結果

問題 No.2114 01 Matching
ユーザー hitonanodehitonanode
提出日時 2022-12-04 20:14:59
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 515 ms / 5,000 ms
コード長 13,350 bytes
コンパイル時間 2,129 ms
コンパイル使用メモリ 198,892 KB
実行使用メモリ 48,640 KB
最終ジャッジ日時 2024-05-03 12:32:16
合計ジャッジ時間 14,897 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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
6,816 KB
testcase_01 AC 1 ms
6,940 KB
testcase_02 AC 173 ms
14,052 KB
testcase_03 AC 74 ms
12,928 KB
testcase_04 AC 101 ms
16,640 KB
testcase_05 AC 43 ms
7,680 KB
testcase_06 AC 169 ms
13,016 KB
testcase_07 AC 166 ms
11,092 KB
testcase_08 AC 140 ms
12,836 KB
testcase_09 AC 110 ms
7,788 KB
testcase_10 AC 170 ms
10,836 KB
testcase_11 AC 501 ms
48,640 KB
testcase_12 AC 490 ms
48,512 KB
testcase_13 AC 120 ms
17,120 KB
testcase_14 AC 113 ms
18,296 KB
testcase_15 AC 113 ms
18,292 KB
testcase_16 AC 169 ms
19,496 KB
testcase_17 AC 170 ms
12,920 KB
testcase_18 AC 86 ms
11,892 KB
testcase_19 AC 121 ms
19,136 KB
testcase_20 AC 488 ms
48,512 KB
testcase_21 AC 138 ms
17,648 KB
testcase_22 AC 86 ms
7,288 KB
testcase_23 AC 110 ms
13,640 KB
testcase_24 AC 32 ms
6,944 KB
testcase_25 AC 31 ms
7,032 KB
testcase_26 AC 515 ms
48,640 KB
testcase_27 AC 507 ms
48,512 KB
testcase_28 AC 220 ms
28,288 KB
testcase_29 AC 486 ms
48,512 KB
testcase_30 AC 172 ms
12,948 KB
testcase_31 AC 506 ms
48,384 KB
testcase_32 AC 142 ms
9,576 KB
testcase_33 AC 174 ms
14,104 KB
testcase_34 AC 125 ms
10,788 KB
testcase_35 AC 158 ms
21,760 KB
testcase_36 AC 490 ms
48,512 KB
testcase_37 AC 113 ms
8,952 KB
testcase_38 AC 168 ms
10,560 KB
testcase_39 AC 60 ms
6,944 KB
testcase_40 AC 151 ms
21,248 KB
testcase_41 AC 140 ms
8,600 KB
testcase_42 AC 102 ms
9,660 KB
testcase_43 AC 171 ms
12,884 KB
testcase_44 AC 170 ms
19,080 KB
testcase_45 AC 257 ms
48,512 KB
testcase_46 AC 42 ms
6,944 KB
testcase_47 AC 496 ms
48,384 KB
testcase_48 AC 515 ms
48,512 KB
testcase_49 AC 116 ms
16,148 KB
testcase_50 AC 51 ms
6,944 KB
testcase_51 AC 169 ms
13,844 KB
testcase_52 AC 121 ms
18,172 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 <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
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) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif


// 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) {
        min_f += b;
        return *this;
    }

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

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

// 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);
        shift(a);
        return *this;
    }

    // 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;
    }
};

int main() {
    dual_slope_trick<lint> dst;
    dst.shift(2).shift(-1);
    dbg(dst.get_at_zero());
    dst.shift(-1);
    dbg(dst.get_at_zero());
    dst.slide_min(0, 3);
    dbg(dst.get_at_zero());
    dst.shift(-1);
    dbg(dst.get_at_zero());
    dst.shift(-1);
    dbg(dst.get_at_zero());
    dst.shift(-1);
    dbg(dst.get_at_zero());
    dst.shift(-1);
    dbg(dst.get_at_zero());
    int N, M, K;
    cin >> N >> M >> K;
    vector<int> A(N), B(M);
    cin >> A >> B;

    map<int, vector<pint>> mp;
    REP(i, N) {
        mp[A.at(i) % K].emplace_back(A.at(i) / K, 0);
    }
    REP(j, M) {
        mp[B.at(j) % K].emplace_back(B.at(j) / K, 1);
    }

    lint 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(ALL(vs));
        dbg(vs);

        dual_slope_trick<lint, 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);
            dbg(make_tuple(dx, tp));
            if (tp == 0) {
                dst.shift(1);
            } else {
                dst.slide_min(-1, 0);
            }
            last_x = x;
        }
        ret += dst.get_at_zero();
        dbg(dst.get_at_zero());

        assert(n0 <= n1);
    }

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

    cout << ret << endl;
}
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