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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#838746 | #8047. DFS Order 4 | ucup-team4435 | TL | 5ms | 3592kb | C++20 | 7.6kb | 2024-12-31 20:40:43 | 2024-12-31 20:40:44 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define all(a) begin(a), end(a)
#define len(a) int((a).size())
#ifdef LOCAL
#include "debug.h"
#else
#define dbg(...)
#define dprint(...)
#define debug if constexpr (false)
#endif // LOCAL
// MOD assumed to be prime
template<typename T>
int normalize(T value, int mod) {
if (value < -mod || value >= 2 * mod)
value %= mod;
if (value < 0)
value += mod;
if (value >= mod)
value -= mod;
return value;
}
template<typename T>
struct dynamic_modular_int {
using mint = dynamic_modular_int<T>;
int value;
dynamic_modular_int() : value(0) {}
dynamic_modular_int(const mint &x) : value(x.value) {}
template<typename U, typename V = std::enable_if_t<std::is_integral<U>::value>>
dynamic_modular_int(U value) : value(normalize(value, T::mod)) {}
template<typename U>
mint power(U degree) const {
mint prod = 1;
mint a = *this;
for (; degree > 0; degree >>= 1, a *= a)
if (degree & 1)
prod *= a;
return prod;
}
mint inv() const {
return power(T::mod - 2);
}
mint& operator=(const mint &x) {
value = x.value;
return *this;
}
mint& operator+=(const mint &x) {
value += x.value;
if (value >= T::mod)
value -= T::mod;
return *this;
}
mint& operator-=(const mint &x) {
value -= x.value;
if (value < 0)
value += T::mod;
return *this;
}
mint& operator*=(const mint &x) {
value = (long long) value * x.value % T::mod;
return *this;
}
mint& operator/=(const mint &x) {
return *this *= x.inv();
}
friend mint operator+(const mint &x, const mint &y) {
return mint(x) += y;
}
friend mint operator-(const mint &x, const mint &y) {
return mint(x) -= y;
}
friend mint operator*(const mint &x, const mint &y) {
return mint(x) *= y;
}
friend mint operator/(const mint &x, const mint &y) {
return mint(x) /= y;
}
mint& operator++() {
++value;
if (value == T::mod)
value = 0;
return *this;
}
mint& operator--() {
--value;
if (value == -1)
value = T::mod - 1;
return *this;
}
mint operator++(int) {
mint prev = *this;
value++;
if (value == T::mod)
value = 0;
return prev;
}
mint operator--(int) {
mint prev = *this;
value--;
if (value == -1)
value = T::mod - 1;
return prev;
}
mint operator-() const {
return mint(0) - *this;
}
bool operator==(const mint &x) const {
return value == x.value;
}
bool operator!=(const mint &x) const {
return value != x.value;
}
template<typename U>
explicit operator U() {
return value;
}
friend std::istream& operator>>(std::istream &in, mint &x) {
std::string s;
in >> s;
x = 0;
bool neg = s[0] == '-';
for (const auto c : s)
if (c != '-')
x = x * 10 + (c - '0');
if (neg)
x *= -1;
return in;
}
friend std::ostream& operator<<(std::ostream &out, const mint &x) {
return out << x.value;
}
static int primitive_root() {
if constexpr (T::mod == 1'000'000'007)
return 5;
if constexpr (T::mod == 998'244'353)
return 3;
if constexpr (T::mod == 786433)
return 10;
static int root = -1;
if (root != -1)
return root;
std::vector<int> primes;
int value = T::mod - 1;
for (int i = 2; i * i <= value; i++)
if (value % i == 0) {
primes.push_back(i);
while (value % i == 0)
value /= i;
}
if (value != 1)
primes.push_back(value);
for (int r = 2;; r++) {
bool ok = true;
for (auto p : primes)
if ((mint(r).power((T::mod - 1) / p)).value == 1) {
ok = false;
break;
}
if (ok)
return root = r;
}
}
};
struct dynamic_modular_int_mod {
static int mod;
};
int dynamic_modular_int_mod::mod = 998244353;
int &MOD = dynamic_modular_int_mod::mod;
using mint = dynamic_modular_int<dynamic_modular_int_mod>;
/*
! WARNING: MOD must be prime.
* Define modular int class above it.
* No need to run any init function, it dynamically resizes the data.
*/
namespace combinatorics {
std::vector<mint> fact_, ifact_, inv_;
void resize_data(int size) {
if (fact_.empty()) {
fact_ = {mint(1), mint(1)};
ifact_ = {mint(1), mint(1)};
inv_ = {mint(0), mint(1)};
}
for (int pos = fact_.size(); pos <= size; pos++) {
fact_.push_back(fact_.back() * mint(pos));
inv_.push_back(-inv_[MOD % pos] * mint(MOD / pos));
ifact_.push_back(ifact_.back() * inv_[pos]);
}
}
struct combinatorics_info {
std::vector<mint> &data;
combinatorics_info(std::vector<mint> &data) : data(data) {}
mint operator[](int pos) {
if (pos >= static_cast<int>(data.size())) {
resize_data(pos);
}
return data[pos];
}
} fact(fact_), ifact(ifact_), inv(inv_);
// From n choose k.
// O(max(n)) in total.
mint choose(int n, int k) {
if (n < k || k < 0 || n < 0) {
return mint(0);
}
return fact[n] * ifact[k] * ifact[n - k];
}
// From n choose k.
// O(min(k, n - k)).
mint choose_slow(int64_t n, int64_t k) {
if (n < k || k < 0 || n < 0) {
return mint(0);
}
k = std::min(k, n - k);
mint result = 1;
for (int i = k; i >= 1; i--) {
result *= (n - i + 1);
result *= inv[i];
}
return result;
}
// Number of balanced bracket sequences with n open and m closing brackets.
mint catalan(int n, int m) {
if (m > n || m < 0) {
return mint(0);
}
return choose(n + m, m) - choose(n + m, m - 1);
}
// Number of balanced bracket sequences with n open and closing brackets.
mint catalan(int n) {
return catalan(n, n);
}
} // namespace combinatorics
using namespace combinatorics;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
int n;
cin >> n >> MOD;
if (n <= 3) {
cout << "1\n";
return 0;
}
vector dp(n + 1, vector<mint>(n + 1));
dp[1][0] = 1;
for (int s = 2; s <= n; s++) {
for (int extra = 0; s + extra <= n; extra++) {
dp[s][extra] += dp[s - 1][0] * choose((s - 2) + extra, extra);
for (int left = 2; left <= s - 2; left++) {
int right = s - left;
dp[s][extra] += dp[left][0] * dp[right][extra] * choose((left - 1) + (right - 1 + extra), left - 1);
dp[s][extra] -= dp[left][right - 1 + extra] * dp[right][extra];
}
}
}
cout << dp[n][0] << '\n';
}
詳細信息
Test #1:
score: 100
Accepted
time: 0ms
memory: 3592kb
input:
4 114514199
output:
2
result:
ok 1 number(s): "2"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3548kb
input:
10 998244353
output:
11033
result:
ok 1 number(s): "11033"
Test #3:
score: 0
Accepted
time: 5ms
memory: 3516kb
input:
100 1000000007
output:
270904395
result:
ok 1 number(s): "270904395"
Test #4:
score: -100
Time Limit Exceeded
input:
756 1001338769
output:
901942543