library
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typical/dp/hakone.cpp
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- Last update: 2023-09-23 21:29:16+09:00
- Link: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1595
Depends on
library/mod/modint.cpp
Code
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1595"
#include "library/template/template.cpp"
//
#include "library/mod/modint.cpp"
const ll mod = 1000000007;
using mint = modint<mod>;
// library
int main() {
int n;
cin >> n;
vc c(n);
scan(c);
vector<mint> dp(n + 1); // dp[i]:=保留した順位の数
dp[0] = 1;
// 前から見ていく
rep(i, n) {
vector<mint> tmp(n + 1);
if (c[i] == '-') {
continue;
}
rep(nokori, n + 1) {
if (c[i] == 'D') {
tmp[nokori] += dp[nokori] * nokori;
if (nokori - 1 >= 0)
tmp[nokori - 1] += dp[nokori] * nokori * nokori;
} else {
if (nokori + 1 <= n) tmp[nokori + 1] += dp[nokori];
tmp[nokori] += dp[nokori] * nokori;
}
}
dp = tmp;
}
print(dp[0]);
}#line 1 "typical/dp/hakone.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1595"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
for (auto &e : v)
cout << e << " ";
cout << endl;
return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
for (auto &i : a)
scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
if (a < b)
{
a = b;
return 1;
}
return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
if (b < a)
{
a = b;
return 1;
}
return 0;
}
template <typename T>
T mypow(T x, ll n)
{
T ret = 1;
while (n > 0)
{
if (n & 1)
(ret *= x);
(x *= x);
n >>= 1;
}
return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
ll ret = 1;
while (n > 0)
{
if (n & 1)
(ret *= x);
(x *= x);
n >>= 1;
x %= mod;
ret %= mod;
}
return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
int n = a.size();
vector<int> id(n);
iota(all(id), 0);
sort(all(id), [&](int i, int j)
{ return a[i] < a[j]; });
return id;
}
long long xor64(long long range) {
static uint64_t x = 88172645463325252ULL;
x ^= x << 13;
x ^= x >> 7;
return (x ^= x << 17) % range;
}
struct Timer
{
clock_t start_time;
void start() { start_time = clock(); }
int lap()
{
// return x ms.
return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
}
};
template <typename T = int>
struct Edge
{
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template <typename T = int>
struct Graph
{
vector<vector<Edge<T>>> g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const { return g.size(); }
void add_directed_edge(int from, int to, T cost = 1)
{
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1)
{
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false,
bool directed = false)
{
for (int i = 0; i < M; i++)
{
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted)
cin >> c;
if (directed)
add_directed_edge(a, b, c);
else
add_edge(a, b, c);
}
}
};
/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 4 "typical/dp/hakone.cpp"
//
#line 2 "library/mod/modint.cpp"
template <int Mod>
struct modint
{
int x;
modint() : x(0) {}
modint(long long y) : x(y >= 0 ? y % Mod : (Mod - (-y) % Mod) % Mod) {}
modint &operator+=(const modint &p)
{
if ((x += p.x) >= Mod)
x -= Mod;
return *this;
}
modint &operator-=(const modint &p)
{
if ((x += Mod - p.x) >= Mod)
x -= Mod;
return *this;
}
modint &operator*=(const modint &p)
{
x = (int)(1LL * x * p.x % Mod);
return *this;
}
modint &operator/=(const modint &p)
{
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint(-x); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return x == p.x; }
bool operator!=(const modint &p) const { return x != p.x; }
modint inverse() const
{
int a = x, b = Mod, u = 1, v = 0, t;
while (b > 0)
{
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return modint(u);
}
modint pow(int64_t n) const
{
modint ret(1), mul(x);
while (n > 0)
{
if (n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const modint &p)
{
return os << p.x;
}
friend istream &operator>>(istream &is, modint &a)
{
long long t;
is >> t;
a = modint<Mod>(t);
return (is);
}
static int get_mod() { return Mod; }
constexpr int get() const { return x; }
};
#line 6 "typical/dp/hakone.cpp"
const ll mod = 1000000007;
using mint = modint<mod>;
// library
int main() {
int n;
cin >> n;
vc c(n);
scan(c);
vector<mint> dp(n + 1); // dp[i]:=保留した順位の数
dp[0] = 1;
// 前から見ていく
rep(i, n) {
vector<mint> tmp(n + 1);
if (c[i] == '-') {
continue;
}
rep(nokori, n + 1) {
if (c[i] == 'D') {
tmp[nokori] += dp[nokori] * nokori;
if (nokori - 1 >= 0)
tmp[nokori - 1] += dp[nokori] * nokori * nokori;
} else {
if (nokori + 1 <= n) tmp[nokori + 1] += dp[nokori];
tmp[nokori] += dp[nokori] * nokori;
}
}
dp = tmp;
}
print(dp[0]);
}