This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub maspypy/library
#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2251" #include "my_template.hpp" #include "other/io.hpp" #include "graph/shortest_path/dijkstra.hpp" #include "graph/dag_path_cover.hpp" #include "graph/toposort.hpp" void solve(ll N, ll M, ll L) { vv(ll, dist, N, N); { Graph<ll> G(N); G.read_graph(M, 1, 0); FOR(v, N) { dist[v] = dijkstra<ll>(G, v).fi; } } VEC(pi, PT, L); N = L; Graph<int, 1> G(N); FOR(a, N) FOR(b, N) { if (a == b) continue; auto [pa, ta] = PT[a]; auto [pb, tb] = PT[b]; if (ta + dist[pa][pb] <= tb) G.add(a, b); } G.build(); auto V = toposort(G); G = G.rearrange(V); auto color = dag_path_cover(G); print(MAX(color) + 1); } signed main() { while (1) { LL(N, M, L); if (N + M + L == 0) break; solve(N, M, L); } return 0; }
#line 1 "test/4_aoj/2251_1.test.cpp" #define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2251" #line 1 "my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else // https://codeforces.com/blog/entry/96344 #pragma GCC optimize("Ofast,unroll-loops") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T> T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template <typename T> T ceil(T x, T y) { return floor(x + y - 1, y); } template <typename T> T bmod(T x, T y) { return x - y * floor(x, y); } template <typename T> pair<T, T> divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 1 "other/io.hpp" #define FASTIO #include <unistd.h> // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template <typename T> void rd_real(T &x) { string s; rd(s); x = stod(s); } template <typename T> void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed<T>::value || is_same_v<T, i128>) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template <class T, class U> void rd(pair<T, U> &p) { return rd(p.first), rd(p.second); } template <size_t N = 0, typename T> void rd_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); rd(x); rd_tuple<N + 1>(t); } } template <class... T> void rd(tuple<T...> &tpl) { rd_tuple(tpl); } template <size_t N = 0, typename T> void rd(array<T, N> &x) { for (auto &d: x) rd(d); } template <class T> void rd(vc<T> &x) { for (auto &d: x) rd(d); } void read() {} template <class H, class... T> void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template <typename T> void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template <typename T> void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template <class T, class U> void wt(const pair<T, U> val) { wt(val.first); wt(' '); wt(val.second); } template <size_t N = 0, typename T> void wt_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get<N>(t); wt(x); wt_tuple<N + 1>(t); } } template <class... T> void wt(tuple<T...> tpl) { wt_tuple(tpl); } template <class T, size_t S> void wt(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template <class T> void wt(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward<Tail>(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #if defined(LOCAL) #define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__) #define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME #define SHOW1(x) print(#x, "=", (x)), flush() #define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush() #define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush() #define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush() #define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush() #define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush() #else #define SHOW(...) #endif #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 2 "graph/base.hpp" template <typename T> struct Edge { int frm, to; T cost; int id; }; template <typename T = int, bool directed = false> struct Graph { static constexpr bool is_directed = directed; int N, M; using cost_type = T; using edge_type = Edge<T>; vector<edge_type> edges; vector<int> indptr; vector<edge_type> csr_edges; vc<int> vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void build(int n) { N = n, M = 0; prepared = 0; edges.clear(); indptr.clear(); csr_edges.clear(); vc_deg.clear(); vc_indeg.clear(); vc_outdeg.clear(); } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } #ifdef FASTIO // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } #endif void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc<int> deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair<vc<int>, vc<int>> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } #ifdef FASTIO void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } #endif vc<int> new_idx; vc<bool> used_e; // G における頂点 V[i] が、新しいグラフで i になるようにする // {G, es} // sum(deg(v)) の計算量になっていて、 // 新しいグラフの n+m より大きい可能性があるので注意 Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) { if (len(new_idx) != N) new_idx.assign(N, -1); int n = len(V); FOR(i, n) new_idx[V[i]] = i; Graph<T, directed> G(n); vc<int> history; FOR(i, n) { for (auto&& e: (*this)[V[i]]) { if (len(used_e) <= e.id) used_e.resize(e.id + 1); if (used_e[e.id]) continue; int a = e.frm, b = e.to; if (new_idx[a] != -1 && new_idx[b] != -1) { history.eb(e.id); used_e[e.id] = 1; int eid = (keep_eid ? e.id : -1); G.add(new_idx[a], new_idx[b], e.cost, eid); } } } FOR(i, n) new_idx[V[i]] = -1; for (auto&& eid: history) used_e[eid] = 0; G.build(); return G; } Graph<T, true> to_directed_tree(int root = -1) { if (root == -1) root = 0; assert(!is_directed && prepared && M == N - 1); Graph<T, true> G1(N); vc<int> par(N, -1); auto dfs = [&](auto& dfs, int v) -> void { for (auto& e: (*this)[v]) { if (e.to == par[v]) continue; par[e.to] = v, dfs(dfs, e.to); } }; dfs(dfs, root); for (auto& e: edges) { int a = e.frm, b = e.to; if (par[a] == b) swap(a, b); assert(par[b] == a); G1.add(a, b, e.cost); } G1.build(); return G1; } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 3 "graph/shortest_path/dijkstra.hpp" template <typename T, typename GT> pair<vc<T>, vc<int>> dijkstra_dense(GT& G, int s) { const int N = G.N; vc<T> dist(N, infty<T>); vc<int> par(N, -1); vc<bool> done(N); dist[s] = 0; while (1) { int v = -1; T mi = infty<T>; FOR(i, N) { if (!done[i] && chmin(mi, dist[i])) v = i; } if (v == -1) break; done[v] = 1; for (auto&& e: G[v]) { if (chmin(dist[e.to], dist[v] + e.cost)) par[e.to] = v; } } return {dist, par}; } template <typename T, typename GT, bool DENSE = false> pair<vc<T>, vc<int>> dijkstra(GT& G, int v) { if (DENSE) return dijkstra_dense<T>(G, v); auto N = G.N; vector<T> dist(N, infty<T>); vector<int> par(N, -1); using P = pair<T, int>; priority_queue<P, vector<P>, greater<P>> que; dist[v] = 0; que.emplace(0, v); while (!que.empty()) { auto [dv, v] = que.top(); que.pop(); if (dv > dist[v]) continue; for (auto&& e: G[v]) { if (chmin(dist[e.to], dist[e.frm] + e.cost)) { par[e.to] = e.frm; que.emplace(dist[e.to], e.to); } } } return {dist, par}; } // 多点スタート。[dist, par, root] template <typename T, typename GT> tuple<vc<T>, vc<int>, vc<int>> dijkstra(GT& G, vc<int> vs) { assert(G.is_prepared()); int N = G.N; vc<T> dist(N, infty<T>); vc<int> par(N, -1); vc<int> root(N, -1); using P = pair<T, int>; priority_queue<P, vector<P>, greater<P>> que; for (auto&& v: vs) { dist[v] = 0; root[v] = v; que.emplace(T(0), v); } while (!que.empty()) { auto [dv, v] = que.top(); que.pop(); if (dv > dist[v]) continue; for (auto&& e: G[v]) { if (chmin(dist[e.to], dist[e.frm] + e.cost)) { root[e.to] = root[e.frm]; par[e.to] = e.frm; que.push(mp(dist[e.to], e.to)); } } } return {dist, par, root}; } #line 1 "flow/maxflow.hpp" // incremental に辺を追加してよい // 辺の容量の変更が可能 // 変更する capacity が F のとき、O((N+M)|F|) 時間で更新 template <typename Cap> struct MaxFlow { struct Edge { int to, rev; Cap cap; // 残っている容量. したがって cap+flow が定数. Cap flow = 0; }; const int N, source, sink; vvc<Edge> edges; vc<pair<int, int>> pos; vc<int> prog, level; vc<int> que; bool calculated; MaxFlow(int N, int source, int sink) : N(N), source(source), sink(sink), edges(N), calculated(0), flow_ans(0) {} void add(int frm, int to, Cap cap, Cap rev_cap = 0) { calculated = 0; assert(0 <= frm && frm < N); assert(0 <= to && to < N); assert(Cap(0) <= cap); int a = len(edges[frm]); int b = (frm == to ? a + 1 : len(edges[to])); pos.eb(frm, a); edges[frm].eb(Edge{to, b, cap, 0}); edges[to].eb(Edge{frm, a, rev_cap, 0}); } void change_capacity(int i, Cap after) { auto [frm, idx] = pos[i]; auto& e = edges[frm][idx]; Cap before = e.cap + e.flow; if (before < after) { calculated = (e.cap > 0); e.cap += after - before; return; } e.cap = after - e.flow; // 差分を押し戻す処理発生 if (e.cap < 0) flow_push_back(e); } void flow_push_back(Edge& e0) { auto& re0 = edges[e0.to][e0.rev]; int a = re0.to; int b = e0.to; /* 辺 e0 の容量が正になるように戻す path-cycle 分解を考えれば、 - uv 辺を含むサイクルを消す - suvt パスを消す 前者は残余グラフで ab パス(flow_ans が変わらない) 後者は残余グラフで tb, as パス */ auto find_path = [&](int s, int t, Cap lim) -> Cap { vc<bool> vis(N); prog.assign(N, 0); auto dfs = [&](auto& dfs, int v, Cap f) -> Cap { if (v == t) return f; for (int& i = prog[v]; i < len(edges[v]); ++i) { auto& e = edges[v][i]; if (vis[e.to] || e.cap <= Cap(0)) continue; vis[e.to] = 1; Cap a = dfs(dfs, e.to, min(f, e.cap)); assert(a >= 0); if (a == Cap(0)) continue; e.cap -= a, e.flow += a; edges[e.to][e.rev].cap += a, edges[e.to][e.rev].flow -= a; return a; } return 0; }; return dfs(dfs, s, lim); }; while (e0.cap < 0) { Cap x = find_path(a, b, -e0.cap); if (x == Cap(0)) break; e0.cap += x, e0.flow -= x; re0.cap -= x, re0.flow += x; } Cap c = -e0.cap; while (c > 0 && a != source) { Cap x = find_path(a, source, c); assert(x > 0); c -= x; } c = -e0.cap; while (c > 0 && b != sink) { Cap x = find_path(sink, b, c); assert(x > 0); c -= x; } c = -e0.cap; e0.cap += c, e0.flow -= c; re0.cap -= c, re0.flow += c; flow_ans -= c; } // frm, to, flow vc<tuple<int, int, Cap>> get_flow_edges() { vc<tuple<int, int, Cap>> res; FOR(frm, N) { for (auto&& e: edges[frm]) { if (e.flow <= 0) continue; res.eb(frm, e.to, e.flow); } } return res; } vc<bool> vis; // 差分ではなくこれまでの総量 Cap flow() { if (calculated) return flow_ans; calculated = true; while (set_level()) { prog.assign(N, 0); while (1) { Cap x = flow_dfs(source, infty<Cap>); if (x == 0) break; flow_ans += x; chmin(flow_ans, infty<Cap>); if (flow_ans == infty<Cap>) return flow_ans; } } return flow_ans; } // 最小カットの値および、カットを表す 01 列を返す pair<Cap, vc<int>> cut() { flow(); vc<int> res(N); FOR(v, N) res[v] = (level[v] >= 0 ? 0 : 1); return {flow_ans, res}; } // O(F(N+M)) くらい使って経路復元 // simple path になる vvc<int> path_decomposition() { flow(); auto edges = get_flow_edges(); vvc<int> TO(N); for (auto&& [frm, to, flow]: edges) { FOR(flow) TO[frm].eb(to); } vvc<int> res; vc<int> vis(N); FOR(flow_ans) { vc<int> path = {source}; vis[source] = 1; while (path.back() != sink) { int to = POP(TO[path.back()]); while (vis[to]) { vis[POP(path)] = 0; } path.eb(to), vis[to] = 1; } for (auto&& v: path) vis[v] = 0; res.eb(path); } return res; } void debug() { print("source", source); print("sink", sink); print("edges (frm, to, cap, flow)"); FOR(v, N) { for (auto& e: edges[v]) { if (e.cap == 0 && e.flow == 0) continue; print(v, e.to, e.cap, e.flow); } } } private: Cap flow_ans; bool set_level() { que.resize(N); level.assign(N, -1); level[source] = 0; int l = 0, r = 0; que[r++] = source; while (l < r) { int v = que[l++]; for (auto&& e: edges[v]) { if (e.cap > 0 && level[e.to] == -1) { level[e.to] = level[v] + 1; if (e.to == sink) return true; que[r++] = e.to; } } } return false; } Cap flow_dfs(int v, Cap lim) { if (v == sink) return lim; Cap res = 0; for (int& i = prog[v]; i < len(edges[v]); ++i) { auto& e = edges[v][i]; if (e.cap > 0 && level[e.to] == level[v] + 1) { Cap a = flow_dfs(e.to, min(lim, e.cap)); if (a > 0) { e.cap -= a, e.flow += a; edges[e.to][e.rev].cap += a, edges[e.to][e.rev].flow -= a; res += a; lim -= a; if (lim == 0) break; } } } return res; } }; #line 2 "ds/unionfind/unionfind.hpp" struct UnionFind { int n, n_comp; vc<int> dat; // par or (-size) UnionFind(int n = 0) { build(n); } void build(int m) { n = m, n_comp = m; dat.assign(n, -1); } void reset() { build(n); } int operator[](int x) { while (dat[x] >= 0) { int pp = dat[dat[x]]; if (pp < 0) { return dat[x]; } x = dat[x] = pp; } return x; } ll size(int x) { x = (*this)[x]; return -dat[x]; } bool merge(int x, int y) { x = (*this)[x], y = (*this)[y]; if (x == y) return false; if (-dat[x] < -dat[y]) swap(x, y); dat[x] += dat[y], dat[y] = x, n_comp--; return true; } vc<int> get_all() { vc<int> A(n); FOR(i, n) A[i] = (*this)[i]; return A; } }; #line 4 "graph/dag_path_cover.hpp" // 各頂点の色をかえす。各色はひとつのパス上にあるようにする template <typename DAG> vc<int> dag_path_cover(DAG& G) { static_assert(DAG::is_directed); for (auto&& e: G.edges) assert(e.frm < e.to); int N = G.N; int source = 2 * N, sink = 2 * N + 1; MaxFlow<int> F(2 * N + 2, source, sink); FOR(v, N) { F.add(source, 2 * v + 1, 1); F.add(2 * v + 0, sink, 1); F.add(2 * v + 0, 2 * v + 1, infty<int>); } for (auto&& e: G.edges) F.add(2 * e.frm + 1, 2 * e.to + 0, infty<int>); F.flow(); auto paths = F.path_decomposition(); UnionFind uf(N); for (auto& P: paths) { int a = P[1], b = P[len(P) - 2]; uf.merge(a / 2, b / 2); } vc<int> ANS(N, -1); int p = 0; FOR(v, N) if (uf[v] == v) ANS[v] = p++; FOR(v, N) if (uf[v] != v) ANS[v] = ANS[uf[v]]; return ANS; }; #line 2 "ds/fastset.hpp" // 64-ary tree // space: (N/63) * u64 struct FastSet { static constexpr u32 B = 64; int n, log; vvc<u64> seg; FastSet() {} FastSet(int n) { build(n); } int size() { return n; } template <typename F> FastSet(int n, F f) { build(n, f); } void build(int m) { seg.clear(); n = m; do { seg.push_back(vc<u64>((m + B - 1) / B)); m = (m + B - 1) / B; } while (m > 1); log = len(seg); } template <typename F> void build(int n, F f) { build(n); FOR(i, n) { seg[0][i / B] |= u64(f(i)) << (i % B); } FOR(h, log - 1) { FOR(i, len(seg[h])) { seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B); } } } bool operator[](int i) const { return seg[0][i / B] >> (i % B) & 1; } void insert(int i) { for (int h = 0; h < log; h++) { seg[h][i / B] |= u64(1) << (i % B), i /= B; } } void add(int i) { insert(i); } void erase(int i) { u64 x = 0; for (int h = 0; h < log; h++) { seg[h][i / B] &= ~(u64(1) << (i % B)); seg[h][i / B] |= x << (i % B); x = bool(seg[h][i / B]); i /= B; } } void remove(int i) { erase(i); } // min[x,n) or n int next(int i) { assert(i <= n); chmax(i, 0); for (int h = 0; h < log; h++) { if (i / B == seg[h].size()) break; u64 d = seg[h][i / B] >> (i % B); if (!d) { i = i / B + 1; continue; } i += lowbit(d); for (int g = h - 1; g >= 0; g--) { i *= B; i += lowbit(seg[g][i / B]); } return i; } return n; } // max [0,x], or -1 int prev(int i) { assert(i >= -1); if (i >= n) i = n - 1; for (int h = 0; h < log; h++) { if (i == -1) break; u64 d = seg[h][i / B] << (63 - i % B); if (!d) { i = i / B - 1; continue; } i -= __builtin_clzll(d); for (int g = h - 1; g >= 0; g--) { i *= B; i += topbit(seg[g][i / B]); } return i; } return -1; } bool any(int l, int r) { return next(l) < r; } // [l, r) template <typename F> void enumerate(int l, int r, F f) { for (int x = next(l); x < r; x = next(x + 1)) f(x); } string to_string() { string s(n, '?'); for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0'); return s; } }; #line 3 "graph/toposort.hpp" // 辞書順最小の toposort を返す template <typename GT> vc<int> toposort(GT& G) { static_assert(GT::is_directed); assert(G.is_prepared()); const int N = G.N; auto [indeg, outdeg] = G.deg_array_inout(); FastSet que(N); vc<int> V; FOR(v, N) if (indeg[v] == 0) que.insert(v); while (1) { int v = que.next(0); if (v == N) break; que.erase(v), V.eb(v); for (auto&& e: G[v]) { if (--indeg[e.to] == 0) que.insert(e.to); } } return (len(V) < N ? vc<int>{} : V); } #line 7 "test/4_aoj/2251_1.test.cpp" void solve(ll N, ll M, ll L) { vv(ll, dist, N, N); { Graph<ll> G(N); G.read_graph(M, 1, 0); FOR(v, N) { dist[v] = dijkstra<ll>(G, v).fi; } } VEC(pi, PT, L); N = L; Graph<int, 1> G(N); FOR(a, N) FOR(b, N) { if (a == b) continue; auto [pa, ta] = PT[a]; auto [pb, tb] = PT[b]; if (ta + dist[pa][pb] <= tb) G.add(a, b); } G.build(); auto V = toposort(G); G = G.rearrange(V); auto color = dag_path_cover(G); print(MAX(color) + 1); } signed main() { while (1) { LL(N, M, L); if (N + M + L == 0) break; solve(N, M, L); } return 0; }