結果

問題 No.535 自然数の収納方法
ユーザー Pachicobue
提出日時 2017-06-29 14:08:27
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 54 ms / 2,000 ms
コード長 4,339 bytes
コンパイル時間 1,415 ms
コンパイル使用メモリ 168,780 KB
実行使用メモリ 66,004 KB
最終ジャッジ日時 2024-10-04 16:36:37
合計ジャッジ時間 2,665 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define RFOR(i, a, b) for (ll i = (b)-1; i >= (a); i--)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep1(i, n) for (ll i = 1; i <= (n); i++)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; i--)
#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define pii pair<int, int>
namespace is_stl_container_impl
{
template <typename T>
struct is_stl_container : false_type {
};
template <typename T, size_t N>
struct is_stl_container<array<T, N>> : true_type {
};
template <typename... Args>
struct is_stl_container<vector<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<deque<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<list<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<forward_list<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<set<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<multiset<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<map<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<multimap<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_set<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_multiset<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_map<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_multimap<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<stack<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<queue<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<priority_queue<Args...>> : true_type {
};
} // namespace is_stl_container_impl
//type trait to utilize the implementation type traits as well as decay the type
template <typename T>
struct is_stl_container {
static constexpr bool const value = is_stl_container_impl::is_stl_container<decay_t<T>>::value;
};
template <typename T>
typename enable_if<is_stl_container<T>::value, ostream&>::type operator<<(ostream& os, const T& container)
{
os << "[";
for (const auto& p : container) {
os << p << ",";
}
os << "]";
return os;
}
template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
os << "(" << p.first << "," << p.second
<< ")";
return os;
}
using ll = long long;
constexpr ll MOD = 1000000007;
template <typename T>
constexpr T INF = numeric_limits<T>::inf() / 100;
constexpr int MAX = 2000;
ll dp[MAX][MAX + 1]; // dp[i:a_i][a_i]
ll sum[MAX][MAX + 1]; // sum[i][j] = dp[i][0]+dp[i][1]+...+dp[i][j]
// a0<=a1
// a1<=a2
// a2<=a3+1
// ...
// a(N-1)<=aN+(N-2)
inline int d(const int n)
{
if (n == 1) {
return 0;
} else {
return n - 2;
}
}
int main()
{
int N;
cin >> N;
for (int i = 1; i <= N; i++) {
dp[0][i] = 1;
sum[0][i] = (sum[0][i - 1] + 1) % MOD;
}
for (int i = 1; i < N; i++) {
for (int j = 1; j <= N; j++) {
const int inf = min(N, j + d(i));
const ll su = sum[i - 1][inf] - sum[i - 1][0];
dp[i][j] = su;
sum[i][j] = (sum[i][j - 1] + su) % MOD;
}
}
ll sumu = 0;
for (int i = 1; i <= N; i++) {
sumu = (sumu + dp[N - 1][i]) % MOD;
}
for (int i = 0; i < N; i++) {
for (int j = 0; j <= N; j++) {
dp[i][j] = 0;
sum[i][j] = 0;
}
}
dp[0][1] = 1;
for (int i = 1; i <= N; i++) {
sum[0][i] = (sum[0][i - 1] + dp[0][i]) % MOD;
}
for (int i = 1; i < N; i++) {
for (int j = 1; j <= N; j++) {
const int inf = min(N, j + d(i));
const ll su = sum[i - 1][inf] - sum[i - 1][0];
dp[i][j] = su;
sum[i][j] = (sum[i][j - 1] + su) % MOD;
}
}
const ll remov = dp[N - 1][N];
cout << (sumu - remov + MOD) % MOD << endl;
return 0;
}
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