verify/yukicoder/1984.test.cpp

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• Last update: 2026-03-12 00:53:37+09:00
• Problem: https://yukicoder.me/problems/no/1984

Depends on

• Algebra/Extended_Algebra.hpp
• 最大流 (Max_Flow/Max_Flow.hpp)
• Max_Flow/Project_Selection_Problem.hpp
• template/bitop.hpp
• template/exception.hpp
• template/inout.hpp
• template/macro.hpp
• template/math.hpp
• template/template.hpp
• template/utility.hpp

Code

#define PROBLEM "https://yukicoder.me/problems/no/1984"

#include"../../template/template.hpp"
#include"../../Max_Flow/Project_Selection_Problem.hpp"

using namespace projection_selection_problem;

void verify() {
    // 変数代入
    int N, M, K, P; cin >> N >> M >> K >> P;
    vector<ll> E(N + 1), F(M + 1), V(K + 1);
    for (int i = 1; i <= N; i++) { cin >> E[i]; }
    for (int j = 1; j <= M; j++) { cin >> F[j]; }
    for (int k = 1; k <= K; k++) { cin >> V[k]; }

    vector<int> L(N + 1);
    vector<vector<int>> A(N + 1);

    for (int i = 1; i <= N; i++) {
        cin >> L[i];
        A[i].resize(L[i]);
        for (int t = 0; t < L[i]; t++) { cin >> A[i][t]; }
    }

    vector<int> I(P), J(P);
    for (int p = 0; p < P; p++) { cin >> I[p] >> J[p]; }

    // 最小カットの設定
    Project_Selection_Problem<ll> B(N + M + K);
    vector<int> X(N + 1), Y(M + 1), Z(K + 1);

    iota(X.begin() + 1, X.end(), 0);
    iota(Y.begin() + 1, Y.end(), N );
    iota(Z.begin() + 1, Z.end(), N + M );

    auto inf = Extended_Algebra<ll>::inf;

    for (int i = 1; i <= N; i++) {
        B.set_one(X[i], E[i]);
        for (int a: A[i]) {
            B.set_zero_one(Z[a], X[i], -inf);
        }
    }

    for (int j = 1; j <= M; j++) {
        B.set_zero(Y[j], F[j]);
    }

    for (int p = 0; p < P; p++) { B.set_zero_one(Y[J[p]], X[I[p]], -inf); }
    for (int k = 1; k <= K; k++) { B.set_one(Z[k], -V[k]); }

    // 最小カットを解く.
    B.solve();
    auto choice = B.choice;

    // 解の計算
    vector<int> goals, actions, preparations;
    for (int i = 1; i <= N; i++) {
        if (choice[X[i]]) goals.emplace_back(i);
    }

    for (int j = 1; j <= M; j++) {
        if (!choice[Y[j]]) actions.emplace_back(j);
    }

    for (int k = 1; k <= K; k++) {
        if (choice[Z[k]]) preparations.emplace_back(k);
    }

    // 解の出力
    cout << B.ans << endl;
    cout << (goals.size() + actions.size() + preparations.size()) << endl;

    for (int k: preparations) { cout << "Preparation " << k << endl; }
    for (int i: goals) { cout << "Goal " << i << endl; }
    for (int j: actions) { cout << "Action " << j << endl; }
}

int main() {
    verify();
}

#line 1 "verify/yukicoder/1984.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1984"

#line 2 "template/template.hpp"

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}

// a の最大値を取得する.
template<typename T>
inline T max(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *max_element(a.begin(), a.end());
}

// vector<T> a の最小値を取得する.
template<typename T>
inline T min(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *min_element(a.begin(), a.end());
}

// vector<T> a の最大値のインデックスを取得する.
template<typename T>
inline size_t argmax(const vector<T> &a){
    if (a.empty()) throw std::invalid_argument("vector is empty.");

    return distance(a.begin(), max_element(a.begin(), a.end()));
}

// vector<T> a の最小値のインデックスを取得する.
template<typename T>
inline size_t argmin(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return distance(a.begin(), min_element(a.begin(), a.end()));
}
#line 61 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 演算子
template<typename T>
T add(const T &x, const T &y) { return x + y; }

template<typename T>
T sub(const T &x, const T &y) { return x - y; }

template<typename T>
T mul(const T &x, const T &y) { return x * y; }

template<typename T>
T neg(const T &x) { return -x; }

template<integral T>
T bitwise_and(const T &x, const T &y) { return x & y; }

template<integral T>
T bitwise_or(const T &x, const T &y) { return x | y; }

template<integral T>
T bitwise_xor(const T &x, const T &y) { return x ^ y; }

// 除算に関する関数

// floor(x / y) を求める.
template<integral T, integral U>
auto div_floor(T x, U y){
    return x / y - ((x % y != 0) && ((x < 0) != (y < 0)));
}

// ceil(x / y) を求める.
template<integral T, integral U>
auto div_ceil(T x, U y){
    return x / y + ((x % y != 0) && ((x < 0) == (y < 0)));
}

// x を y で割った余りを求める.
template<integral T, integral U>
auto safe_mod(T x, U y){
    auto q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<integral T, integral U>
auto divmod(T x, U y){
    auto q = div_floor(x, y);
    return make_pair(q, x - q * y);
}

// 四捨五入を求める.
template<integral T, integral U>
auto round(T x, U y){
    auto [q, r] = divmod(x, y);
    if (y < 0) return (r <= div_floor(y, 2)) ? q + 1 : q;
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 奇数かどうか判定する.
template<integral T>
bool is_odd(const T &x) { return x % 2 != 0; }

// 偶数かどうか判定する.
template<integral T>
bool is_even(const T &x) { return x % 2 == 0; }

// m の倍数かどうか判定する.
template<integral T, integral U>
bool is_multiple(const T &x, const U &m) { return x % m == 0; }

// 正かどうか判定する.
template<typename T>
bool is_positive(const T &x) { return x > 0; }

// 負かどうか判定する.
template<typename T>
bool is_negative(const T &x) { return x < 0; }

// ゼロかどうか判定する.
template<typename T>
bool is_zero(const T &x) { return x == 0; }

// 非負かどうか判定する.
template<typename T>
bool is_non_negative(const T &x) { return x >= 0; }

// 非正かどうか判定する.
template<typename T>
bool is_non_positive(const T &x) { return x <= 0; }

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
template<typename T, integral U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

template<typename T>
T sum(const vector<T> &X) {
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

template<typename T>
T gcd(const T x, const T y) {
    return y == 0 ? x : gcd(y, x % y);
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
template<integral T>
tuple<T, T, T> Extended_Euclid(T a, T b) {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
        auto [q, r] = divmod(a, b);
        a = b;
        b = r;
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrtl(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 64 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
    os << P.first << " " << P.second;
    return os;
}

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
    int s = (int)X.size();
    for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
std::vector<T> input_vector(size_t n, size_t offset = 0) {
    std::vector<T> res;
    // 最初に必要な全容量を確保（再確保を防ぐ）
    res.reserve(n + offset);
    // offset 分をデフォルト値で埋める（特別 indexed 用）
    res.assign(offset, T());
    
    for (size_t i = 0; i < n; ++i) {
        T el;
        if (!(std::cin >> el)) break;
        res.push_back(std::move(el));
    }
    return res;
}
#line 67 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 70 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 73 "template/template.hpp"

// exception
#line 2 "template/exception.hpp"

class NotExist: public exception {
    private:
    string message;

    public:
    NotExist() : message("求めようとしていたものは存在しません.") {}

    const char* what() const noexcept override {
        return message.c_str();
    }
};
#line 2 "Max_Flow/Project_Selection_Problem.hpp"

#line 2 "Algebra/Extended_Algebra.hpp"

#line 4 "Algebra/Extended_Algebra.hpp"

class IndeterminateOperationError : public std::runtime_error {
    public:
    IndeterminateOperationError(const std::string& msg): std::runtime_error(msg) {}
};

template<typename R>
struct Extended_Algebra {
    R val;
    signed char inf_flag; // 0: finite, 1: +inf, -1: -inf
    constexpr Extended_Algebra(R val, signed char inf_flag): val(val), inf_flag(inf_flag) {}

    public:
    constexpr Extended_Algebra(): val(R()), inf_flag(0) {}
    constexpr Extended_Algebra(R val): val(val), inf_flag(0) {}

    constexpr Extended_Algebra operator-() const { return Extended_Algebra(-val, -inf_flag); }

    static constexpr Extended_Algebra inf = Extended_Algebra(R(), 1);

    constexpr bool is_finite() const { return inf_flag == 0; }
    constexpr bool is_infinite() const { return !is_finite(); }

    constexpr bool is_positive(const bool zero = false) const {
        if(is_infinite()) { return inf_flag > 0; }

        return zero ? val >= R() : val > R();
    }

    constexpr bool is_negative(const bool zero = false) const {
        if(is_infinite()) { return inf_flag < 0; }

        return zero ? val <= R() : val < R();
    }

    constexpr bool is_positive_infinite() const { return inf_flag == 1; }
    constexpr bool is_negative_infinite() const { return inf_flag == -1; }

    constexpr inline bool is_zero() const { return inf_flag == 0 && val == R(); }

    constexpr Extended_Algebra& operator+=(const Extended_Algebra &rhs) {
        if (is_positive_infinite() && rhs.is_negative_infinite()) {
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf + (-inf))");
        }
        if (is_negative_infinite() && rhs.is_positive_infinite()) {
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form ((-inf) + inf)");
        }

        if (is_finite() && rhs.is_finite()) { val += rhs.val; }
        else if (is_positive_infinite() || rhs.is_positive_infinite()) { inf_flag = 1; }
        else if (is_negative_infinite() || rhs.is_negative_infinite()) { inf_flag = -1; }

        return *this;
    }

    friend constexpr Extended_Algebra operator+(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) += rhs; }

    constexpr Extended_Algebra& operator-=(const Extended_Algebra &rhs) {
        if (this->is_positive_infinite() && rhs.is_positive_infinite()) { 
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf - inf)");
        }
        if (this->is_negative_infinite() && rhs.is_negative_infinite()) {
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form ((-inf) - (-inf))");
        }

        if (is_finite() && rhs.is_finite()) { val -= rhs.val; }
        else if (is_positive_infinite() || rhs.is_negative_infinite()) { inf_flag = 1; }
        else if (is_negative_infinite() || rhs.is_positive_infinite()) { inf_flag = -1; }

        return *this;
    }

    friend constexpr Extended_Algebra operator-(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) -= rhs; }

    constexpr Extended_Algebra& operator*=(const Extended_Algebra &rhs) {
        if (is_zero() || rhs.is_zero()) {
            val = R();
            inf_flag = 0;
            return *this;
        }

        if (is_finite() && rhs.is_finite()) { val *= rhs.val; return *this; }

        if (is_positive() == rhs.is_positive()) { inf_flag = 1; }
        else { inf_flag = -1; }

        return *this;
    }

    friend constexpr Extended_Algebra operator*(const Extended_Algebra &lhs, const Extended_Algebra &rhs) { return Extended_Algebra(lhs) *= rhs; }

    constexpr Extended_Algebra& operator/=(const Extended_Algebra &rhs) {
        // 0-1. 未定義形: (± inf) / (± inf)
        if (this->is_infinite() && rhs.is_infinite()) {
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (inf / inf)");
        }
        // 0-2. 未定義形: 0 / 0
        if (this->is_zero() && rhs.is_zero()) {
            throw IndeterminateOperationError("Extended_Algebra: Indeterminate form (0 / 0)");
        }

        // 1. ゼロ除算: finite (non-zero) / 0 -> ±inf
        if (rhs.is_zero()) {
            // 分母が 0 であるが, 0-2 を通り抜けているので, 分子が 0 にはなり得ない.
            inf_flag = is_positive() ? 1 : -1;
            val = R();
            return *this;
        }

        // 2. どちらも有限 (分母 != 0)
        if (is_finite() && rhs.is_finite()) { 
            // ゼロ除算は上記 1 で処理済み
            val /= rhs.val; 
            return *this;
        }

        // 3. 無限大を含む確定的な計算
        // inf / finite (non-zero) または finite (zero) / inf
        val = R(); // 結果は inf / 0

        if (this->is_infinite() && rhs.is_finite()) {
            // inf / finite -> 符号は乗算と同じ
            inf_flag = (is_positive() == rhs.is_positive()) ? 1 : -1;
        } else { // finite / inf -> 0 (既に is_zero()で処理されているべきだが安全のため)
            inf_flag = 0;
        }

        return *this;
    }

    // 非複合演算子
    friend constexpr Extended_Algebra operator/(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {  return Extended_Algebra(lhs) /= rhs; }

    // 比較
    friend constexpr bool operator==(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {
        if (lhs.inf_flag != rhs.inf_flag) { return false; }

        if (lhs.is_finite()) { return lhs.val == rhs.val; }

        return true;
    }

    friend constexpr bool operator<(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {
        if (lhs.inf_flag != rhs.inf_flag) { return lhs.inf_flag < rhs.inf_flag; }

        if (lhs.is_finite()) { return lhs.val < rhs.val; }

        return false;
    }

    friend constexpr bool operator!=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return !(lhs == rhs);}
    friend constexpr bool operator> (const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return rhs < lhs;}
    friend constexpr bool operator<=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return (lhs < rhs) || (lhs == rhs);}
    friend constexpr bool operator>=(const Extended_Algebra &lhs, const Extended_Algebra &rhs) {return (lhs > rhs) || (lhs == rhs);}

    // 出力
    friend ostream &operator<<(ostream &os, const Extended_Algebra &x) {
        if (x.is_positive_infinite()) { return os << "inf"; }
        if (x.is_negative_infinite()) { return os << "-inf"; }
        return os << x.val;
    }
};
#line 2 "Max_Flow/Max_Flow.hpp"

#line 4 "Max_Flow/Max_Flow.hpp"

namespace max_flow {
    template<typename Cap>
    struct Arc {
        int id, source, target;
        Cap cap, flow;
        bool direction;
        Arc* rev;

        Arc(int id, int source, int target, Cap cap, Cap flow, bool direction):
            id(id), source(source), target(target), cap(cap), flow(flow), direction(direction), rev(nullptr) {}

        inline bool is_flowable() const { return flow < cap; }
        inline Cap remain() const { return cap - flow; }

        void push(Cap d) {
            flow += d;
            rev->flow -= d;
        }
    };

    template<typename Cap>
    struct Max_Flow {
        private:
        using V = int;
        vector<vector<Arc<Cap>*>> adj_out;
        vector<Arc<Cap>*> arcs;
        vector<int> level, iter;

        bool bfs(const V s, const V t) {
            level.assign(order(), -1);
            queue<V> Q;

            Q.push(s);
            level[s] = 0;

            while (!Q.empty()) {
                V v = Q.front(); Q.pop();

                for (Arc<Cap>* arc: adj_out[v]) {
                    unless(arc->is_flowable() && level[arc->target] == -1) { continue; }

                    level[arc->target] = level[v] + 1;
                    if (arc->target == t) { return true; }

                    Q.push(arc->target);
                }
            }

            return false;
        }

        Cap dfs(const V v, const V t, const Cap f) {
            if (v == t) { return f; }

            for (int i = iter[v]; i < adj_out[v].size(); ++i) {
                Arc<Cap>* arc = adj_out[v][i];

                unless(arc->is_flowable() && level[v] < level[arc->target]) { continue; }

                Cap d = (f == -1) ? dfs(arc->target, t, arc->remain()) : dfs(arc->target, t, min(f, arc->remain()));

                unless(d > 0) { continue; }

                arc->push(d);
                return d;
            }

            return 0;
        }

        public:
        Max_Flow(int N = 0) {
            adj_out.resize(N);
            level.resize(N);
            iter.resize(N);
        }

        ~Max_Flow() {
            for (Arc<Cap>* arc : arcs) {
                if (arc->rev) { delete arc->rev; }
                delete arc;
            }
        }

        inline int order() const { return adj_out.size(); }
        inline int size() const { return arcs.size(); }

        int add_arc(const V u, const V v, const Cap cap) {
            int m = size();

            Arc<Cap>* arc = new Arc<Cap>(m, u, v, cap, 0, true);
            Arc<Cap>* rev_arc = new Arc<Cap>(m, v, u, 0, 0, false);

            arc->rev = rev_arc;
            rev_arc->rev = arc;

            adj_out[u].emplace_back(arc);
            adj_out[v].emplace_back(rev_arc);
            arcs.emplace_back(arc);

            return m;
        }

        int add_vertex() {
            adj_out.emplace_back({});
            level.emplace_back(-1);
            iter.emplace_back(0);

            return order() - 1;
        }

        Cap max_flow(const V source, const V target) {
            Cap flow = 0;
            while (bfs(source, target)) {
                iter.assign(order(), 0);
                Cap f;
                while ((f = dfs(source, target, -1)) > 0) {
                    flow += f;
                }
            }

            return flow;
        }

        Cap max_flow(const V source, const V target, Cap flow_limit) {
            Cap flow = 0;
            while (flow < flow_limit && bfs(source, target)) {
                iter.assign(order(), 0);
                Cap f;
                while ((f = dfs(source, target, -1)) > 0) {
                    flow += f;
                }
            }

            return flow;
        }

        vector<vector<tuple<int, V, Cap>>> get_flow() const {
            vector<vector<tuple<int, V, Cap>>> flow(order());

            for (Arc<Cap>* arc: arcs) {
                flow[arc->source].emplace_back(
                    arc->id,
                    arc->target,
                    arc->flow
                );
            }

            return flow;
        }

        vector<bool> min_cut(const int s) {
            vector<bool> group(order(), true); group[s] = false;

            deque<V> Q{s};

            while (!Q.empty()) {
                V x = Q.front(); Q.pop_front();

                for (Arc<Cap>* arc: adj_out[x]) {
                    V y = arc->target;
                    unless(arc->is_flowable() && group[y]) { continue; }

                    group[y] = false;
                    Q.emplace_back(y);
                }
            }

            return group;
        }
    };
}
#line 5 "Max_Flow/Project_Selection_Problem.hpp"

namespace projection_selection_problem {
    template<typename T>
    class Project_Selection_Problem {
        using ET = Extended_Algebra<T>;
        using V = int;

        private:
        int N, ver_num;
        V source, target;
        ET base;
        vector<vector<ET>> indivi;
        vector<pair<pair<V, V>, ET>> mutual;
        vector<vector<bool>> guard;

        V add_vertex_inner() {
            V n = ver_num++;
            indivi.emplace_back(vector<ET>{ET(0), ET(0)});
            guard.emplace_back(vector<bool>{true, true});
            return n;
        }

        public:
        ET ans;
        vector<bool> choice;
        Project_Selection_Problem(const int N):
            N(N), ver_num(N + 2), source(N), target(N + 1),
            base(0), indivi(N + 2, { ET(0), ET(0) }), guard(N + 2, {false, false})
            {}

        V add_vertex() {
            V n = ver_num++;
            indivi.emplace_back(vector<ET>{ET(0), ET(0)});
            guard.emplace_back(vector<bool>{false, false});
            return n;
        }

        vector<V> add_vertices(const int k) {
            vector<V> ids;
            for (int i = 1; i <= k; i++) {
                ids.emplace_back(add_vertex());
            }

            return ids;
        }

        void set_zero_one(const V x, const V y, ET a) {
            assert(a.is_negative(true));

            pair<V, V> arc(x, y);
            mutual.emplace_back(arc, -a);
        }

        inline void set_zero(const V x, const ET a) { indivi[x][0] += a; }
        inline void set_one(const V x, const ET a) { indivi[x][1] += a; }

        void set_all_zero(const vector<V>& Xs, const ET a) {
            assert(a.is_positive(true));

            V k = add_vertex_inner();
            base += a;

            indivi[k][0] -= a;
            guard[k][0] = false;

            for(V x: Xs) {
                pair<V, V> arc(k, x);
                mutual.emplace_back(arc, ET::inf);
            }
        }

        void set_all_one(const vector<V>& Xs, const ET a) {
            assert(a.is_positive());

            V k = add_vertex_inner();
            base += a;

            indivi[k][1] -= a;
            guard[k][1] = false;

            for(V x: Xs) {
                pair<V, V> arc(x, k);
                mutual.emplace_back(arc, ET::inf);
            }
        }

        void set_not_equal(const V x, const V y, const ET a) {
            assert(a.is_negative(true));

            set_zero_one(x, y, a);
            set_zero_one(y, x, a);
        }

        void set_equal(const V x, const V y, const ET a) {
            set_all_zero({x, y}, a);
            set_all_one({x, y}, a);
        }

        void ban_zero(const V x) { set_zero(x, -ET::inf); }
        void ban_one(const V x) { set_one(x, -ET::inf); }

        void force_zero(const V x) { ban_one(x); }
        void force_one(const V x) { ban_zero(x); }

        void solve() {
            max_flow::Max_Flow<ET> F(ver_num);

            for (int i = 0; i < N; i++) {
                F.add_arc(source, i, 0);
                F.add_arc(i, target, 0);

                if (indivi[i][0].is_positive(true)) {
                    base += indivi[i][0];
                    F.add_arc(source, i, indivi[i][0]);
                } else {
                    F.add_arc(i, target, -indivi[i][0]);
                }

                if (indivi[i][1].is_positive(true)) {
                    base += indivi[i][1];
                    F.add_arc(i, target, indivi[i][1]);
                } else {
                    F.add_arc(source, i, -indivi[i][1]);
                }
            }

            for (int i = target + 1; i < ver_num; i++) {
                if (!guard[i][0]) { F.add_arc(source, i, -indivi[i][0]); }
                if (!guard[i][1]) { F.add_arc(i, target, -indivi[i][1]); }
            }

            for(auto &[arc, a]: mutual) {
                V x, y;
                tie(x, y) = arc;
                F.add_arc(x, y, a);
            }

            ET alpha = F.max_flow(source, target);
            ans = base - alpha;
            choice = F.min_cut(source);
        }
    };
}
#line 5 "verify/yukicoder/1984.test.cpp"

using namespace projection_selection_problem;

void verify() {
    // 変数代入
    int N, M, K, P; cin >> N >> M >> K >> P;
    vector<ll> E(N + 1), F(M + 1), V(K + 1);
    for (int i = 1; i <= N; i++) { cin >> E[i]; }
    for (int j = 1; j <= M; j++) { cin >> F[j]; }
    for (int k = 1; k <= K; k++) { cin >> V[k]; }

    vector<int> L(N + 1);
    vector<vector<int>> A(N + 1);

    for (int i = 1; i <= N; i++) {
        cin >> L[i];
        A[i].resize(L[i]);
        for (int t = 0; t < L[i]; t++) { cin >> A[i][t]; }
    }

    vector<int> I(P), J(P);
    for (int p = 0; p < P; p++) { cin >> I[p] >> J[p]; }

    // 最小カットの設定
    Project_Selection_Problem<ll> B(N + M + K);
    vector<int> X(N + 1), Y(M + 1), Z(K + 1);

    iota(X.begin() + 1, X.end(), 0);
    iota(Y.begin() + 1, Y.end(), N );
    iota(Z.begin() + 1, Z.end(), N + M );

    auto inf = Extended_Algebra<ll>::inf;

    for (int i = 1; i <= N; i++) {
        B.set_one(X[i], E[i]);
        for (int a: A[i]) {
            B.set_zero_one(Z[a], X[i], -inf);
        }
    }

    for (int j = 1; j <= M; j++) {
        B.set_zero(Y[j], F[j]);
    }

    for (int p = 0; p < P; p++) { B.set_zero_one(Y[J[p]], X[I[p]], -inf); }
    for (int k = 1; k <= K; k++) { B.set_one(Z[k], -V[k]); }

    // 最小カットを解く.
    B.solve();
    auto choice = B.choice;

    // 解の計算
    vector<int> goals, actions, preparations;
    for (int i = 1; i <= N; i++) {
        if (choice[X[i]]) goals.emplace_back(i);
    }

    for (int j = 1; j <= M; j++) {
        if (!choice[Y[j]]) actions.emplace_back(j);
    }

    for (int k = 1; k <= K; k++) {
        if (choice[Z[k]]) preparations.emplace_back(k);
    }

    // 解の出力
    cout << B.ans << endl;
    cout << (goals.size() + actions.size() + preparations.size()) << endl;

    for (int k: preparations) { cout << "Preparation " << k << endl; }
    for (int i: goals) { cout << "Goal " << i << endl; }
    for (int j: actions) { cout << "Action " << j << endl; }
}

int main() {
    verify();
}

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