#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() #define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin()) #define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin()) using ll=long long int; using ull=unsigned long long; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} templateT ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);} templateT floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);} templateint popcnt(T x){return __builtin_popcountll(x);} templateint topbit(T x){return (x==0?-1:63-__builtin_clzll(x));} templateint lowbit(T x){return (x==0?-1:__builtin_ctzll(x));} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__int128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__uint128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(double x){ ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); _write(s); } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ _write(head); write(tail...); if(space)_write(' '); } inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Graph/mincostflow.hpp" templateclass MinCostFlow{ struct ptr{int v_id,e_id;}; struct edge{ int from,to; Flow flow,cap; Cost weight; int rev; edge(int _f,int _t,Flow _c,Cost _w,int _r) :from(_f),to(_t),flow(0),cap(_c),weight(_w),rev(_r){} Flow residual_cap()const{return cap-flow;} }; int n; vector> g; vector b,pot; vector ptrs; Cost farthest; vector dist; vector par; vector exc,def; void push(edge& e,Flow amount){ e.flow+=amount; g[e.to][e.rev].flow-=amount; } Cost residual_cost(int from,int to,edge& e){ return e.weight+pot[from]-pot[to]; } bool dual(const Flow& delta){ dist.assign(n,numeric_limits::max()); par.assign(n,nullptr); exc.erase(remove_if(ALL(exc),[&](int v){return b[v]-delta;}),def.end()); priority_queue,vector>,greater<>> pq; for(auto& v:exc)pq.push({dist[v]=0,v}); farthest=0; int def_cnt=0; while(!pq.empty()){ auto [d,u]=pq.top(); pq.pop(); if(dist[u]=(int)def.size())break; for(auto& e:g[u]){ if(e.residual_cap()=dist[v])continue; pq.push({dist[v]=nd,v}); par[v]=&e; } } rep(v,0,n)pot[v]+=min(dist[v],farthest); return def_cnt>0; } void primal(const Flow& delta){ for(auto& t:def){ if(dist[t]>farthest)continue; Flow f=-b[t]; int v; for(v=t;par[v]!=nullptr;v=par[v]->from){ chmin(f,par[v]->residual_cap()); } chmin(f,b[v]); f-=f%delta; if(f<=0)continue; for(v=t;par[v]!=nullptr;){ auto& e=*par[v]; push(e,f); int u=par[v]->from; if(e.residual_cap()<=0)par[v]=nullptr; v=u; } b[t]+=f; b[v]-=f; } } public: MinCostFlow(int _n):n(_n),g(_n),b(_n),pot(_n){} void add_edge(int from,int to,Flow lb,Flow ub,Cost cost){ int f_id=g[from].size(),t_id=(from==to?f_id+1:g[to].size()); g[from].push_back(edge(from,to,ub,Maximize?-cost:cost,t_id)); g[to].push_back(edge(to,from,-lb,Maximize?cost:-cost,f_id)); ptrs.push_back(ptr{from,f_id}); } void add_supply(int v,Flow amount){b[v]+=amount;} void add_demand(int v,Flow amount){b[v]-=amount;} Flow get_pot(int v){return pot[v];} Flow get_flow(int v){return g[ptrs[v].v_id][ptrs[v].e_id].flow;} templatepair run(const Flow& sf=2){ Flow max_flow=1; for(auto& t:b)chmax(max_flow,abs(t)); for(auto& es:g)for(auto& e:es)chmax(max_flow,abs(e.residual_cap())); Flow delta=1; while(delta0?exc:def).push_back(v); } while(dual(delta))primal(delta); } T res=0; for(auto& es:g)for(auto& e:es)res+=T(e.flow)*T(e.weight); res>>=1; if(exc.empty() and def.empty())return {1,Maximize?-res:res}; else return {0,Maximize?-res:res}; } }; /** * @brief Minimum Cost b-flow */ #line 5 "sol.cpp" FastIO io; int main() { int n, m, k, L; io.read(n, m, k, L); vector x(L), y(L), z(L); rep(i, 0, L) { io.read(x[i], y[i], z[i]); } MinCostFlow buf(n + m + 1); int S = n + m; rep(i, 0, n) { buf.add_edge(S, i, 0, 1, 0); } rep(i, 0, m) { buf.add_edge(n + i, S, 0, 1, 0); } rep(i, 0, L) { buf.add_edge(x[i] - 1, y[i] - 1 + n, 0, 1, 1 << z[i]); } auto [_, ret] = buf.run(); io.write(ret); return 0; }