結果

問題 No.2114 01 Matching
ユーザー 👑 hitonanodehitonanode
提出日時 2022-12-04 20:23:31
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 569 ms / 5,000 ms
コード長 6,520 bytes
コンパイル時間 1,681 ms
コンパイル使用メモリ 130,488 KB
実行使用メモリ 47,216 KB
最終ジャッジ日時 2023-08-16 02:55:20
合計ジャッジ時間 14,907 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
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
4,380 KB
testcase_01 AC 2 ms
4,376 KB
testcase_02 AC 161 ms
12,648 KB
testcase_03 AC 75 ms
12,556 KB
testcase_04 AC 116 ms
16,400 KB
testcase_05 AC 45 ms
7,308 KB
testcase_06 AC 169 ms
11,028 KB
testcase_07 AC 164 ms
9,232 KB
testcase_08 AC 136 ms
11,448 KB
testcase_09 AC 104 ms
6,788 KB
testcase_10 AC 164 ms
9,440 KB
testcase_11 AC 532 ms
47,060 KB
testcase_12 AC 530 ms
47,028 KB
testcase_13 AC 116 ms
14,844 KB
testcase_14 AC 115 ms
17,264 KB
testcase_15 AC 115 ms
17,356 KB
testcase_16 AC 168 ms
18,228 KB
testcase_17 AC 169 ms
11,024 KB
testcase_18 AC 81 ms
10,908 KB
testcase_19 AC 119 ms
16,344 KB
testcase_20 AC 556 ms
46,996 KB
testcase_21 AC 136 ms
17,356 KB
testcase_22 AC 84 ms
6,280 KB
testcase_23 AC 105 ms
12,404 KB
testcase_24 AC 32 ms
4,444 KB
testcase_25 AC 32 ms
6,472 KB
testcase_26 AC 567 ms
47,024 KB
testcase_27 AC 545 ms
47,024 KB
testcase_28 AC 252 ms
27,416 KB
testcase_29 AC 546 ms
47,072 KB
testcase_30 AC 169 ms
11,092 KB
testcase_31 AC 569 ms
47,216 KB
testcase_32 AC 149 ms
7,908 KB
testcase_33 AC 167 ms
12,244 KB
testcase_34 AC 124 ms
9,108 KB
testcase_35 AC 180 ms
21,144 KB
testcase_36 AC 549 ms
47,032 KB
testcase_37 AC 107 ms
7,836 KB
testcase_38 AC 165 ms
8,872 KB
testcase_39 AC 60 ms
5,668 KB
testcase_40 AC 166 ms
20,840 KB
testcase_41 AC 124 ms
7,256 KB
testcase_42 AC 102 ms
8,452 KB
testcase_43 AC 170 ms
11,028 KB
testcase_44 AC 156 ms
17,544 KB
testcase_45 AC 265 ms
46,936 KB
testcase_46 AC 40 ms
4,776 KB
testcase_47 AC 543 ms
46,924 KB
testcase_48 AC 562 ms
47,136 KB
testcase_49 AC 112 ms
15,296 KB
testcase_50 AC 50 ms
4,788 KB
testcase_51 AC 164 ms
11,932 KB
testcase_52 AC 110 ms
16,904 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 # 

#line 1 "other_algorithms/test/dual_slope_trick.yuki2114.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2114"
#line 2 "other_algorithms/slope_trick.hpp"
#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <utility>

// Slope trick: fast operations for convex piecewise-linear functions
// Implementation idea:
// - https://maspypy.com/slope-trick-1-%E8%A7%A3%E8%AA%AC%E7%B7%A8
// - https://ei1333.github.io/library/structure/others/slope-trick.cpp
template <class T, T INF = std::numeric_limits<T>::max() / 2> class slope_trick {
    T min_f;
    T displacement_l, displacement_r;
    std::priority_queue<T, std::vector<T>, std::less<T>> L;
    std::priority_queue<T, std::vector<T>, std::greater<T>> R;
    void pushR(const T &a) { R.push(a - displacement_r); }
    T topR() const { return R.empty() ? INF : R.top() + displacement_r; }
    T popR() {
        auto ret = topR();
        if (R.size()) R.pop();
        return ret;
    }
    void pushL(const T &a) { L.push(a + displacement_l); }
    T topL() const { return L.empty() ? -INF : L.top() - displacement_l; }
    T popL() {
        auto ret = topL();
        if (L.size()) L.pop();
        return ret;
    }

public:
    // Initialize, f(x) = 0 everywhere
    // Complexity: O(1)
    slope_trick() : min_f(0), displacement_l(0), displacement_r(0) {
        static_assert(INF > 0, "INF must be greater than 0");
    }
    inline int sizeL() const noexcept { return L.size(); }
    inline int sizeR() const noexcept { return R.size(); }

    // argmin f(x), min f(x)
    // Complexity: O(1)
    using Q = struct { T min, lo, hi; };
    Q get_min() const { return {min_f, topL(), topR()}; }

    // f(x) += b
    // Complexity: O(1)
    slope_trick &add_const(const T &b) { return min_f += b, *this; }

    // f(x) += max(x - a, 0)  _/
    // Complexity: O(log n)
    slope_trick &add_relu(const T &a) {
        return min_f += std::max(T(0), topL() - a), pushL(a), pushR(popL()), *this;
    }

    // f(x) += max(a - x, 0)  \_
    // Complexity: O(log n)
    slope_trick &add_irelu(const T &a) {
        return min_f += std::max(T(0), a - topR()), pushR(a), pushL(popR()), *this;
    }

    // f(x) += |x - a|  \/
    // Complexity: O(log n)
    slope_trick &add_abs(const T &a) { return add_relu(a).add_irelu(a); }

    // f(x) <- min_{0 <= y <= w} f(x + y)  .\ -> \_
    // Complexity: O(1)
    slope_trick &move_left_curve(const T &w) { return assert(w >= 0), displacement_l += w, *this; }

    // f(x) <- min_{0 <= y <= w} f(x - y)  /. -> _/
    // Complexity: O(1)
    slope_trick &move_right_curve(const T &w) {
        return assert(w >= 0), displacement_r += w, *this;
    }

    // f(x) <- f(x - dx) \/. -> .\/
    // Complexity: O(1)
    slope_trick &translate(const T &dx) {
        return displacement_l -= dx, displacement_r += dx, *this;
    }

    // return f(x), f destructive
    T get_destructive(const T &x) {
        T ret = get_min().min;
        while (L.size()) ret += std::max(T(0), popL() - x);
        while (R.size()) ret += std::max(T(0), x - popR());
        return ret;
    }

    // f(x) += g(x), g destructive
    slope_trick &merge_destructive(slope_trick<T, INF> &g) {
        if (sizeL() + sizeR() > g.sizeL() + g.sizeR()) {
            std::swap(min_f, g.min_f);
            std::swap(displacement_l, g.displacement_l);
            std::swap(displacement_r, g.displacement_r);
            std::swap(L, g.L);
            std::swap(R, g.R);
        }
        min_f += g.get_min().min;
        while (g.L.size()) add_irelu(g.popL());
        while (g.R.size()) add_relu(g.popR());
        return *this;
    }
};
#line 3 "other_algorithms/dual_slope_trick.hpp"

// https://maspypy.com/slope-trick-3-slope-trick-%E3%81%AE%E5%87%B8%E5%85%B1%E5%BD%B9
template <class T, T INF = std::numeric_limits<T>::max() / 2>
class dual_slope_trick : private slope_trick<T, INF> {
public:
    using Base = slope_trick<T, INF>;

    // Initialize: f(x) = 0 (x == 0), inf (otherwise)
    // Complexity: O(1)
    dual_slope_trick() : Base() {}

    // Get f(0)
    // Complexity: O(1)
    T get_at_zero() const { return -Base::get_min().min; }

    // f(x) <- f(x - d) (Move graph to right by d)
    // Complexity: O(log n)
    dual_slope_trick &shift(int d) {
        while (d > 0) --d, Base::add_relu(-INF).add_const(-INF);
        while (d < 0) ++d, Base::add_irelu(INF).add_const(-INF);
        return *this;
    }

    // f(x) += ax + b
    // Complexity: O(1)
    dual_slope_trick &add_linear(T a, T b) { return Base::translate(a).add_const(b), *this; }

    // f(x) += max(c(x - a), 0)
    // Complexity: O(|a| log n + 1)
    dual_slope_trick &add_linear_or_zero(T c, int a) {
        shift(-a);
        if (c > T()) Base::move_right_curve(c);
        if (c < T()) Base::move_left_curve(-c);
        return shift(a);
    }

    // f(x) <- min f(x - d), a <= d <= b
    // Complexity: O((|a| + |b|) log n)
    dual_slope_trick &slide_min(int a, int b) {
        assert(a <= b);
        shift(a);
        for (int t = 0; t < b - a; ++t) Base::add_relu(T());
        return *this;
    }
};
#line 4 "other_algorithms/test/dual_slope_trick.yuki2114.test.cpp"
#include <iostream>
#include <map>
#line 7 "other_algorithms/test/dual_slope_trick.yuki2114.test.cpp"
#include <vector>
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    int N, M, K;
    cin >> N >> M >> K;
    map<int, vector<pair<int, int>>> mp;
    for (int i = 0; i < N; ++i) {
        int a;
        cin >> a;
        mp[a % K].emplace_back(a / K, 0);
    }
    for (int i = 0; i < M; ++i) {
        int b;
        cin >> b;
        mp[b % K].emplace_back(b / K, 1);
    }

    long long ret = 0;
    int nmatch = 0;
    for (auto [key, vs] : mp) {
        int n0 = 0, n1 = 0;
        for (auto [x, t] : vs) (t ? n1 : n0)++;

        nmatch += min(n0, n1);

        if (n0 > n1) {
            swap(n0, n1);
            for (auto &[x, t] : vs) t ^= 1;
        }
        sort(vs.begin(), vs.end());

        dual_slope_trick<long long, 1LL << 40> dst;
        int last_x = vs.front().first;
        for (auto [x, tp] : vs) {
            int dx = x - last_x;
            dst.add_linear_or_zero(dx, 0).add_linear_or_zero(-dx, 0);
            if (tp == 0) {
                dst.shift(1);
            } else {
                dst.slide_min(-1, 0);
            }
            last_x = x;
        }
        ret += dst.get_at_zero();
    }

    if (nmatch < min(N, M)) ret = -1;

    cout << ret << endl;
}
0