#define PROBLEM "https://yukicoder.me/problems/no/119" // ============ #include template class MongeMinCut { int n; std::vector k; std::vector offset; int s; int t; T all; atcoder::mf_graph graph; T big; void add_v(int v, T f0, T f1) { if (f0 <= f1) { add_0(f0); graph.add_edge(s, v, f1 - f0); } else { add_0(f1); graph.add_edge(v, t, f0 - f1); } } public: MongeMinCut(const std::vector &k, T big) : n((int)k.size()), k(k), offset(n, 0), s(0), t(0), all(0), graph(0), big(big) { for (int i = 0; i < n; ++i) { assert(k[i] >= 1); } for (int i = 0; i < n - 1; ++i) { offset[i + 1] = offset[i] + k[i] - 1; } s = 0; for (int i = 0; i < n; ++i) { s += k[i]; } t = s + 1; graph = atcoder::mf_graph(s + 2); for (int i = 0; i < n; ++i) { for (int j = 0; j < k[i] - 2; ++j) { graph.add_edge(offset[i] + j + 1, offset[i] + j, big); } } } void add_0(T v) { all += v; } void add_1(int i, const std::vector &f) { assert(0 <= i && i < n && (int)f.size() == k[i]); add_0(f[0]); for (int j = 0; j < k[i] - 1; ++j) { add_v(offset[i] + j, f[j + 1] - f[j], 0); } } void add_2(int x, int y, std::vector> f) { assert(0 <= x && x < n); assert(0 <= y && y < n); assert((int)f.size() == k[x]); for (int i = 0; i < k[x]; ++i) { assert((int)f[i].size() == k[y]); } std::vector tmp(k[x]); for (int i = 0; i < k[x]; ++i) { tmp[i] = f[i][0]; } add_1(x, tmp); for (int i = 0; i < k[x]; ++i) { for (int j = 0; j < k[y]; ++j) { f[i][j] -= tmp[i]; } } tmp = f[0]; add_1(y, tmp); for (int i = 0; i < k[x]; ++i) { for (int j = 0; j < k[y]; ++j) { f[i][j] -= tmp[j]; } } for (int i = 0; i < k[x] - 1; ++i) { for (int j = 0; j < k[y] - 1; ++j) { T val = f[i][j] + f[i + 1][j + 1] - f[i + 1][j] - f[i][j + 1]; assert(val <= 0); add_0(val); graph.add_edge(offset[x] + i, offset[y] + j, -val); graph.add_edge(s, offset[x] + i, -val); } } } std::pair> solve() { T cost = graph.flow(s, t) + all; std::vector cut = graph.min_cut(s); std::vector ans(n, 0); for (int i = 0; i < n; ++i) { for (int j = 0; j < k[i] - 1; ++j) { if (cut[offset[i] + j]) { ++ans[i]; } } } return std::pair>(cost, ans); } }; // ============ // ============ #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i) #define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i) #define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__) #define ALL(x) begin(x), end(x) #define LEN(x) (i32)(x.size()) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; using pi = pair; using pl = pair; template using V = vector; template using VV = V>; template using VVV = V>>; template using VVVV = V>>>; template using PQR = priority_queue, greater>; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } template i32 lob(const V &arr, const T &v) { return (i32)(lower_bound(ALL(arr), v) - arr.begin()); } template i32 upb(const V &arr, const T &v) { return (i32)(upper_bound(ALL(arr), v) - arr.begin()); } template V argsort(const V &arr) { V ret(arr.size()); iota(ALL(ret), 0); sort(ALL(ret), [&](i32 i, i32 j) -> bool { if (arr[i] == arr[j]) { return i < j; } else { return arr[i] < arr[j]; } }); return ret; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; void scan(char &x) { cin >> x; } void scan(u32 &x) { cin >> x; } void scan(u64 &x) { cin >> x; } void scan(i32 &x) { cin >> x; } void scan(i64 &x) { cin >> x; } void scan(string &x) { cin >> x; } template void scan(V &x) { for (T &ele : x) { scan(ele); } } void read() {} template void read(Head &head, Tail &...tail) { scan(head); read(tail...); } #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__); #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__); #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__); #define I32(...) \ i32 __VA_ARGS__; \ read(__VA_ARGS__); #define I64(...) \ i64 __VA_ARGS__; \ read(__VA_ARGS__); #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__); #define VEC(type, name, size) \ V name(size); \ read(name); #define VVEC(type, name, size1, size2) \ VV name(size1, V(size2)); \ read(name); // ============ int main() { I32(n); V b(n), c(n); REP(i, n) { read(b[i], c[i]); } I32(m) V edge(m); for (auto &[u, v] : edge) { read(u, v); } MongeMinCut mincut(V(n, 3), INF); REP(i, n) { V f(3, 0); f[0] = -b[i]; f[2] = -c[i]; mincut.add_1(i, f); } for (auto [u, v] : edge) { VV f(3, V(3, 0)); f[0][2] = INF / m; mincut.add_2(u, v, f); } cout << -mincut.solve().first << '\n'; }