結果
| 問題 |
No.1309 テスト
|
| コンテスト | |
| ユーザー |
maspy
|
| 提出日時 | 2023-11-30 01:35:26 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2,284 ms / 4,000 ms |
| コード長 | 18,444 bytes |
| コンパイル時間 | 4,470 ms |
| コンパイル使用メモリ | 306,424 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-09-26 13:47:16 |
| 合計ジャッジ時間 | 20,865 ms |
|
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
(要ログイン)
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 85 |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
void solve() {
// P 上限
// X 中央
// Y 最頻値の平均
LL(N, P, X, Y);
bool CHECK = (N == 3 && P == 100 && X == 0 && Y == 0);
++P;
ll ANS = -1;
auto range_sum = [&](ll a, ll b) -> ll { return (a + b - 1) * (b - a) / 2; };
auto to_range = [&](ll S, ll n) -> tuple<ll, ll, ll> {
if (n == 0) {
assert(S == 0);
return {0, 0, -1};
}
// L+...+(L+(n-1))<=S
ll rhs = S - (n - 1) * n / 2;
ll L = floor(rhs, n);
ll R = L + n;
ll ex = range_sum(L, R + 1) - S;
assert(L <= ex && ex <= R);
if (ex == R) return {L, R, -1};
return {L, R + 1, ex};
};
auto greedy = [&](ll& sm, ll& n, ll L, ll R, ll can) -> void {
assert(n >= 0);
if (can == 0) return;
if ((R - L) * can <= n) {
n -= (R - L) * can;
sm += range_sum(L, R) * can;
return;
}
ll k = n / can;
n -= can * k;
sm += range_sum(R - k, R) * can;
sm += (R - k - 1) * n;
n = 0;
};
auto solve_0 = [&](ll n, ll a, ll b) -> void {
// X が最頻値でないとき
//・最頻値の頻度 n
//・上側最頻値の個数 a
//・下側最頻値の個数 b
if (n == 1) return;
if (a + b == 0) return;
if (a * n > N / 2) return;
if (b * n > N / 2) return;
if (a > X || b > P - (X + 1)) return;
ll use_X_upper = (N / 2) - (b * n + (P - X - 1 - b) * (n - 1));
chmax(use_X_upper, 0);
if (use_X_upper + 1 >= n) return;
ll use_X_lower = (N / 2) - (a * n);
chmin(use_X_lower, (n - 1) - 1 - use_X_upper);
if (N / 2 < use_X_lower + n * a) return;
if (N / 2 < use_X_upper + n * b) return;
auto F = [&](ll S1) -> void {
ll S2 = Y * (a + b) - S1;
if (S1 < range_sum(0, a)) return;
if (range_sum(X - a, X) < S1) return;
if (S2 < range_sum(X + 1, X + 1 + b)) return;
if (range_sum(P - b, P) < S2) return;
if (a == 0 && S1 != 0) return;
if (b == 0 && S2 != 0) return;
auto [L1, R1, ex1] = to_range(S1, a);
auto [L2, R2, ex2] = to_range(S2, b);
if (L1 == R1) L1 = X, R1 = X;
if (L2 == R2) L2 = P, R2 = P;
ll sm = n * (S1 + S2) + X * (1 + use_X_lower + use_X_upper);
ll n1 = N / 2 - use_X_lower - n * a;
ll n2 = N / 2 - use_X_upper - n * b;
greedy(sm, n1, R1, X, n - 1);
if (ex1 != -1) greedy(sm, n1, ex1, ex1 + 1, n - 1);
greedy(sm, n1, 0, L1, n - 1);
greedy(sm, n2, R2, P, n - 1);
if (ex2 != -1) greedy(sm, n2, ex2, ex2 + 1, n - 1);
greedy(sm, n2, X + 1, L2, n - 1);
// if (CHECK) { print(__LINE__, n, a, b, S1, S2, n1, n2, sm); }
if (n1 == 0 && n2 == 0) { chmax(ANS, sm); }
};
// FOR(S, N * P + 1) F(S);
vi X1, X2;
X1.eb(range_sum(0, a));
X1.eb(range_sum(X - a, X));
if (a != 0) {
ll r = N / 2 - use_X_lower - n * a;
ll k = r / (n - 1);
for (auto& kk: {k - 2, k - 1, k, k + 1, k + 2})
X1.eb(range_sum(X - kk - a, X - kk));
}
X2.eb(range_sum(X + 1, X + b + 1));
X2.eb(range_sum(P - b, P));
if (b != 0) {
ll r = N / 2 - use_X_upper - n * b;
ll k = r / (n - 1);
for (auto& kk: {k - 2, k - 1, k, k + 1, k + 2})
X2.eb(range_sum(P - kk - b, P - kk));
}
if (b == 0) X1.eb(Y * a);
if (a == 0) X2.eb(Y * b);
for (auto& x: X1) F(x);
for (auto& x: X2) F(Y * (a + b) - x);
};
auto solve_1 = [&](ll n, ll a, ll b) -> void {
// X が最頻値である
//・最頻値の頻度 n
//・上側最頻値の個数 a
//・下側最頻値の個数 b
// 大体同じことができる
if (a * n > N / 2) return;
if (b * n > N / 2) return;
if (a > X || b > P - (X + 1)) return;
if (n == 1) {
if (a != N / 2 || b != N / 2) return;
ll lo = range_sum(0, a) + X + range_sum(X + 1, X + 1 + b);
ll hi = range_sum(X - a, X) + X + range_sum(P - b, P);
if (lo <= Y * N && Y * N <= hi) { chmax(ANS, Y * N); }
return;
}
// 上側ではあまり X を使いたくない
// 下側でなるべく X を消費
ll can_lower = (N / 2) - (a * n);
chmin(can_lower, n - 1);
ll need_upper = n - 1 - can_lower;
chmax(need_upper, (N / 2) - (b * n) - (P - X - b) * (n - 1));
if (need_upper >= n) return;
ll use_X_upper = need_upper;
ll use_X_lower = n - 1 - use_X_upper;
if (N / 2 < use_X_lower + n * a) return;
if (N / 2 < use_X_upper + n * b) return;
auto F = [&](ll S1) -> void {
ll S2 = Y * (a + b + 1) - X - S1;
if (S1 < range_sum(0, a)) return;
if (range_sum(X - a, X) < S1) return;
if (S2 < range_sum(X + 1, X + 1 + b)) return;
if (range_sum(P - b, P) < S2) return;
if (a == 0 && S1 != 0) return;
if (b == 0 && S2 != 0) return;
auto [L1, R1, ex1] = to_range(S1, a);
auto [L2, R2, ex2] = to_range(S2, b);
if (L1 == R1) L1 = X, R1 = X;
if (L2 == R2) L2 = P, R2 = P;
ll sm = n * (S1 + S2) + X * (1 + use_X_lower + use_X_upper);
ll n1 = N / 2 - use_X_lower - n * a;
ll n2 = N / 2 - use_X_upper - n * b;
greedy(sm, n1, R1, X, n - 1);
if (ex1 != -1) greedy(sm, n1, ex1, ex1 + 1, n - 1);
greedy(sm, n1, 0, L1, n - 1);
greedy(sm, n2, R2, P, n - 1);
if (ex2 != -1) greedy(sm, n2, ex2, ex2 + 1, n - 1);
greedy(sm, n2, X + 1, L2, n - 1);
// if (CHECK) { print(__LINE__, n, a, b, S1, S2, n1, n2, sm); }
if (n1 == 0 && n2 == 0) { chmax(ANS, sm); }
};
vi X1, X2;
X1.eb(range_sum(0, a));
X1.eb(range_sum(X - a, X));
if (a != 0) {
ll r = N / 2 - use_X_lower - n * a;
ll k = r / (n - 1);
for (auto& kk: {k - 2, k - 1, k, k + 1, k + 2})
X1.eb(range_sum(X - kk - a, X - kk));
}
X2.eb(range_sum(X + 1, X + b + 1));
X2.eb(range_sum(P - b, P));
if (b != 0) {
ll r = N / 2 - use_X_upper - n * b;
ll k = r / (n - 1);
for (auto& kk: {k - 2, k - 1, k, k + 1, k + 2})
X2.eb(range_sum(P - kk - b, P - kk));
}
if (b == 0) X1.eb(Y * (a + 1) - X);
if (a == 0) X2.eb(Y * (b + 1) - X);
for (auto& x: X1) F(x);
for (auto& x: X2) F(Y * (a + b + 1) - X - x);
};
FOR(n, 1, N + 1) {
FOR(a, N / n + 1) {
FOR(b, N / n - a + 1) {
solve_0(n, a, b);
solve_1(n, a, b);
}
}
}
print(ANS);
}
signed main() {
int T = 10;
FOR(T) solve();
return 0;
}
maspy