結果

問題 No.1495 パンの仕入れ
ユーザー hitonanodehitonanode
提出日時 2021-05-11 20:14:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 251 ms / 2,000 ms
コード長 8,221 bytes
コンパイル時間 2,456 ms
コンパイル使用メモリ 210,840 KB
最終ジャッジ日時 2025-01-21 10:04:38
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2
other AC * 46
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 # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#else
#define dbg(x) (x)
#endif


// \minimize $\sum_i a_i x_i^2 + b_i x_i + c_i$ s.t. $\sum_i x_i = C, lb_i \leq x_i \leq ub_i$
// https://codeforces.com/contest/1344/problem/D
// https://yukicoder.me/problems/no/1495
template <typename Int, Int INF> struct QuadraticSumMinimizationUnderLinearConstraint {
    Int quad_slope(Int a, Int b, Int slope) {
        // x 個取った時のコストが ax^2 + bx であるとき，追加コストが slope 以下の範囲で取れる個数
        if (a == 0) return b <= slope ? INF : -INF;
        return (slope + a - b) / (a * 2);
    }
    Int quad_next_cost(Int a, Int b, Int n) {
        // x 個取った時のコストが ax^2 + bx であるとき，n 個目を更に取る際に生じる追加コスト
        return 2 * a * n - a + b;
    }
    static Int clmp(const Int &x, const Int &lo, const Int &hi) noexcept { return x > hi ? hi : x < lo ? lo : x; } // std::clamp
    std::pair<Int, std::vector<std::vector<std::pair<Int, Int>>>> operator()(
        const std::vector<Int> &k, const std::vector<Int> &a, const std::vector<Int> &b, const std::vector<Int> &c,
        const std::vector<Int> &lb, const std::vector<Int> &ub, Int C) {
        assert(k.size() == a.size() and k.size() == b.size() and k.size() == c.size() and k.size() == lb.size() and k.size() == ub.size());
        assert(k.size() > 0);
        assert(*std::min_element(a.begin(), a.end()) >= 0);
        if (std::accumulate(lb.begin(), lb.end(), Int(0)) > C) return {};
        if (std::accumulate(ub.begin(), ub.end(), Int(0)) < C) return {};

        const int N = k.size();
        Int few = -INF, enough = INF; // コスト few 以下を取るだけでは C 個に達しない / コスト enough まで取ると十分
        Int fewc = 0;
        while (enough - few > 1) {
            auto slope = few + (enough - few) / 2;
            Int cnt = 0;
            for (int i = 0; i < N; i++) {
                auto tmp = clmp(quad_slope(a[i], b[i], slope), lb[i], ub[i]);
                cnt += tmp * k[i];
                if (cnt >= C) break;
            }
            if (cnt >= C) {
                enough = slope;
            } else {
                few = slope;
                fewc = cnt;
            }
        }

        std::vector<std::vector<std::pair<Int, Int>>> ret(N);
        std::vector<int> additional;
        Int ctmp = 0;
        Int sol = 0;
        for (int i = 0; i < N; i++) {
            auto xlo = clmp(quad_slope(a[i], b[i], few), lb[i], ub[i]);
            auto xhi = clmp(quad_slope(a[i], b[i], few + 1), lb[i], ub[i]);
            ctmp += k[i] * xlo;
            ret[i].emplace_back(xlo, k[i]);
            if (xlo < xhi) additional.push_back(i);
            sol += k[i] * (a[i] * xlo * xlo + b[i] * xlo + c[i]);
        }
        sol += (C - ctmp) * (few + 1);
        while (additional.size()) {
            int i = additional.back();
            additional.pop_back();
            Int add = C - ctmp > k[i] ? k[i] : C - ctmp;
            auto x = ret[i][0].first;
            ret[i][0].second -= add;
            if (ret[i][0].second == 0) ret[i].pop_back();
            ret[i].emplace_back(x + 1, add);
            ctmp += add;
        }
        Int ret2 = 0;
        for (int i = 0; i < N; i++) {
            for (auto p : ret[i]) {
                Int x = p.first, n = p.second;
                Int y = a[i] * x * x + b[i] * x + c[i];
                ret2 += y * n;
            }
        }
        assert(sol == ret2);
        return {sol, ret};
    }
};

lint solve() {
    int N, M, K;
    cin >> N >> M >> K;
    vector<lint> a(N), b(N), c(N);
    while (M--) {
        int x;
        lint y;
        cin >> x >> y;
        x--;
        a[x]++;
        b[x] -= y * 2;
        c[x] += y * y;
    }
    vector<lint> lb(N, 0), ub(N, K);
    QuadraticSumMinimizationUnderLinearConstraint<lint, 1LL << 60> solver;
    auto sol = solver(vector<lint>(N, 1), a, b, c, vector<lint>(N, 0), vector<lint>(N, K), K);
    return sol.first;
}

int main() {
    int T;
    cin >> T;
    while (T--) cout << solve() << '\n';
}
0