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:heavy_check_mark: Verify/LC_general_weighted_matching.test.cpp

Depends on

Code

#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;
}
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