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#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B" #include <vector> #include <iostream> #include <queue> #include <cassert> using namespace std; #include "../../lib/00-util/FastIO.cpp" #include "../../lib/40-graph/PrimalDualMinCostFlow.cpp" int main() { cin.tie(0);ios::sync_with_stdio(false); int N,M,F; read(N),read(M),read(F); PrimalDualMinCostFlow<int,int> pdmcf(N, 123456789); for(int i=0;i<M;++i) { int u,v,c,d; read(u),read(v),read(c),read(d); pdmcf.make_edge(u,v,c,d); } auto [flow,cost] = pdmcf.min_cost_flow(0,N-1,F); if(flow < F) cost = -1; cout << cost << endl; return 0; }
#line 1 "test/graph/PrimalDualMinCostFlow.test.cpp" #define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B" #include <vector> #include <iostream> #include <queue> #include <cassert> using namespace std; #line 1 "lib/00-util/FastIO.cpp" /* * @title FastIO * @docs md/util/FastIO.md */ class FastIO{ private: inline static constexpr int ch_0='0'; inline static constexpr int ch_9='9'; inline static constexpr int ch_n='-'; inline static constexpr int ch_s=' '; inline static constexpr int ch_l='\n'; inline static void endline_skip(char& ch) { while(ch==ch_l) ch=getchar(); } template<typename T> inline static void read_integer(T &x) { int neg=0; char ch; x=0; ch=getchar(); endline_skip(ch); if(ch==ch_n) neg=1,ch=getchar(); for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0); if(neg) x*=-1; } template<typename T> inline static void read_unsigned_integer(T &x) { char ch; x=0; ch=getchar(); endline_skip(ch); for(;(ch_0 <= ch && ch <= ch_9); ch = getchar()) x = x*10 + (ch-ch_0); } inline static void read_string(string &x) { char ch; x=""; ch=getchar(); endline_skip(ch); for(;(ch != ch_s && ch!=ch_l); ch = getchar()) x.push_back(ch); } inline static char ar[40]; inline static char *ch_ar; template<typename T> inline static void write_integer(T x) { ch_ar=ar; if(x< 0) putchar(ch_n), x=-x; if(x==0) putchar(ch_0); for(;x;x/=10) *ch_ar++=(ch_0+x%10); while(ch_ar--!=ar) putchar(*ch_ar); } public: inline static void read(int &x) {read_integer<int>(x);} inline static void read(long long &x) {read_integer<long long>(x);} inline static void read(unsigned int &x) {read_unsigned_integer<unsigned int>(x);} inline static void read(unsigned long long &x) {read_unsigned_integer<unsigned long long>(x);} inline static void read(string &x) {read_string(x);} inline static void read(__int128_t &x) {read_integer<__int128_t>(x);} inline static void write(__int128_t x) {write_integer<__int128_t>(x);} inline static void write(char x) {putchar(x);} }; #define read(arg) FastIO::read(arg) #define write(arg) FastIO::write(arg) #line 1 "lib/40-graph/PrimalDualMinCostFlow.cpp" /* * @title PrimalDualMinCostFlow - 最短路反復の最小費用流 * @docs md/graph/PrimalDualMinCostFlow.md */ template<class TypeFlow, class TypeCost> class PrimalDualMinCostFlow { using Pair = pair<TypeCost,size_t>; struct Edge { size_t to; size_t rev; TypeFlow cap; TypeCost cost; }; vector<vector<Edge>> edge; const size_t N; const TypeCost inf_cost; vector<TypeCost> min_cost; vector<TypeCost> potential; vector<size_t> prev_vertex,prev_edge; TypeFlow max_flow=0; public: PrimalDualMinCostFlow(const size_t N, const TypeCost inf_cost) : N(N), edge(N), min_cost(N), potential(N,0), prev_vertex(N,N), prev_edge(N,N), inf_cost(inf_cost) {} // costは単位流量あたりのコスト inline void make_edge(const size_t from, const size_t to, const TypeFlow cap, const TypeCost cost) { assert(cost < inf_cost); edge[from].push_back({ to, edge[to].size(), cap, cost }); edge[to].push_back({ from, edge[from].size() - 1, 0, -cost }); max_flow += cap; } pair<TypeFlow,TypeCost> min_cost_flow(const size_t s, const size_t g) { return min_cost_flow(s,g,max_flow); } pair<TypeFlow,TypeCost> min_cost_flow(const size_t s, const size_t g, const TypeFlow limit_flow) { assert(0 <= s && s < N && 0 <= g && g < N && s != g); priority_queue<Pair,vector<Pair>,greater<Pair>> pq; TypeCost sum_cost=0; TypeFlow sum_flow=0; while(sum_flow < limit_flow) { min_cost.assign(N, inf_cost); { pq.emplace(0,s); min_cost[s]=0; } while(pq.size()) { auto [from_cost, from] = pq.top(); pq.pop(); if(min_cost[from] < from_cost) continue; for(int i=0; i < edge[from].size(); ++i) { auto [to, rev, cap, cost] = edge[from][i]; TypeCost to_cost = from_cost + cost + (potential[from] - potential[to]); if(cap > 0 && min_cost[to] > to_cost) { pq.emplace(to_cost, to); prev_vertex[to] = from; prev_edge[to] = i; min_cost[to] = to_cost; } } } if(min_cost[g]==inf_cost) break; for(size_t i=0; i<N; ++i) potential[i] += min_cost[i]; TypeFlow diff_flow = limit_flow - sum_flow; for(size_t i=g; i!=s; i = prev_vertex[i]) { diff_flow = min(diff_flow, edge[prev_vertex[i]][prev_edge[i]].cap); } sum_flow += diff_flow; sum_cost += diff_flow * potential[g]; for(size_t i=g; i!=s; i = prev_vertex[i]) { auto& [_to,rev,cap,_cost] = edge[prev_vertex[i]][prev_edge[i]]; auto& [_r_to,_r_rev,r_cap,_r_cost] = edge[i][rev]; cap -= diff_flow; r_cap += diff_flow; } } return {sum_flow, sum_cost}; } }; #line 10 "test/graph/PrimalDualMinCostFlow.test.cpp" int main() { cin.tie(0);ios::sync_with_stdio(false); int N,M,F; read(N),read(M),read(F); PrimalDualMinCostFlow<int,int> pdmcf(N, 123456789); for(int i=0;i<M;++i) { int u,v,c,d; read(u),read(v),read(c),read(d); pdmcf.make_edge(u,v,c,d); } auto [flow,cost] = pdmcf.min_cost_flow(0,N-1,F); if(flow < F) cost = -1; cout << cost << endl; return 0; }