#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> 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 T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &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 #include #include namespace linear_sum_assignment { template T augment(int nr, int nc, const std::vector> &C, std::vector &f, std::vector &g, int s, std::vector &mate, std::vector &mate_inv) { assert(0 <= s and s < nr); assert(mate.at(s) < 0); static std::vector dist; static std::vector 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 done(nc); int t = -1; std::vector 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 std::tuple, std::vector, std::vector> _solve(int nr, int nc, const std::vector> &C) { assert(nr <= nc); std::vector mate(nr, -1); std::vector mate_inv(nc, -1); std::vector 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 std::tuple, std::vector, std::vector> solve(int nr, int nc, const std::vector> &C) { const bool transpose = (nr > nc); if (!transpose) return _solve(nr, nc, C); std::vector trans(nc, std::vector(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 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(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'; }