verifying_test/AtCoder/ABC155/linear_system_incidence.test.cpp

• View this file on GitHub
• Last update: 2022-02-11 15:15:07+09:00
• Link: View error logs on GitHub Actions
• Link: https://atcoder.jp/contests/abc155/tasks/abc155_f

Depends on

• 接続行列を係数に持つ線形方程式のソルバ (graph/linear_system_incidence.cpp)
• math/math_017_modint.cpp

Code

#define IGNORE
#define PROBLEM "https://atcoder.jp/contests/abc155/tasks/abc155_f"

// #define _GLIBCXX_DEBUG // for STL debug (optional)
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>
using namespace std;
using ll = long long int;
using int64 = long long int;
 
template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}
 
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const int INF = 1LL << 29;
const ll LONGINF = 1LL << 60;
const ll MOD = 1000000007LL;

#include "../../../graph/linear_system_incidence.cpp"
#include "../../../math/math_017_modint.cpp"
using mint = ModInt<2>;
 
int main() {
    int N, M; cin >> N >> M;
    vector< pair<int, int> > bomb;
    for(int i=0; i<N; i++) {
        int A, B; cin >> A >> B;
        bomb.emplace_back(A, B);
    }
    sort(bomb.begin(), bomb.end());

    // 隣接 xor
    vector<mint> b(N + 1);
    b[0] = mint(bomb.front().second);
    for(int i=0; i+1<N; i++) {
        b[i+1] = mint(bomb[i].second ^ bomb[i+1].second);
    }
    b[N] = mint(bomb.back().second);

    vector< pair<int, int> > edges;
    vector<int> ids;
    for(int i=0; i<M; i++) {
        int L, R; cin >> L >> R;
        // 範囲内にある爆弾のインデックス [bl, br)
        int bl = lower_bound(bomb.begin(), bomb.end(), make_pair(L, 0)) - bomb.begin();
        int br = upper_bound(bomb.begin(), bomb.end(), make_pair(R, 1)) - bomb.begin();

        if(bl >= br) continue;
        edges.emplace_back(bl, br);
        ids.emplace_back(i);
    }
    M = edges.size();

    // Ax + b = 0 -> Ax = b (mod 2)
    LinearSystemIncidence<mint> lsi(N+1, edges);
    auto ans = lsi.solve(b);
    if(!ans.first) cout << -1 << endl;
    else {
        vector<int> vec;
        for(int i=0; i<M; i++) {
            if(ans.second[i] == mint(1)) vec.emplace_back(ids[i]);
        }

        cout << vec.size() << endl;
        for(size_t i=0; i<vec.size(); i++) cout << vec[i] + 1 << " \n"[i + 1 == vec.size()];
    }
    return 0;
}

#line 1 "verifying_test/AtCoder/ABC155/linear_system_incidence.test.cpp"
#define IGNORE
#define PROBLEM "https://atcoder.jp/contests/abc155/tasks/abc155_f"

// #define _GLIBCXX_DEBUG // for STL debug (optional)
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>
using namespace std;
using ll = long long int;
using int64 = long long int;
 
template<typename T> void chmax(T &a, T b) {a = max(a, b);}
template<typename T> void chmin(T &a, T b) {a = min(a, b);}
template<typename T> void chadd(T &a, T b) {a = a + b;}
 
int dx[] = {0, 0, 1, -1};
int dy[] = {1, -1, 0, 0};
const int INF = 1LL << 29;
const ll LONGINF = 1LL << 60;
const ll MOD = 1000000007LL;

#line 2 "graph/linear_system_incidence.cpp"

/**
 * @brief 接続行列を係数に持つ線形方程式のソルバ
 * @docs docs/graph/linear_system_incidence.md
 */

#line 10 "graph/linear_system_incidence.cpp"
#include <tuple>
#line 12 "graph/linear_system_incidence.cpp"

template <typename Tp>
class LinearSystemIncidence {
public:
    struct Edge {
        int id, to;
        bool is_forward;
        Edge(int id, int to, int is_forward) : id(id), to(to), is_forward(is_forward) {}
    };

    LinearSystemIncidence(int N, const vector< pair<int, int> >& edges) : N(N), M(edges.size()), G(N) {
        for(int i=0; i<M; i++) {
            int u, v; tie(u, v) = edges[i];
            G[u].emplace_back(i, v, true);
            G[v].emplace_back(i, u, false);
        }
    }

    Tp dfs(int u, const vector<Tp> &b) {
        assert(!used[u]);
        used[u] = true;
        Tp res = b[u];
        for(const auto &e : G[u]) {
            if(used[e.to]) continue;
            Tp res_to = dfs(e.to, b);
            if(e.is_forward) x[e.id] = res_to;
            else x[e.id] = -res_to;
            res += res_to;
        }
        return res;
    }

    pair< bool, vector<Tp> > solve(vector<Tp> &b) {
        assert(static_cast<int>(b.size()) == N);
        used.assign(N, false);
        x.assign(M, Tp(0));
        for(int i=0; i<N; i++) {
            if(used[i]) continue;
            Tp v = dfs(i, b);
            if(v != Tp(0)) return make_pair(false, vector<Tp>());
        }
        return {true, move(x)};
    }

private:
    int N, M;
    vector< vector<Edge> > G;
    vector<bool> used;
    vector<Tp> x; // Ax = b
};
#line 1 "math/math_017_modint.cpp"
// ModInt begin


using ll = long long;
template<ll mod>
struct ModInt {
    ll v;
    ll mod_pow(ll x, ll n) const {
        return (!n) ? 1 : (mod_pow((x*x)%mod,n/2) * ((n&1)?x:1)) % mod;
    }
    ModInt(ll a = 0) : v((a %= mod) < 0 ? a + mod : a) {}
    ModInt operator+ ( const ModInt& b ) const {
        return (v + b.v >= mod ? ModInt(v + b.v - mod) : ModInt(v + b.v));
    }
    ModInt operator- () const {
        return ModInt(-v);
    }
    ModInt operator- ( const ModInt& b ) const {
        return (v - b.v < 0 ? ModInt(v - b.v + mod) : ModInt(v - b.v));
    }
    ModInt operator* ( const ModInt& b ) const {return (v * b.v) % mod;}
    ModInt operator/ ( const ModInt& b ) const {return (v * mod_pow(b.v, mod-2)) % mod;}
    
    bool operator== ( const ModInt &b ) const {return v == b.v;}
    bool operator!= ( const ModInt &b ) const {return !(*this == b); }
    ModInt& operator+= ( const ModInt &b ) {
        v += b.v;
        if(v >= mod) v -= mod;
        return *this;
    }
    ModInt& operator-= ( const ModInt &b ) {
        v -= b.v;
        if(v < 0) v += mod;
        return *this;
    }
    ModInt& operator*= ( const ModInt &b ) {
        (v *= b.v) %= mod;
        return *this;
    }
    ModInt& operator/= ( const ModInt &b ) {
        (v *= mod_pow(b.v, mod-2)) %= mod;
        return *this;
    }
    ModInt pow(ll x) { return ModInt(mod_pow(v, x)); }
    // operator int() const { return int(v); }

    // operator long long int() const { return v; }

};

template<ll mod>
ModInt<mod> pow(ModInt<mod> n, ll k) {
    return ModInt<mod>(n.mod_pow(n.v, k));
}

template<ll mod>
ostream& operator<< (ostream& out, ModInt<mod> a) {return out << a.v;}
template<ll mod>
istream& operator>> (istream& in, ModInt<mod>& a) {
    in >> a.v;
    return in;
}

// ModInt end

#line 46 "verifying_test/AtCoder/ABC155/linear_system_incidence.test.cpp"
using mint = ModInt<2>;
 
int main() {
    int N, M; cin >> N >> M;
    vector< pair<int, int> > bomb;
    for(int i=0; i<N; i++) {
        int A, B; cin >> A >> B;
        bomb.emplace_back(A, B);
    }
    sort(bomb.begin(), bomb.end());

    // 隣接 xor
    vector<mint> b(N + 1);
    b[0] = mint(bomb.front().second);
    for(int i=0; i+1<N; i++) {
        b[i+1] = mint(bomb[i].second ^ bomb[i+1].second);
    }
    b[N] = mint(bomb.back().second);

    vector< pair<int, int> > edges;
    vector<int> ids;
    for(int i=0; i<M; i++) {
        int L, R; cin >> L >> R;
        // 範囲内にある爆弾のインデックス [bl, br)
        int bl = lower_bound(bomb.begin(), bomb.end(), make_pair(L, 0)) - bomb.begin();
        int br = upper_bound(bomb.begin(), bomb.end(), make_pair(R, 1)) - bomb.begin();

        if(bl >= br) continue;
        edges.emplace_back(bl, br);
        ids.emplace_back(i);
    }
    M = edges.size();

    // Ax + b = 0 -> Ax = b (mod 2)
    LinearSystemIncidence<mint> lsi(N+1, edges);
    auto ans = lsi.solve(b);
    if(!ans.first) cout << -1 << endl;
    else {
        vector<int> vec;
        for(int i=0; i<M; i++) {
            if(ans.second[i] == mint(1)) vec.emplace_back(ids[i]);
        }

        cout << vec.size() << endl;
        for(size_t i=0; i<vec.size(); i++) cout << vec[i] + 1 << " \n"[i + 1 == vec.size()];
    }
    return 0;
}

Back to top page