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#define PROBLEM "https://judge.yosupo.jp/problem/general_weighted_matching" #include "Template/template.hpp" #include "Utility/fastio.hpp" #include "Graph/generalweightedmatching.hpp" int main(){ int n,m; read(n,m); GeneralWeightedMatching solver(n); vector g(n,vector<ll>(n)); rep(_,0,m){ int u,v,w; read(u,v,w); g[u][v]=g[v][u]=w; solver.add_edge(u,v,w); } auto res=solver.run(); ll r1=0,r2=0; rep(i,0,n)if(res[i]>i){ r1++; r2+=g[res[i]][i]; } print(r1,r2); rep(i,0,n)if(res[i]>i)print(res[i],i); return 0; }
#line 1 "Verify/LC_general_weighted_matching.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/general_weighted_matching" #line 1 "Template/template.hpp" #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b-1); i >= (int)(a); 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 uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template <typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template <typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template <typename T, typename U> T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T> int popcnt(T x) { return __builtin_popcountll(x); } template <typename T> int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template <typename T> int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template <typename T> void _show(int i, T name) { cerr << '\n'; } template <typename T1, typename T2, typename... T3> void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template <typename T, template <class> class C> ostream &operator<<(ostream &os, const C<T> &v) { os << "["; for (auto d : v) os << d << ", "; os << "]"; return os; } #line 2 "Utility/fastio.hpp" #include <unistd.h> 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() { memmove(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(uint &x) { rd_integer(x); } void rd(ull &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); } 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(vector<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(uint x) { wt_integer(x); } void wt(ull 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); } 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)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 5 "Verify/LC_general_weighted_matching.test.cpp" #line 2 "Graph/generalweightedmatching.hpp" // reference: http://www.cs.kent.edu/~dragan/GraphAn/p23-galil.pdf class GeneralWeightedMatching{ struct E{int u,v; ll w;}; int n,m,in; vector<vector<E>> G; vector<int> mate,slack,root,par,isS,used; vector<vector<int>> flower,belong; vector<ll> dual; queue<int> que; ll dist(const E& e){return dual[e.u]+dual[e.v]-e.w;} void update(int u,int v){ if(!slack[v] or dist(G[u][v])<dist(G[slack[v]][v]))slack[v]=u; } void recalc(int v){ slack[v]=0; rep(i,1,n+1)if(G[i][v].w and root[i]!=v and isS[root[i]]==1)update(i,v); } void push(int v){ if(v<=n)que.push(v); else for(auto& nxt:flower[v])push(nxt); } void set(int v,int rt){ root[v]=rt; if(v>n)for(auto& nxt:flower[v])set(nxt,rt); } int findeven(int b,int v){ int pos=find(ALL(flower[b]),v)-flower[b].begin(); if(pos&1){ reverse(flower[b].begin()+1,flower[b].end()); pos=flower[b].size()-pos; } return pos; } void match(int u,int v){ mate[u]=G[u][v].v; if(u>n){ int x=belong[u][G[u][v].u]; int pos=findeven(u,x); rep(i,0,pos)match(flower[u][i],flower[u][i^1]); match(x,v); rotate(flower[u].begin(),flower[u].begin()+pos,flower[u].end()); } } void link(int u,int v){ for(;;){ int nv=root[mate[u]]; match(u,v); if(!nv)break; v=nv,u=root[par[nv]]; match(v,u); } } void make(int u,int v,int lca){ int id=n+1; while(id<=m and root[id])id++; if(id>m)m++; flower[id].clear(); rep(i,1,m+1)G[id][i].w=G[i][id].w=0; rep(i,1,n+1)belong[id][i]=0; isS[id]=1,dual[id]=0,mate[id]=mate[lca]; while(u!=lca){ flower[id].push_back(u); u=root[mate[u]]; push(u); flower[id].push_back(u); u=root[par[u]]; } flower[id].push_back(lca); reverse(ALL(flower[id])); while(v!=lca){ flower[id].push_back(v); v=root[mate[v]]; push(v); flower[id].push_back(v); v=root[par[v]]; } set(id,id); for(auto& c:flower[id]){ rep(i,1,m+1)if(!G[id][i].w or dist(G[c][i])<dist(G[id][i])){ G[id][i]=G[c][i],G[i][id]=G[i][c]; } rep(i,1,n+1)if(belong[c][i])belong[id][i]=c; } recalc(id); } void expand(int b){ for(auto& c:flower[b])set(c,c); int x=belong[b][G[b][par[b]].u]; isS[x]=2,par[x]=par[b]; int pos=findeven(b,x); for(int i=0;i<pos;i+=2){ int T=flower[b][i],S=flower[b][i+1]; isS[S]=1,isS[T]=2; par[T]=G[S][T].u; slack[S]=slack[T]=0; push(S); } rep(i,pos+1,flower[b].size()){ isS[flower[b][i]]=0; recalc(flower[b][i]); } flower[b].clear(); root[b]=0; } bool path(const E& e){ int u=root[e.u],v=root[e.v]; if(!isS[v]){ par[v]=e.u; isS[v]=2; int nu=root[mate[v]]; slack[v]=slack[nu]=0; isS[nu]=1; push(nu); } else if(isS[v]==1){ int lca=0,bu=u,bv=v; in++; while(bu){ used[bu]=in; bu=root[mate[bu]]; if(bu)bu=root[par[bu]]; } while(bv){ if(used[bv]==in){ lca=bv; break; } bv=root[mate[bv]]; if(bv)bv=root[par[bv]]; } if(lca)make(u,v,lca); else{ link(u,v),link(v,u); return true; } } return false; } bool augment(){ isS=slack=par=vector<int>(n*2); que=queue<int>(); rep(i,1,m+1)if(root[i]==i and !mate[i]){ isS[i]=1; push(i); } if(que.empty())return false; for(;;){ while(!que.empty()){ int v=que.front(); que.pop(); rep(i,1,n+1)if(G[v][i].w and root[i]!=root[v]){ if(!dist(G[v][i])){ if(path(G[v][i]))return true; } else if(isS[root[i]]!=2)update(v,root[i]); } } ll delta=INF; rep(i,n+1,m+1)if(root[i]==i and isS[i]==2)chmin(delta,dual[i]/2); rep(i,1,m+1)if(root[i]==i and slack[i] and isS[i]!=2){ if(!isS[i])chmin(delta,dist(G[slack[i]][i])); else chmin(delta,dist(G[slack[i]][i])/2); } rep(i,1,n+1){ if(isS[root[i]]==1){ dual[i]-=delta; if(dual[i]<=0)return false; } else if(isS[root[i]]==2)dual[i]+=delta; } rep(i,n+1,m+1)if(root[i]==i and isS[i]){ if(isS[i]==1)dual[i]+=delta*2; else dual[i]-=delta*2; } rep(i,1,m+1)if(root[i]==i and slack[i] and root[slack[i]]!=i){ if(dist(G[slack[i]][i])==0 and path(G[slack[i]][i]))return true; } rep(i,n+1,m+1)if(root[i]==i and isS[i]==2 and dual[i]==0)expand(i); } } public: GeneralWeightedMatching(int _n):n(_n),m(n),in(0),G(n*2,vector<E>(n*2)), mate(n*2),root(n*2),used(n*2),flower(n*2),belong(n*2,vector<int>(n*2)),dual(n*2){ rep(i,0,n+1){ root[i]=i; belong[i][i]=i; if(i)dual[i]=INF; rep(j,0,n+1)G[i][j]=E{i,j,0}; } } void add_edge(int u,int v,ll w){ u++,v++; chmax(G[u][v].w,w*2); chmax(G[v][u].w,w*2); } vector<int> run(){ while(augment()); vector<int> res(n,-1); rep(i,1,n+1)if(mate[i])res[i-1]=mate[i]-1; return res; } }; /** * @brief General Weighted Matching */ #line 7 "Verify/LC_general_weighted_matching.test.cpp" int main(){ int n,m; read(n,m); GeneralWeightedMatching solver(n); vector g(n,vector<ll>(n)); rep(_,0,m){ int u,v,w; read(u,v,w); g[u][v]=g[v][u]=w; solver.add_edge(u,v,w); } auto res=solver.run(); ll r1=0,r2=0; rep(i,0,n)if(res[i]>i){ r1++; r2+=g[res[i]][i]; } print(r1,r2); rep(i,0,n)if(res[i]>i)print(res[i],i); return 0; }