結果
| 問題 | No.2988 Min-Plus Convolution Query |
| ユーザー |
 NyaanNyaan
|
| 提出日時 | 2024-12-13 01:41:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 18,384 bytes |
| コンパイル時間 | 6,445 ms |
| コンパイル使用メモリ | 297,596 KB |
| 実行使用メモリ | 43,132 KB |
| 最終ジャッジ日時 | 2024-12-13 01:42:49 |
| 合計ジャッジ時間 | 56,695 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 6 ms
18,324 KB |
| testcase_01 | AC | 8 ms
16,384 KB |
| testcase_02 | TLE | - |
| testcase_03 | TLE | - |
| testcase_04 | TLE | - |
| testcase_05 | AC | 39 ms
17,192 KB |
| testcase_06 | AC | 7 ms
11,136 KB |
| testcase_07 | AC | 8 ms
11,136 KB |
| testcase_08 | AC | 6 ms
11,136 KB |
| testcase_09 | AC | 49 ms
13,696 KB |
| testcase_10 | AC | 58 ms
13,904 KB |
| testcase_11 | AC | 11 ms
12,160 KB |
| testcase_12 | AC | 17 ms
11,520 KB |
| testcase_13 | AC | 262 ms
14,080 KB |
| testcase_14 | AC | 19 ms
11,776 KB |
| testcase_15 | AC | 465 ms
15,872 KB |
| testcase_16 | TLE | - |
| testcase_17 | AC | 139 ms
15,872 KB |
| testcase_18 | AC | 122 ms
15,872 KB |
| testcase_19 | AC | 88 ms
15,744 KB |
| testcase_20 | TLE | - |
| testcase_21 | TLE | - |
| testcase_22 | TLE | - |
| testcase_23 | TLE | - |
| testcase_24 | TLE | - |
| testcase_25 | TLE | - |
| testcase_26 | TLE | - |
| testcase_27 | TLE | - |
| testcase_28 | TLE | - |
| testcase_29 | TLE | - |
| testcase_30 | TLE | - |
| testcase_31 | TLE | - |
| testcase_32 | AC | 7 ms
11,008 KB |
| testcase_33 | AC | 7 ms
11,136 KB |
| testcase_34 | AC | 6 ms
11,264 KB |
| testcase_35 | AC | 5 ms
11,008 KB |
| testcase_36 | AC | 7 ms
11,008 KB |
| testcase_37 | AC | 5 ms
11,136 KB |
| testcase_38 | AC | 6 ms
11,008 KB |
| testcase_39 | AC | 7 ms
11,136 KB |
| testcase_40 | AC | 6 ms
11,136 KB |
| testcase_41 | AC | 7 ms
40,624 KB |
ソースコード
/**
* date : 2024-12-13 01:41:42
* author : Nyaan
*/
#define NDEBUG
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
constexpr P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#endif
#ifndef NyaanDebug
#define trc(...) (void(0))
#endif
#ifndef NyaanLocal
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
namespace nachia {
template <class Elem>
struct SmawkAlgorithm {
template <class Gen, class Cmp = std::less<Elem>>
std::vector<std::pair<Elem, int>> Solve(int height, int width, Gen gen,
Cmp cmp = Cmp()) {
if (height == 0) return std::vector<std::pair<Elem, int>>(0);
auto reduce = [&](int yst,
const std::vector<int>& cols) -> std::vector<int> {
int w = int(cols.size());
std::vector<int> idx;
int r = -1;
for (int q = 0; q < w; q++) {
if (idx.empty()) {
idx.push_back(q);
r += yst;
continue;
}
int a = cols[idx.back()];
int b = cols[q];
if (cmp(gen(r, a), gen(r, b))) {
if (r + yst < height) {
idx.push_back(q);
r += yst;
}
} else {
idx.pop_back();
q--;
r -= yst;
}
}
return idx;
};
auto ysts = std::vector<int>(1, 1);
auto cols = std::vector<std::vector<int>>(1);
for (int i = 0; i < width; i++) cols[0].push_back(i);
cols[0] = reduce(1, cols[0]);
while (true) {
int nxst = ysts.back() * 2;
if (height < nxst) break;
auto nxc = reduce(nxst, cols.back());
int w = nxc.size();
for (int i = 0; i < w; i++) nxc[i] = cols.back()[nxc[i]];
cols.push_back(move(nxc));
ysts.push_back(nxst);
}
std::vector<std::pair<Elem, int>> ans(height, std::make_pair(gen(0, 0), 0));
while (cols.size()) {
auto x = std::move(cols.back());
cols.pop_back();
int st = ysts.back();
ysts.pop_back();
int p = 0;
for (int y = st - 1; y < height; y += st * 2) {
int r = y + st < height ? ans[y + st].second : width - 1;
ans[y] = std::make_pair(gen(y, x[p]), x[p]);
while (p + 1 < int(x.size()) && x[p + 1] <= r) {
int xp = x[++p];
auto fxp = gen(y, xp);
if (!cmp(ans[y].first, fxp)) ans[y] = std::make_pair(fxp, xp);
}
}
}
return ans;
}
};
} // namespace nachia
namespace nachia {
template <class Elem>
std::vector<std::pair<Elem, int>> ConvexMinPlusConvolution(
const std::vector<Elem>& a, const std::vector<Elem>& b, Elem Inf) {
int n = a.size();
int m = b.size();
return nachia::SmawkAlgorithm<Elem>().Solve(
n + m - 1, m, [&](int y, int x) -> Elem {
return (y < x || n <= y - x) ? Inf : a[y - x] + b[x];
});
}
} // namespace nachia
//
using namespace std;
using namespace std;
// NxN 行列がある
// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する
// f(i, j, k) :
// A[i][j] と A[i][k] を比較 (j < k が保証されている)
// A[i][j] <= A[i][k] のとき true を返す関数を入れる (等号はどちらでもよい)
vector<int> monotone_minima(int N, int M,
const function<bool(int, int, int)>& f) {
vector<int> res(N);
auto dfs = [&](auto rc, int is, int ie, int l, int r) -> void {
if (is == ie) return;
int i = (is + ie) / 2;
int m = l;
for (int k = l + 1; k < r; k++) {
if (!f(i, m, k)) m = k;
}
res[i] = m;
rc(rc, is, i, l, m + 1);
rc(rc, i + 1, ie, m, r);
};
dfs(dfs, 0, N, 0, M);
return res;
}
// NxM 行列がある
// m_i := argmin_j (A_{i,j}) が単調増加であるときに m_i を列挙する
// A(i, j) : A[i][j] を返す関数
template <typename T>
vector<int> monotone_minima(int N, int M, const function<T(int, int)>& A) {
function<bool(int, int, int)> f = [&](int i, int j, int k) -> bool {
return A(i, j) <= A(i, k);
};
return monotone_minima(N, M, f);
}
/**
* @brief monotone minima
*/
// a は下に凸, b は自由
template <typename T>
vector<T> concave_min_plus_convolution(const vector<T>& a, const vector<T>& b) {
if (a.empty() or b.empty()) return {};
int n = a.size(), m = b.size();
auto argmin = monotone_minima(n + m - 1, m, [&](int i, int j, int k) {
if (i < k) return true;
if (i - j >= n) return false;
return a[i - j] + b[j] <= a[i - k] + b[k];
});
vector<T> ans(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
int j = argmin[i];
ans[i] = a[i - j] + b[j];
}
return ans;
}
// a は上に凸, b は自由
template <typename T>
vector<T> concave_max_plus_convolution(const vector<T>& a, const vector<T>& b) {
if (a.empty() or b.empty()) return {};
int n = a.size(), m = b.size();
auto argmin = monotone_minima(n + m - 1, m, [&](int i, int j, int k) {
if (i < k) return true;
if (i - j >= n) return false;
return a[i - j] + b[j] >= a[i - k] + b[k];
});
vector<T> ans(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
int j = argmin[i];
ans[i] = a[i - j] + b[j];
}
return ans;
}
using namespace std;
struct Timer {
chrono::high_resolution_clock::time_point st;
Timer() { reset(); }
void reset() { st = chrono::high_resolution_clock::now(); }
long long elapsed() {
auto ed = chrono::high_resolution_clock::now();
return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
}
long long operator()() { return elapsed(); }
};
using namespace Nyaan;
using u32 = unsigned int;
int N, Q;
vl A, B;
ll B2[TEN(6)];
void q() {
Timer timer;
in(N, Q);
A.resize(N), B.resize(N);
in(A, B);
rep(i, TEN(6)) B2[i] = infLL;
ll* b = B2 + 5 * TEN(5);
rep(i, N) b[i] = B[i];
vl P(Q), X(Q), K(Q);
in3(P, X, K);
each(p, P)-- p;
each(k, K) k -= 2;
int S = 1800;
for (int is = 0; is < Q; is += S) {
int ie = min(Q, is + S);
vl A2 = A;
vector<int> pos;
reg(i, is, ie) {
pos.push_back(P[i]);
A2[P[i]] = TEN(10);
}
auto C = nachia::ConvexMinPlusConvolution<ll>(B, A2, TEN(11));
pos = mkuni(pos);
/*
reg(i, is, ie) {
ll ans = C[K[i]].fi;
A[P[i]] = X[i];
each(p, pos) {
int q = K[i] - p;
if ((0 <= q and q < N)) amin(ans, A[p] + B[q]);
}
out(ans);
}
*/
reg(i, is, ie) {
ll ans[8];
rep(ii, 8) ans[ii] = infLL;
ans[0] = C[K[i]].fi;
A[P[i]] = X[i];
int j = 0;
for (; j + 4 <= sz(pos); j += 4) {
ans[0] = min(ans[0], A[pos[j + 0]] + b[K[i] - pos[j + 0]]);
ans[1] = min(ans[1], A[pos[j + 1]] + b[K[i] - pos[j + 1]]);
ans[2] = min(ans[2], A[pos[j + 2]] + b[K[i] - pos[j + 2]]);
ans[3] = min(ans[3], A[pos[j + 3]] + b[K[i] - pos[j + 3]]);
}
for (; j < sz(pos); j++) {
int p = pos[j];
ans[0] = min(ans[0], A[p] + b[K[i] - p]);
}
out(*min_element(ans, ans + 8));
}
}
trc2(timer());
/*
struct Line {
int x, i;
Line() : i(-1), x(0) {}
Line(int _i, int _x) : i(_i), x(_x) {}
ll operetor(ll k) {
if (i == -1) return infLL;
int j = k - i;
if (!(0 <= j and j < N)) return infLL;
return x + B[j];
}
};
*/
/*
int len = 1;
while (len < Q) len *= 2;
DivideInterval di{len};
// (p,x)
VV<pi> qs(2 * len);
{
vi lastA = A;
vi lastT(N);
rep(t, Q) {
int p = P[t], x = X[t];
di.apply(lastT[p], t, [&](int i) { qs[i].emplace_back(p, lastA[p]); });
lastA[p] = x;
lastT[p] = t;
}
rep(p, N) {
di.apply(lastT[p], Q, [&](int i) { qs[i].emplace_back(p, lastA[p]); });
}
}
vl xs;
rep(i, 2 * N - 1) xs.push_back(i);
LiChaoTree<Line, true, false> lct(xs, Line{});
*/
}
void Nyaan::solve() {
int t = 1;
// in(t);
while (t--) q();
}