, T rhs){ return !(lhs == rhs); }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> bool operator!=(T lhs, const modular_fixed_base<_mod> &rhs){ return !(lhs == rhs); }
template<uint _mod> bool operator<(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data < rhs.data; }
template<uint _mod> bool operator>(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data > rhs.data; }
template<uint _mod> bool operator<=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data <= rhs.data; }
template<uint _mod> bool operator>=(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return lhs.data >= rhs.data; }
template<uint _mod> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator+(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) += rhs; }
template<uint _mod> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator-(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) -= rhs; }
template<uint _mod> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(const modular_fixed_base<_mod> &lhs, T rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator*(T lhs, const modular_fixed_base<_mod> &rhs){ return modular_fixed_base<_mod>(lhs) *= rhs; }
template<uint _mod> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, const modular_fixed_base<_mod> &rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(const modular_fixed_base<_mod> &lhs, T rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod, class T, typename enable_if<is_integral<T>::value>::type* = nullptr> modular_fixed_base<_mod> operator/(T lhs, const modular_fixed_base<_mod> &rhs) { return modular_fixed_base<_mod>(lhs) /= rhs; }
template<uint _mod> istream &operator>>(istream &in, modular_fixed_base<_mod> &number){
long long x;
in >> x;
number.data = modular_fixed_base<_mod>::normalize(x);
return in;
}
// #define _PRINT_AS_FRACTION
template<uint _mod> ostream &operator<<(ostream &out, const modular_fixed_base<_mod> &number){
#ifdef LOCAL
#ifdef _PRINT_AS_FRACTION
out << number();
cerr << "(";
for(auto d = 1; ; ++ d){
if((number * d).data <= 1000000){
cerr << (number * d).data << "/" << d;
break;
}
else if((-number * d).data <= 1000000){
cerr << "-" << (-number * d).data << "/" << d;
break;
}
}
cerr << ")";
return out;
#else
return out << number();
#endif
#else
return out << number();
#endif
}
#undef _PRINT_AS_FRACTION
const uint mod = 1e9 + 7; // 1000000007
// const uint mod = (119 << 23) + 1; // 998244353
// const uint mod = 1e9 + 9; // 1000000009
using Z = modular_fixed_base<mod>;
int n, L, a[105];
Z dp[105][105][5][1005];
#define FOR(i, a, b) for(int i = a; i < b; ++i)
void solve() {
cin >> n >> L;
for (int i = 1; i <= n; ++i)
cin >> a[i];
if (n == 1) {
cout << 1 << endl;
return;
}
sort(a + 1, a + n + 1);
dp[0][0][0][0] = 1;
FOR(i, 0, n) FOR(cc, 0, n) FOR(nend, 0, 3) FOR(sum, 0, L + 1) {
Z val = dp[i][cc][nend][sum];
int nsum = sum + (a[i + 1] - a[i]) * (2 * cc - nend);
if (nsum < sum || nsum > L) continue;
// case 1: new cc
dp[i + 1][cc + 1][nend][nsum] += val * (cc + 1 - nend);
// case 2: append to cc
dp[i + 1][cc][nend][nsum] += val * (2 * cc - nend);
// case 3: merge 2 cc
if (cc) dp[i + 1][cc - 1][nend][nsum] += val * (cc - 1);
// case 4: new end
dp[i + 1][cc + 1][nend + 1][nsum] += val * (2 - nend);
// case 5: append to make end
dp[i + 1][cc][nend + 1][nsum] += val * (2 - nend);
// cout << dp[i + 1][cc][nend + 1][nsum] << endl;
}
cout << accumulate(dp[n][1][2], dp[n][1][2] + L + 1, Z(0)) << endl;
}
signed main() {
#ifndef CDuongg
if(fopen(taskname".inp", "r"))
assert(freopen(taskname".inp", "r", stdin)), assert(freopen(taskname".out", "w", stdout));
#else
freopen("bai3.inp", "r", stdin);
freopen("bai3.out", "w", stdout);
auto start = chrono::high_resolution_clock::now();
#endif
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1; //cin >> t;
while(t--) solve();
#ifdef CDuongg
auto end = chrono::high_resolution_clock::now();
cout << "\n"; for(int i = 1; i <= 100; ++i) cout << '=';
cout << "\nExecution time: " << chrono::duration_cast<chrono::milliseconds> (end - start).count() << "[ms]" << endl;
#endif
}
Compilation message
skyscraper.cpp: In instantiation of 'static uint modular_fixed_base<_mod>::normalize(const T&) [with T = int; typename std::enable_if<std::is_integral<T>::value>::type* <anonymous> = 0; unsigned int _mod = 1000000007; uint = unsigned int]':
skyscraper.cpp:70:131: required from 'modular_fixed_base<_mod>::modular_fixed_base(const T&) [with T = int; typename std::enable_if<std::is_integral<T>::value>::type* <anonymous> = 0; unsigned int _mod = 1000000007]'
skyscraper.cpp:192:22: required from here
skyscraper.cpp:73:24: warning: comparison of integer expressions of different signedness: 'unsigned int' and 'int' [-Wsign-compare]
73 | uint v = _mod <= sign * x ? sign * x % _mod : sign * x;
| ~~~~~^~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
604 KB |
Output is correct |
| 4 |
Correct |
1 ms |
860 KB |
Output is correct |
| 5 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 6 |
Correct |
2 ms |
1384 KB |
Output is correct |
| 7 |
Correct |
1 ms |
1236 KB |
Output is correct |
| 8 |
Correct |
1 ms |
1372 KB |
Output is correct |
| 9 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 10 |
Correct |
1 ms |
1372 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
2908 KB |
Output is correct |
| 2 |
Correct |
2 ms |
2652 KB |
Output is correct |
| 3 |
Correct |
2 ms |
3676 KB |
Output is correct |
| 4 |
Correct |
2 ms |
2652 KB |
Output is correct |
| 5 |
Correct |
2 ms |
2904 KB |
Output is correct |
| 6 |
Correct |
2 ms |
3160 KB |
Output is correct |
| 7 |
Correct |
1 ms |
2652 KB |
Output is correct |
| 8 |
Correct |
2 ms |
3420 KB |
Output is correct |
| 9 |
Correct |
2 ms |
3672 KB |
Output is correct |
| 10 |
Correct |
2 ms |
2648 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
1 ms |
604 KB |
Output is correct |
| 4 |
Correct |
1 ms |
860 KB |
Output is correct |
| 5 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 6 |
Correct |
2 ms |
1384 KB |
Output is correct |
| 7 |
Correct |
1 ms |
1236 KB |
Output is correct |
| 8 |
Correct |
1 ms |
1372 KB |
Output is correct |
| 9 |
Correct |
2 ms |
1372 KB |
Output is correct |
| 10 |
Correct |
1 ms |
1372 KB |
Output is correct |
| 11 |
Correct |
2 ms |
2908 KB |
Output is correct |
| 12 |
Correct |
2 ms |
2652 KB |
Output is correct |
| 13 |
Correct |
2 ms |
3676 KB |
Output is correct |
| 14 |
Correct |
2 ms |
2652 KB |
Output is correct |
| 15 |
Correct |
2 ms |
2904 KB |
Output is correct |
| 16 |
Correct |
2 ms |
3160 KB |
Output is correct |
| 17 |
Correct |
1 ms |
2652 KB |
Output is correct |
| 18 |
Correct |
2 ms |
3420 KB |
Output is correct |
| 19 |
Correct |
2 ms |
3672 KB |
Output is correct |
| 20 |
Correct |
2 ms |
2648 KB |
Output is correct |
| 21 |
Correct |
8 ms |
14172 KB |
Output is correct |
| 22 |
Correct |
148 ms |
115024 KB |
Output is correct |
| 23 |
Correct |
156 ms |
122456 KB |
Output is correct |
| 24 |
Correct |
156 ms |
143880 KB |
Output is correct |
| 25 |
Correct |
167 ms |
126152 KB |
Output is correct |
| 26 |
Correct |
147 ms |
125532 KB |
Output is correct |
| 27 |
Correct |
103 ms |
165460 KB |
Output is correct |
| 28 |
Correct |
128 ms |
167740 KB |
Output is correct |
| 29 |
Correct |
158 ms |
166244 KB |
Output is correct |
| 30 |
Correct |
162 ms |
125008 KB |
Output is correct |
