| # |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
| 408637 |
2021-05-19T11:40:52 Z |
tranxuanbach |
Boat (APIO16_boat) |
C++17 |
|
145 ms |
5188 KB |
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define endl '\n'
#define fi first
#define se second
#define For(i, l, r) for (int i = l; i < r; i++)
#define ForE(i, l, r) for (int i = l; i <= r; i++)
#define FordE(i, l, r) for (int i = l; i >= r; i--)
#define Fora(v, a) for (auto v: a)
#define bend(a) a.begin(), a.end()
#define isz(a) ((signed)a.size())
typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef vector <int> vi;
typedef vector <pii> vpii;
typedef vector <vi> vvi;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend std::istream& operator>>(std::istream& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, int64_t>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
const int N = 5e2 + 5, mod = 1e9 + 7;
int n;
pii a[N];
Mint invfac[N], C[N][N];
void init_C(){
invfac[0] = 1;
For(i, 1, N){
invfac[i] = invfac[i - 1] / i;
}
C[0][0] = 1;
For(i, 1, N){
ForE(j, 0, i){
C[i][j] = C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
}
}
}
int m;
vpii ranges;
void coordinate_compress(){
vpii vcac;
ForE(i, 1, n){
vcac.emplace_back(a[i].fi, 0);
vcac.emplace_back(a[i].se + 1, 0);
}
sort(bend(vcac));
ForE(i, 1, n){
For(j, 0, isz(vcac)){
if (a[i].fi <= vcac[j].fi and vcac[j].fi <= a[i].se){
vcac[j].se = 1;
}
}
}
ranges.emplace_back(-1, -1);
For(j, 0, isz(vcac) - 1){
if (vcac[j].se){
ranges.emplace_back(vcac[j].fi, vcac[j + 1].fi - 1);
}
}
ForE(i, 1, n){
a[i].fi = lower_bound(bend(ranges), make_pair(a[i].fi, -1)) - ranges.begin();
a[i].se = (--lower_bound(bend(ranges), make_pair(a[i].se + 1, -1))) - ranges.begin();
}
m = isz(ranges) - 1;
}
Mint Crange[2 * N][N];
void init_Crange(){
ForE(i, 1, m){
int len = ranges[i].se - ranges[i].fi + 1;
Mint ans = 1;
ForE(j, 0, n){
if (j > len){
Crange[i][j] = 0;
continue;
}
Crange[i][j] = ans;
ans /= j + 1; ans *= len - j;
}
}
}
Mint calchoose[N][2 * N];
void init_calchoose(){
ForE(i, 1, n){
ForE(j, 1, m){
For(neg1, 0, i){
calchoose[i][j] += C[i - 1][neg1] * Crange[j][i - neg1];
}
}
}
}
Mint dp[N][N];
signed main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
// freopen("KEK.inp", "r", stdin);
// freopen("KEK.out", "w", stdout);
init_C();
cin >> n;
ForE(i, 1, n){
cin >> a[i].fi >> a[i].se;
}
coordinate_compress();
init_Crange();
init_calchoose();
ForE(i, 0, n){
dp[i][0] = 1;
}
ForE(j, 1, m){
dp[0][j] = 1;
}
ForE(i, 1, n){
ForE(j, 1, m){
dp[i][j] = dp[i][j - 1];
FordE(ti, i, 1){
if (a[ti].fi > j or a[ti].se < j){
break;
}
dp[i][j] += calchoose[i - ti + 1][j] * dp[ti - 1][j - 1];
}
}
}
cout << dp[n][m] << endl;
}
/*
Tim so day so A = (A_1, A_2, ..., A_n) thoa man dieu kien sau:
- A_i = -1 hoac a_i <= A_i <= b_i
- Neu i < j, A_i != -1 va A_j != -1 thi A_i < A_j.
nen so thanh n doan, sau do thi
dp[i][j] la so cach de chon i so dau va moi so <= j (sau khi nen).
dp[i][j] = dp[i][j - 1] + (so cach chon (i - i' + 1) so co gia tri = j hoac -1 sau khi nen, so dau phai bang j) * dp[i' - 1][j - 1]
so cach chon tren: goi len = i - i'.
so cach = \sum_{neg1 = 0}^{len} C(len, neg1) * C(range(j), len + 1 - neg1)
==================================================+
INPUT: |
--------------------------------------------------|
2
1 2
2 3
--------------------------------------------------|
==================================================+
OUTPUT: |
--------------------------------------------------|
--------------------------------------------------|
==================================================+
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
145 ms |
5188 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
145 ms |
5188 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
7 ms |
2256 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
145 ms |
5188 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
