結果

問題 No.1495 パンの仕入れ
ユーザー 👑 hitonanodehitonanode
提出日時 2021-05-11 21:34:10
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 271 ms / 2,000 ms
コード長 8,296 bytes
コンパイル時間 4,576 ms
コンパイル使用メモリ 216,252 KB
実行使用メモリ 40,792 KB
最終ジャッジ日時 2023-10-22 03:05:47
合計ジャッジ時間 10,182 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge11
このコードへのチャレンジ
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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 2 ms
4,348 KB
testcase_01 AC 2 ms
4,348 KB
testcase_02 AC 166 ms
4,348 KB
testcase_03 AC 165 ms
4,348 KB
testcase_04 AC 164 ms
4,348 KB
testcase_05 AC 163 ms
4,348 KB
testcase_06 AC 165 ms
4,348 KB
testcase_07 AC 167 ms
4,348 KB
testcase_08 AC 168 ms
4,348 KB
testcase_09 AC 167 ms
4,348 KB
testcase_10 AC 167 ms
4,348 KB
testcase_11 AC 168 ms
4,348 KB
testcase_12 AC 45 ms
4,348 KB
testcase_13 AC 44 ms
4,348 KB
testcase_14 AC 44 ms
4,348 KB
testcase_15 AC 44 ms
4,348 KB
testcase_16 AC 44 ms
4,348 KB
testcase_17 AC 44 ms
4,348 KB
testcase_18 AC 45 ms
4,348 KB
testcase_19 AC 44 ms
4,348 KB
testcase_20 AC 44 ms
4,348 KB
testcase_21 AC 44 ms
4,348 KB
testcase_22 AC 271 ms
40,792 KB
testcase_23 AC 268 ms
40,792 KB
testcase_24 AC 32 ms
4,348 KB
testcase_25 AC 32 ms
4,348 KB
testcase_26 AC 32 ms
4,348 KB
testcase_27 AC 32 ms
4,348 KB
testcase_28 AC 255 ms
40,792 KB
testcase_29 AC 257 ms
40,792 KB
testcase_30 AC 35 ms
4,348 KB
testcase_31 AC 35 ms
4,348 KB
testcase_32 AC 36 ms
4,348 KB
testcase_33 AC 35 ms
4,348 KB
testcase_34 AC 35 ms
4,348 KB
testcase_35 AC 44 ms
4,348 KB
testcase_36 AC 44 ms
4,348 KB
testcase_37 AC 43 ms
4,348 KB
testcase_38 AC 43 ms
4,348 KB
testcase_39 AC 43 ms
4,348 KB
testcase_40 AC 32 ms
4,348 KB
testcase_41 AC 32 ms
4,348 KB
testcase_42 AC 32 ms
4,348 KB
testcase_43 AC 32 ms
4,348 KB
testcase_44 AC 32 ms
4,348 KB
testcase_45 AC 2 ms
4,348 KB
testcase_46 AC 2 ms
4,348 KB
testcase_47 AC 2 ms
4,348 KB
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
// ax^2 + bx + c (convex)
struct Quadratic {
    using Int = long long;
    Int a, b, c, lb, ub;
    Quadratic(Int a, Int b, Int c, Int lb, Int ub) : a(a), b(b), c(c), lb(lb), ub(ub) {}
    Int slope(Int s) const noexcept {
        if (a == 0) return b <= s ? ub : lb;
        auto ret = (s + a - b) / (a * 2);
        return ret > ub ? ub : ret < lb ? lb : ret;
    }
    Int eval(Int x) const noexcept { return (a * x + b) * x + c; }
    Int next_cost(Int x) const noexcept { return 2 * a * x - a + b; }
};

// x^3 - ax, x \geq 0 (convex)
struct Cubic {
    int a, lb, ub;
    Cubic(int a, int ub) : a(a), lb(0), ub(ub) {}
    int slope(long long s) const noexcept {
        int lo = lb, hi = ub + 1;
        while (hi - lo > 1) {
            int x = (lo + hi) / 2;
            (next_cost(x) <= s ? lo : hi) = x;
        }
        return lo;
    }
    long long eval(long long x) const noexcept { return (x * x - a) * x; }
    long long next_cost(long long x) const noexcept { return 3 * x * x - 3 * x + 1 - a; }
};

template <typename F, typename Int, Int INF> struct ConvexSumMinimizationUnderLinearConstraint {
    std::pair<Int, std::vector<std::vector<std::pair<Int, Int>>>> solve(const std::vector<Int> &k, const std::vector<F> &f, Int C) {
        assert(k.size() == f.size());
        assert(k.size() > 0);
        Int lbsum = 0, ubsum = 0;
        for (auto func : f) lbsum += func.lb, ubsum += func.ub;
        if (lbsum > C or ubsum < 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 = f[i].slope(slope);
                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 = f[i].slope(few);
            auto xhi = f[i].slope(few + 1);
            ctmp += k[i] * xlo;
            ret[i].emplace_back(xlo, k[i]);
            if (xlo < xhi) additional.push_back(i);
            sol += k[i] * f[i].eval(xlo);
        }
        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;
            if (add) {
                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 = f[i].eval(x);
        //         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<Quadratic> costs;
    REP(i, N) costs.emplace_back(a[i], b[i], c[i], 0, K);
    ConvexSumMinimizationUnderLinearConstraint<Quadratic, lint, 1LL << 60> solver;
    auto sol = solver.solve(vector<lint>(N, 1), costs, K);
    return sol.first;
}

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