結果

問題 No.2573 moving up
ユーザー 👑 hitonanodehitonanode
提出日時 2023-12-02 15:46:37
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 6 ms / 2,000 ms
コード長 12,734 bytes
コンパイル時間 2,437 ms
コンパイル使用メモリ 203,632 KB
実行使用メモリ 6,676 KB
最終ジャッジ日時 2023-12-06 15:48:28
合計ジャッジ時間 3,513 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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
6,676 KB
testcase_01 AC 3 ms
6,676 KB
testcase_02 AC 3 ms
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testcase_03 AC 5 ms
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testcase_04 AC 6 ms
6,676 KB
testcase_05 AC 6 ms
6,676 KB
testcase_06 AC 6 ms
6,676 KB
testcase_07 AC 6 ms
6,676 KB
testcase_08 AC 2 ms
6,676 KB
testcase_09 AC 4 ms
6,676 KB
testcase_10 AC 5 ms
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testcase_11 AC 3 ms
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testcase_12 AC 4 ms
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testcase_13 AC 5 ms
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testcase_14 AC 2 ms
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testcase_15 AC 2 ms
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testcase_16 AC 2 ms
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testcase_17 AC 3 ms
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testcase_18 AC 3 ms
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testcase_19 AC 4 ms
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testcase_20 AC 2 ms
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testcase_21 AC 2 ms
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testcase_22 AC 3 ms
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testcase_23 AC 2 ms
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testcase_24 AC 3 ms
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testcase_25 AC 5 ms
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testcase_26 AC 3 ms
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testcase_27 AC 2 ms
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testcase_28 AC 2 ms
6,676 KB
testcase_29 AC 2 ms
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testcase_30 AC 2 ms
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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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
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 << ')'; }
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

#include <cassert>
#include <tuple>
#include <vector>

namespace linear_sum_assignment {

template <class T>
T augment(int nr, int nc, const std::vector<std::vector<T>> &C, std::vector<T> &f,
          std::vector<T> &g, int s, std::vector<int> &mate, std::vector<int> &mate_inv) {

    assert(0 <= s and s < nr);
    assert(mate.at(s) < 0);

    static std::vector<T> dist;
    static std::vector<int> prv;
    dist.resize(nc);
    prv.resize(nc);

    f.at(s) = C.at(s).at(0) - g.at(0);
    for (int j = 1; j < nc; ++j) f.at(s) = std::min(f.at(s), C.at(s).at(j) - g.at(j));

    for (int j = 0; j < nc; ++j) {
        dist.at(j) = C.at(s).at(j) - f.at(s) - g.at(j);
        prv.at(j) = s;
    }

    std::vector<bool> done(nc);

    int t = -1;
    std::vector<int> stk;

    while (t == -1) {
        int j1 = -1;
        for (int j = 0; j < nc; ++j) {
            if (done.at(j)) continue;
            if (j1 == -1 or dist.at(j) < dist.at(j1) or
                (dist.at(j) == dist.at(j1) and mate_inv.at(j) < 0)) {
                j1 = j;
            }
        }

        if (j1 == -1) return false;

        if (mate_inv.at(j1) < 0) {
            t = j1;
            break;
        }

        done.at(j1) = 1;
        stk = {j1};

        while (!stk.empty()) {
            const int i = mate_inv.at(stk.back());
            if (i < 0) {
                t = stk.back();
                break;
            }
            stk.pop_back();

            for (int j = 0; j < nc; ++j) {
                if (done.at(j)) continue;

                const T len = C.at(i).at(j) - f.at(i) - g.at(j);

                if (dist.at(j) > dist.at(j1) + len) {
                    dist.at(j) = dist.at(j1) + len;
                    prv.at(j) = i;
                }

                if (len == T()) {
                    stk.push_back(j);
                    done.at(j) = 1;
                }
            }
        }
    }

    const T len = dist.at(t);

    f.at(s) += len;

    T ret = len;

    for (int j = 0; j < nc; ++j) {
        if (!done.at(j)) continue;

        g.at(j) -= len - dist.at(j);
        if (mate_inv.at(j) >= 0) {
            f.at(mate_inv.at(j)) += len - dist.at(j);
        } else {
            ret -= len - dist.at(j);
        }
    }

    for (int cur = t; cur >= 0;) {
        const int i = prv.at(cur);
        mate_inv.at(cur) = i;
        if (i == -1) break;
        std::swap(cur, mate.at(i));
    }

    return ret;
}

// Complexity: O(nr^2 nc)
template <class T>
std::tuple<T, std::vector<int>, std::vector<T>, std::vector<T>>
_solve(int nr, int nc, const std::vector<std::vector<T>> &C) {

    assert(nr <= nc);

    std::vector<int> mate(nr, -1);
    std::vector<int> mate_inv(nc, -1);
    std::vector<T> f(nr), g(nc); // dual variables, f[i] + g[j] <= C[i][j] holds

    if (nr == 0 or nc == 0) return {T(), mate, f, g};

    if (nr == nc) {
        // Column reduction
        for (int j = nc - 1; j >= 0; --j) {
            g.at(j) = C.at(0).at(j) - f.at(0);
            int imin = 0;
            for (int i = 1; i < nr; ++i) {
                if (g.at(j) > C.at(i).at(j) - f.at(i)) {
                    imin = i;
                    g.at(j) = C.at(i).at(j) - f.at(i);
                }
            }

            if (mate.at(imin) < 0) {
                mate.at(imin) = j;
                mate_inv.at(j) = imin;
            } else if (g.at(j) < g.at(mate.at(imin))) {
                mate_inv.at(mate.at(imin)) = -1;
                mate.at(imin) = j;
                mate_inv.at(j) = imin;
            }
        }

        // Reduction transfer (can be omitted)
        if (nc > 1) {
            for (int i = 0; i < nr; ++i) {
                if (mate.at(i) < 0) continue;
                T best = C.at(i).at(0) - g.at(0), second_best = C.at(i).at(1) - g.at(1);
                int argbest = 0;
                if (best > second_best) std::swap(best, second_best), argbest = 1;

                for (int j = 2; j < nc; ++j) {
                    if (T val = C.at(i).at(j) - g.at(j); val < best) {
                        second_best = best;
                        best = val;
                        argbest = j;
                    } else if (val < second_best) {
                        second_best = val;
                    }
                }

                g.at(argbest) -= second_best - best;
                f.at(i) = second_best;
            }
        }

        // Augmenting row reduction: not implemented
    }

    // Augmentation
    for (int i = 0; i < nr; ++i) {
        if (mate.at(i) < 0) augment(nr, nc, C, f, g, i, mate, mate_inv);
    }

    T ret = 0;
    for (int i = 0; i < nr; ++i) ret += C.at(i).at(mate.at(i));

    return {ret, mate, std::move(f), std::move(g)};
}

// Jonker–Volgenant algorithm: find minimum weight assignment
// Dual problem (nr == nc): maximize sum(f) + sum(g) s.t. f_i + g_j <= C_ij
// Complexity: O(nr nc min(nr, nc))
template <class T>
std::tuple<T, std::vector<int>, std::vector<T>, std::vector<T>>
solve(int nr, int nc, const std::vector<std::vector<T>> &C) {

    const bool transpose = (nr > nc);

    if (!transpose) return _solve(nr, nc, C);

    std::vector trans(nc, std::vector<T>(nr));

    for (int i = 0; i < nr; ++i) {
        for (int j = 0; j < nc; ++j) trans.at(j).at(i) = C.at(i).at(j);
    }

    auto [v, mate, f, g] = _solve(nc, nr, trans);

    std::vector<int> mate2(nr, -1);
    for (int j = 0; j < nc; ++j) {
        if (mate.at(j) >= 0) mate2.at(mate.at(j)) = j;
    }

    return {v, mate2, g, f};
}

} // namespace linear_sum_assignment



int main() {
    int H, W;
    cin >> H >> W;
    vector cost(W, vector<int>(W));
    REP(i, W) {
        int x, y;
        cin >> x >> y;
        REP(j, W) {
            const int h = x - 1;
            const int ylo = y - h, yhi = y;
            int ytgt = j + 1;

            int cost_row = 0;
            if (ytgt < ylo) cost_row = ylo - ytgt;
            if (yhi < ytgt) cost_row = ytgt - yhi;
            cost.at(i).at(j) = cost_row + h;
        }
    }
    dbg(cost);
    auto ret = linear_sum_assignment::solve(W, W, cost);
    dbg(ret);

    cout << get<0>(ret) << '\n';
}
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