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View the Project on GitHub maspypy/library
#include "flow/bipartite_dense.hpp"
#include "ds/my_bitset.hpp" // vc<bitset> で biadj matrix を渡す // N_1^2N_2/w. // (5000,5000) で 300ms 程度で動く場合がある // https://qoj.ac/problem/6308 // (10000?, 5000) 655ms // https://codeforces.com/contest/1045/problem/A // (10000, 20000) で 3837ms // https://codeforces.com/contest/786/problem/E // (10000, 10000) 6500ms TLE. row, col とも shuffle で 3000ms AC. // bitset の方が My_Bitset より高速?(2024/05/27) template <typename BS> struct BipartiteMatching_Dense { int N1, N2; vc<BS>& adj; vc<int> match_1, match_2; vc<int> que; vc<int> prev; BS vis; BipartiteMatching_Dense(vc<BS>& adj, int N1, int N2) : N1(N1), N2(N2), adj(adj), match_1(N1, -1), match_2(N2, -1) { if constexpr (is_same_v<BS, My_Bitset>) vis.resize(N2); FOR(s, N1) bfs(s); } void bfs(int s) { if (match_1[s] != -1) return; que.resize(N1), prev.resize(N1); int l = 0, r = 0; prev[s] = -1; vis.set(); que[r++] = s; while (l < r) { int u = que[l++]; BS cand = vis & adj[u]; for (int v = cand._Find_first(); v < N2; v = cand._Find_next(v)) { vis[v] = 0; if (match_2[v] != -1) { que[r++] = match_2[v]; prev[match_2[v]] = u; continue; } int a = u, b = v; while (a != -1) { int t = match_1[a]; match_1[a] = b, match_2[b] = a, a = prev[a], b = t; } return; } } return; } vc<pair<int, int>> matching() { vc<pair<int, int>> res; FOR(v, N1) if (match_1[v] != -1) res.eb(v, match_1[v]); return res; } pair<vc<int>, vc<int>> vertex_cover() { vc<int> que(N1); int l = 0, r = 0; vis.set(); vc<bool> done(N1); FOR(i, N1) { if (match_1[i] == -1) done[i] = 1, que[r++] = i; } while (l < r) { int a = que[l++]; BS cand = adj[a] & vis; for (int b = cand._Find_first(); b < N2; b = cand._Find_next(b)) { vis[b] = 0; int to = match_2[b]; assert(to != -1); if (!done[to]) done[to] = 1, que[r++] = to; } } vc<int> left, right; FOR(i, N1) if (!done[i]) left.eb(i); FOR(i, N2) if (!vis[i]) right.eb(i); return {left, right}; } };
#line 2 "ds/my_bitset.hpp" // https://codeforces.com/contest/914/problem/F // https://yukicoder.me/problems/no/142 // わずかに普通の bitset より遅いときもあるようだが, // 固定長にしたくないときや slice 操作が必要なときに使う struct My_Bitset { using T = My_Bitset; int N; vc<u64> dat; // x で埋める My_Bitset(int N = 0, int x = 0) : N(N) { assert(x == 0 || x == 1); u64 v = (x == 0 ? 0 : -1); dat.assign((N + 63) >> 6, v); if (N) dat.back() >>= (64 * len(dat) - N); } int size() { return N; } void resize(int size) { dat.resize((size + 63) >> 6); int remainingBits = size & 63; if (remainingBits != 0) { u64 mask = (u64(1) << remainingBits) - 1; dat.back() &= mask; } N = size; } static T from_string(string &S) { int N = len(S); T ANS(N); FOR(i, N) ANS[i] = (S[i] == '1'); return ANS; } // thanks to chatgpt! class Proxy { public: Proxy(vc<u64> &d, int i) : dat(d), index(i) {} operator bool() const { return (dat[index >> 6] >> (index & 63)) & 1; } Proxy &operator=(u64 value) { dat[index >> 6] &= ~(u64(1) << (index & 63)); dat[index >> 6] |= (value & 1) << (index & 63); return *this; } void flip() { dat[index >> 6] ^= (u64(1) << (index & 63)); // XOR to flip the bit } private: vc<u64> &dat; int index; }; Proxy operator[](int i) { return Proxy(dat, i); } bool operator==(const T &p) { assert(N == p.N); FOR(i, len(dat)) if (dat[i] != p.dat[i]) return false; return true; } T &operator&=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] &= p.dat[i]; return *this; } T &operator|=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] |= p.dat[i]; return *this; } T &operator^=(const T &p) { assert(N == p.N); FOR(i, len(dat)) dat[i] ^= p.dat[i]; return *this; } T operator&(const T &p) const { return T(*this) &= p; } T operator|(const T &p) const { return T(*this) |= p; } T operator^(const T &p) const { return T(*this) ^= p; } T operator~() const { T p = (*this); p.flip_range(0, N); return p; } int count() { int ans = 0; for (u64 val: dat) ans += popcnt(val); return ans; } int dot(T &p) { assert(N == p.N); int ans = 0; FOR(i, len(dat)) ans += popcnt(dat[i] & p.dat[i]); return ans; } int dot_mod_2(T &p) { assert(N == p.N); int ans = 0; FOR(i, len(dat)) ans ^= popcnt_mod_2(dat[i] & p.dat[i]); return ans; } int next(int i) { chmax(i, 0); if (i >= N) return N; int k = i >> 6; { u64 x = dat[k]; int s = i & 63; x = (x >> s) << s; if (x) return (k << 6) | lowbit(x); } FOR(idx, k + 1, len(dat)) { if (dat[idx] == 0) continue; return (idx << 6) | lowbit(dat[idx]); } return N; } int prev(int i) { chmin(i, N - 1); if (i <= -1) return -1; int k = i >> 6; if ((i & 63) < 63) { u64 x = dat[k]; x &= (u64(1) << ((i & 63) + 1)) - 1; if (x) return (k << 6) | topbit(x); --k; } FOR_R(idx, k + 1) { if (dat[idx] == 0) continue; return (idx << 6) | topbit(dat[idx]); } return -1; } My_Bitset range(int L, int R) { assert(L <= R); My_Bitset p(R - L); int rm = (R - L) & 63; FOR(rm) { p[R - L - 1] = bool((*this)[R - 1]); --R; } int n = (R - L) >> 6; int hi = L & 63; int lo = 64 - hi; int s = L >> 6; if (hi == 0) { FOR(i, n) { p.dat[i] ^= dat[s + i]; } } else { FOR(i, n) { p.dat[i] ^= (dat[s + i] >> hi) ^ (dat[s + i + 1] << lo); } } return p; } My_Bitset slice(int L, int R) { return range(L, R); } int count_range(int L, int R) { assert(L <= R); int cnt = 0; while ((L < R) && (L & 63)) cnt += (*this)[L++]; while ((L < R) && (R & 63)) cnt += (*this)[--R]; int l = L >> 6, r = R >> 6; FOR(i, l, r) cnt += popcnt(dat[i]); return cnt; } // [L,R) に p を代入 void assign_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { (*this)[L++] = bool(p[a++]); } while (L < R && (R & 63)) { (*this)[--R] = bool(p[--b]); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] = p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] = (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // [L,R) に p を xor void xor_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { dat[L >> 6] ^= u64(p[a]) << (L & 63); ++a, ++L; } while (L < R && (R & 63)) { --b, --R; dat[R >> 6] ^= u64(p[b]) << (R & 63); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] ^= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] ^= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // 行列基本変形で使うやつ // p は [i:N) にしかないとして p を xor する void xor_suffix(int i, My_Bitset &p) { assert(N == p.N && 0 <= i && i < N); FOR(k, i / 64, len(dat)) { dat[k] ^= p.dat[k]; } } // [L,R) に p を and void and_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { if (!p[a]) (*this)[L] = 0; a++, L++; } while (L < R && (R & 63)) { --b, --R; if (!p[b]) (*this)[R] = 0; } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] &= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] &= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // [L,R) に p を or void or_to_range(int L, int R, My_Bitset &p) { assert(p.N == R - L); int a = 0, b = p.N; while (L < R && (L & 63)) { dat[L >> 6] |= u64(p[a]) << (L & 63); ++a, ++L; } while (L < R && (R & 63)) { --b, --R; dat[R >> 6] |= u64(p[b]) << (R & 63); } // p[a:b] を [L:R] に int l = L >> 6, r = R >> 6; int s = a >> 6, t = b >> t; int n = r - l; if (!(a & 63)) { FOR(i, n) dat[l + i] |= p.dat[s + i]; } else { int hi = a & 63; int lo = 64 - hi; FOR(i, n) dat[l + i] |= (p.dat[s + i] >> hi) | (p.dat[1 + s + i] << lo); } } // 行列基本変形で使うやつ // p は [i:N) にしかないとして p を or する void or_suffix(int i, My_Bitset &p) { assert(N == p.N && 0 <= i && i < N); FOR(k, i / 64, len(dat)) { dat[k] |= p.dat[k]; } } // [L,R) を 1 に変更 void set_range(int L, int R) { while (L < R && (L & 63)) { set(L++); } while (L < R && (R & 63)) { set(--R); } FOR(i, L >> 6, R >> 6) dat[i] = u64(-1); } // [L,R) を 1 に変更 void reset_range(int L, int R) { while (L < R && (L & 63)) { reset(L++); } while (L < R && (R & 63)) { reset(--R); } FOR(i, L >> 6, R >> 6) dat[i] = u64(0); } // [L,R) を flip void flip_range(int L, int R) { while (L < R && (L & 63)) { flip(L++); } while (L < R && (R & 63)) { flip(--R); } FOR(i, L >> 6, R >> 6) dat[i] ^= u64(-1); } // bitset に仕様を合わせる void set(int i) { (*this)[i] = 1; } void reset(int i) { (*this)[i] = 0; } void flip(int i) { (*this)[i].flip(); } void set() { fill(all(dat), u64(-1)); resize(N); } void reset() { fill(all(dat), 0); } void flip() { FOR(i, len(dat) - 1) { dat[i] = u64(-1) ^ dat[i]; } int i = len(dat) - 1; FOR(k, 64) { if (64 * i + k >= size()) break; flip(64 * i + k); } } bool any() { FOR(i, len(dat)) { if (dat[i]) return true; } return false; } bool ALL() { dat.resize((N + 63) >> 6); int r = N & 63; if (r != 0) { u64 mask = (u64(1) << r) - 1; if (dat.back() != mask) return 0; } for (int i = 0; i < N / 64; ++i) if (dat[i] != u64(-1)) return false; return true; } int _Find_first() { return next(0); } int _Find_next(int p) { return next(p + 1); } static string TO_STR[256]; string to_string() const { if (TO_STR[0].empty()) precompute(); string S; for (auto &x: dat) { FOR(i, 8) S += TO_STR[(x >> (8 * i) & 255)]; } S.resize(N); return S; } static void precompute() { FOR(s, 256) { string x; FOR(i, 8) x += '0' + (s >> i & 1); TO_STR[s] = x; } } }; string My_Bitset::TO_STR[256]; #line 2 "flow/bipartite_dense.hpp" // vc<bitset> で biadj matrix を渡す // N_1^2N_2/w. // (5000,5000) で 300ms 程度で動く場合がある // https://qoj.ac/problem/6308 // (10000?, 5000) 655ms // https://codeforces.com/contest/1045/problem/A // (10000, 20000) で 3837ms // https://codeforces.com/contest/786/problem/E // (10000, 10000) 6500ms TLE. row, col とも shuffle で 3000ms AC. // bitset の方が My_Bitset より高速?(2024/05/27) template <typename BS> struct BipartiteMatching_Dense { int N1, N2; vc<BS>& adj; vc<int> match_1, match_2; vc<int> que; vc<int> prev; BS vis; BipartiteMatching_Dense(vc<BS>& adj, int N1, int N2) : N1(N1), N2(N2), adj(adj), match_1(N1, -1), match_2(N2, -1) { if constexpr (is_same_v<BS, My_Bitset>) vis.resize(N2); FOR(s, N1) bfs(s); } void bfs(int s) { if (match_1[s] != -1) return; que.resize(N1), prev.resize(N1); int l = 0, r = 0; prev[s] = -1; vis.set(); que[r++] = s; while (l < r) { int u = que[l++]; BS cand = vis & adj[u]; for (int v = cand._Find_first(); v < N2; v = cand._Find_next(v)) { vis[v] = 0; if (match_2[v] != -1) { que[r++] = match_2[v]; prev[match_2[v]] = u; continue; } int a = u, b = v; while (a != -1) { int t = match_1[a]; match_1[a] = b, match_2[b] = a, a = prev[a], b = t; } return; } } return; } vc<pair<int, int>> matching() { vc<pair<int, int>> res; FOR(v, N1) if (match_1[v] != -1) res.eb(v, match_1[v]); return res; } pair<vc<int>, vc<int>> vertex_cover() { vc<int> que(N1); int l = 0, r = 0; vis.set(); vc<bool> done(N1); FOR(i, N1) { if (match_1[i] == -1) done[i] = 1, que[r++] = i; } while (l < r) { int a = que[l++]; BS cand = adj[a] & vis; for (int b = cand._Find_first(); b < N2; b = cand._Find_next(b)) { vis[b] = 0; int to = match_2[b]; assert(to != -1); if (!done[to]) done[to] = 1, que[r++] = to; } } vc<int> left, right; FOR(i, N1) if (!done[i]) left.eb(i); FOR(i, N2) if (!vis[i]) right.eb(i); return {left, right}; } };