結果
| 問題 | No.803 Very Limited Xor Subset |
| ユーザー |
 minato
|
| 提出日時 | 2020-11-19 20:58:12 |
| 言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 3 ms / 2,000 ms |
| コード長 | 9,727 bytes |
| コンパイル時間 | 12,515 ms |
| コンパイル使用メモリ | 288,616 KB |
| 最終ジャッジ日時 | 2025-01-16 01:46:11 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 43 |
ソースコード
#ifdef ONLINE_JUDGE#pragma GCC target("avx2,avx")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#endif#include <bits/stdc++.h>using namespace std;using ll = long long;using ull = unsigned long long;using i128 = __int128_t;using pii = pair<int, int>;using pll = pair<long long, long long>;#define rep(i, n) for (int i = 0; i < (n); i++)#define rrep(i, n) for (int i = int(n) - 1; i >= 0; i--)#define all(x) (x).begin(), (x).end()constexpr char ln = '\n';istream& operator>>(istream& is, __int128_t& x) {x = 0;string s;is >> s;int n = int(s.size()), it = 0;if (s[0] == '-') it++;for (; it < n; it++) x = (x * 10 + s[it] - '0');if (s[0] == '-') x = -x;return is;}ostream& operator<<(ostream& os, __int128_t x) {if (x == 0) return os << 0;if (x < 0) os << '-', x = -x;deque<int> deq;while (x) deq.emplace_front(x % 10), x /= 10;for (int e : deq) os << e;return os;}template<class T1, class T2>ostream& operator<<(ostream& os, const pair<T1, T2>& p) {return os << "(" << p.first << ", " << p.second << ")";}template<class T>ostream& operator<<(ostream& os, const vector<T>& v) {os << "{";for (int i = 0; i < int(v.size()); i++) {if (i) os << ", ";os << v[i];}return os << "}";}template<class Container> inline int SZ(Container& v) { return int(v.size()); }template<class T> inline void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }template<class T1, class T2> inline bool chmax(T1& a, T2 b) { if (a < b) {a = b; return true ;} return false ;}template<class T1, class T2> inline bool chmin(T1& a, T2 b) { if (a > b) {a = b; return true ;} return false ;}inline int topbit(int x) { return x == 0 ? -1 : 31 - __builtin_clz(x); }inline int topbit(long long x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }inline int botbit(int x) { return x == 0 ? 32 : __builtin_ctz(x); }inline int botbit(long long x) { return x == 0 ? 64 : __builtin_ctzll(x); }inline int popcount(int x) { return __builtin_popcount(x); }inline int popcount(long long x) { return __builtin_popcountll(x); }inline int kthbit(long long x, int k) { return (x>>k) & 1; }inline constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x-1) * 10; }inline void print() { cout << "\n"; }template<class T>inline void print(const vector<T>& v) {for (int i = 0; i < int(v.size()); i++) {if (i) cout << " ";cout << v[i];}print();}template<class T, class... Args>inline void print(const T& x, const Args& ... args) {cout << x << " ";print(args...);}#ifdef MINATO_LOCALinline void debug_out() { cerr << endl; }template <class T, class... Args>inline void debug_out(const T& x, const Args& ... args) {cerr << " " << x;debug_out(args...);}#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)#define dump(x) cerr << __LINE__ << " : " << #x << " = " << (x) << endl#else#define debug(...) (void(0))#define dump(x) (void(0))#endifstruct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////template<int m>struct ModInt {public:static constexpr int mod() { return m; }static ModInt raw(int v) {ModInt x;x._v = v;return x;}ModInt() : _v(0) {}ModInt(long long v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}unsigned int val() const { return _v; }ModInt& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}ModInt& operator--() {if (_v == 0) _v = umod();_v--;return *this;}ModInt operator++(int) {ModInt result = *this;++*this;return result;}ModInt operator--(int) {ModInt result = *this;--*this;return result;}ModInt& operator+=(const ModInt& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}ModInt& operator-=(const ModInt& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}ModInt& operator*=(const ModInt& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}ModInt& operator^=(long long n) {ModInt x = *this;*this = 1;if (n < 0) x = x.inv(), n = -n;while (n) {if (n & 1) *this *= x;x *= x;n >>= 1;}return *this;}ModInt& operator/=(const ModInt& rhs) { return *this = *this * rhs.inv(); }ModInt operator+() const { return *this; }ModInt operator-() const { return ModInt() - *this; }ModInt pow(long long n) const {ModInt r = *this;r ^= n;return r;}ModInt inv() const {int a = _v, b = umod(), y = 1, z = 0, t;for (; ; ) {t = a / b; a -= t * b;if (a == 0) {assert(b == 1 || b == -1);return ModInt(b * z);}y -= t * z;t = b / a; b -= t * a;if (b == 0) {assert(a == 1 || a == -1);return ModInt(a * y);}z -= t * y;}}friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) += rhs; }friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) -= rhs; }friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) *= rhs; }friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) { return ModInt(lhs) /= rhs; }friend ModInt operator^(const ModInt& lhs, long long rhs) { return ModInt(lhs) ^= rhs; }friend bool operator==(const ModInt& lhs, const ModInt& rhs) { return lhs._v == rhs._v; }friend bool operator!=(const ModInt& lhs, const ModInt& rhs) { return lhs._v != rhs._v; }friend ModInt operator+(long long lhs, const ModInt& rhs) { return (ModInt(lhs) += rhs); }friend ModInt operator-(long long lhs, const ModInt& rhs) { return (ModInt(lhs) -= rhs); }friend ModInt operator*(long long lhs, const ModInt& rhs) { return (ModInt(lhs) *= rhs); }friend ostream &operator<<(ostream& os, const ModInt& rhs) { return os << rhs._v; }private:unsigned int _v;static constexpr unsigned int umod() { return m; }};constexpr int MOD = 1000000007;//constexpr int MOD = 998244353;using mint = ModInt<MOD>;template<int MAX_COL>struct BitMatrix {int N,M;vector<bitset<MAX_COL>> A;BitMatrix() {}BitMatrix(int N) : N(N), M(MAX_COL), A(N) {}BitMatrix(int N, int M) : N(N), M(M), A(N) {}const bitset<MAX_COL> &operator[](int k) const {return A[k];}bitset<MAX_COL> &operator[](int k) {return A[k];}void clear() {for (int i = 0; i < N; i++) A[i].clear();}// xor subset 最大化は掃き出し法で解ける// ex 集合{65,66} の部分和(和は xor ) は集合{65,65^66} の部分和と一致する// 各列について立っている bit を一つにしてどう集合から部分和を選ぶと和が最大になるか明らかにするint GaussJordan(int isextened = 0) {int rank = 0;//左の列から掃き出していくfor (int col = 0; col < M - isextened; col++) {int pivot = -1;for (int row = rank; row < N; row++) {if (A[row][col]) {pivot = row;break;}}if (pivot == -1) continue;// 最も左の bit が対角に並んでいくswap(A[pivot], A[rank]);for (int row = 0; row < N; row++) {// pivot のある列の値がすべて 0 になるように掃き出すif (row != rank && A[row][col]) A[row] ^= A[rank];}rank++;}return rank;}};constexpr int COL = 301;using BM = BitMatrix<COL>;//連立一次方程式 Ax = b の解を求める//解なしなら -1 ,そうでないなら rank を返す//解の個数は M - rank// O(N * M^2 / 64)//N : タテ,式の個数, M : ヨコ,変数の個数pair<int, vector<int>> linear_equation(const BM& A, const vector<int>& b) {int N = A.N;int M = A.M;assert(N == int(b.size()));BM mat(N,M+1);for (int i = 0; i < N; i++) {for (int j = 0; j < M; j++) {mat[i][j] = A[i][j];}mat[i][M] = b[i];}int rank = mat.GaussJordan(1);for (int i = rank; i < N; i++) {if (mat[i][M]) return {-1, vector<int>{}};}vector<int> ret(M);for (int i = 0; i < rank; i++) ret[i] = mat[i][M];return {rank,ret};};int main() {int N,M,X; cin >> N >> M >> X;vector<int> A(N);rep(i,N) cin >> A[i];BM mat(30+M,N);vector<int> b(30+M);rep(k,30) {rep(i,N) if (kthbit(A[i],k)) mat[k][i] = 1;b[k] = kthbit(X,k);}rep(i,M) {int t,l,r; cin >> t >> l >> r;l--;for (int j = l; j < r; j++) {mat[30+i][j] = 1;}b[30+i] = t;}auto[rank,ret] = linear_equation(mat,b);if (rank==-1) {cout << 0 << ln;return 0;}cout << mint(2).pow(N-rank) << ln;}