#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 #include #include #include #include // 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 ::max() / 2> class slope_trick { T min_f; T displacement_l, displacement_r; std::priority_queue, std::less> L; std::priority_queue, std::greater> 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 &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 ::max() / 2> class dual_slope_trick : private slope_trick { public: using Base = slope_trick; // 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 #include #line 7 "other_algorithms/test/dual_slope_trick.yuki2114.test.cpp" #include using namespace std; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, M, K; cin >> N >> M >> K; map>> 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 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; }