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wusa!~(•㉨•)

「轉載】張 正錦 菌給的模板 I 圖論

发表于 Valine：

第一輯 圖論

  • LCA
    • 倍增求LCA
    • 樹鏈剖分求LCA
  • 最短路
    • Dijkstra
    • SPFA (判負環)
    • SPFA (不判負環)
    • Floyd (多源最短路)
    • 次短路
  • 分層圖
  • 樹鏈剖分
  • 樹上差分
  • 差分約束
  • 二分圖匹配
    • Hungary算法 (社會主義分老婆)
  • 最小生成樹
    • Kruskal
  • 强連通分量
    • Tarjan縮點 + 染色

LCA

by Binary Lifting

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#include<iostream>
#include<algorithm>
#include<cstdio>
#include<string.h>
#include<queue>
#define nqp main

using namespace std;

const int maxn = 500010;
int head[maxn],f[maxn][21],deep[maxn];
int n,m,root,cur;

struct hzw
{
    int to,next;
}tree[maxn<<1];

void add(int u, int v)
{
    tree[++cur].next = head[u];
    tree[cur].to = v;
    head[u] = cur;
}

void dfs(int u, int fa)
{
    f[u][0] = fa;
    deep[u] = deep[fa] + 1;
    for(int i=head[u]; i; i=tree[i].next)
    {
        int v = tree[i].to;
        if(v == fa) continue;
        dfs(v,u);
    }
}

int LCA(int a, int b)
{
    if(deep[a] > deep[b]) swap(a,b);
    for(int i=20; i>=0; i--)
    {
        if(deep[a] <= deep[b] - (1<<i))
        {
            b = f[b][i];
        }
    }
    if(a == b) return a;
    for(int i=20; i>=0; i--)
    {
        if(f[a][i] == f[b][i]) continue;
        a = f[a][i];
        b = f[b][i];
    }
    return f[a][0];
}

int nqp()
{
    ios :: sync_with_stdio(false);
    cin >> n >> m >> root;
    for(int i=1; i<=n; i++)
    {
        int u,v;
        cin >> u >> v;
        add(u,v);
        add(v,u);
    }
    dfs(root,0);
    for(int i=1; i<=20; i++)
    {
        for(int j=1; j<=n; j++)
        {
            f[j][i] = f[f[j][i-1]][i-1];
        }
    }
    int ans = 0;
    for(int i=1; i<=m; i++)
    {
        int a,b;
        cin >> a >> b;
        int ans = LCA(a,b);
        cout << ans << endl;
    }
    return 0;
}

by HLD

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#include <iostream>
#include <algorithm>
#include <string.h>
#include <queue>
#include <cstdio>

using namespace std;

int read()
{
    char c = ' ';
    while(c<'0' || c>'9') c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v * 10 + c - '0';
        c = getchar();
    }
    return v;
}

const int maxn = 100010;
int head[maxn],cur,n,m,s,son[maxn],id[maxn],size[maxn],f[maxn],top[maxn],deep[maxn];

struct hzw
{
    int next,to;
}edge[maxn<<1];

void add(int u, int v)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    head[u] = cur;
}

void dfs1(int u, int fa, int dep)
{
    size[u] = 1;
    deep[u] = dep;
    f[u] = fa;
    for(int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(v == fa) continue;
        dfs1(v,u,dep+1);
        size[u] += size[v];
        if(son[u] == -1 || size[v] > size[son[u]]) son[u] = v;
    }
}

void dfs2(int u, int t)
{
    top[u] = t;
    if(son[u]==-1) return;
    dfs2(son[u],t);
    for(int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(v == f[u] || v == son[u]) continue;
        dfs2(v,v); 
    }
}
int LCA(int x, int y)
{
    while(top[x] != top[y])
    {
        if(deep[top[x]] < deep[top[y]]) swap(x,y);
        x = f[top[x]];
    }    
    if(deep[x] > deep[y]) swap(x,y);
    return x;
}

int main()
{
    memset(son,-1,sizeof(son));
    memset(head,-1,sizeof(head));
    n = read(), m = read(), s = read();
    for(int i=1; i<=n-1; i++)
    {
        int a,b;
        a = read(), b = read();
        add(a,b);
        add(b,a);
    }
    dfs1(s,0,0);
    dfs2(s,s);
    for(int i=1; i<=m; i++)
    {
        int a,b;
        a = read(), b = read();
        cout << LCA(a,b) << endl;
    }
    return 0;
}

Shortest Path

Dijkstra

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#include <iostream>
#include <algorithm>
#include <string.h>
#include <cstdio>
#include <queue>
using namespace std;
const int maxn = 100010;
int head[maxn],cur,n,m,vis[maxn],dis[maxn]; //dis[i]到i的最短路

struct hzw
{
    int next,to,w;
}edge[maxn];

void add(int u, int v, int w) //边表建图
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}

struct heapnode //小根堆
{
    int d,u;
    bool operator < (const heapnode & h) const
    {
        return d > h.d;
    }
};

void dijkstra(int s)
{
    priority_queue <heapnode> q;
    memset(dis,0x3f,sizeof(dis));
    dis[s] = 0;
    q.push((heapnode){dis[s],s});
    while(!q.empty())
    {
        heapnode p = q.top();
        q.pop();
        int u = p.u;
        if(vis[u]) continue; //如果已经访问过则跳过
        vis[u] = 1;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            if(dis[edge[i].to] > dis[u] + edge[i].w)
                dis[edge[i].to] = dis[u] + edge[i].w;
            q.push((heapnode){dis[edge[i].to],edge[i].to}); //扩展下一个点
        }
    }
}

int main()
{
    memset(head,-1,sizeof(head));
    cin >> n >> m;
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        cin >> a >> b >> c;
        add(a,b,c);
    }
    dijkstra(1);
    cout << dis[n];
    return 0;
}

SPFA (with judging negative ring)

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#include<iostream>
#include<algorithm>
#include<cstdio>
#include<string.h>
#include<queue>
#define nqp main 

using namespace std;

const int maxn = 500050;
int head[maxn],cur,n,m,s,dis[maxn],vis[maxn];

struct hzw
{
    int to,next,w;
}edge[maxn];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}
int flag;int num[maxn]; 
void SPFA(int s)
{
    for(int i=1; i<=n; i++) dis[i] = 2147483647;
    queue <int> q;
    dis[s] = 0;
    q.push(s);
    while(!q.empty())
    {
        int p;
        p = q.front();
        q.pop();
        vis[p] = 0;
        for(int i=head[p]; i!=-1; i=edge[i].next)
        {
            int v = edge[i].to;
            if(dis[v] > dis[p]+edge[i].w)
            {
                if(num[v]>n)
                {
                    flag = 2333;
                    return ;
                }
                dis[v] = dis[p]+edge[i].w;
                if(!vis[v])
                {
                    q.push(v);
                    vis[v] = 1;
                    num[v] = num[s]+1;
                }
            }
        }
    }
}
int nqp()
{
    memset(head,-1,sizeof(head));
    cin >> n >> m >> s;
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        cin >> a >> b >> c;
        add(a,b,c);
    }
    SPFA(s);
   

	for(int i=1; i<=n; i++)
    {
        cout << dis[i] << " ";
    }
    return 0;
}

SPFA (without judging negative ring)

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#include <iostream>
#include <algorithm>
#include <string.h>
#include <cstdio>
#include <queue>

using namespace std;

const int maxn = 500010;
int head[maxn],cur,n,m,dis[maxn],vis[maxn];

struct hzw
{
    int next,to,w;
}edge[maxn];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}

void SPFA(int u)
{
    queue <int> q;
       memset(dis,0x3f,sizeof(dis));
       dis[u] = 0;
       q.push(u);
       vis[u] = 1;
       while(!q.empty())
       {
           int p = q.front();
           q.pop();
           vis[p] = 0;
           for(int i=head[p]; i!=-1; i=edge[i].next)
           {
               if(dis[edge[i].to] > dis[p] + edge[i].w)
               {
                   dis[edge[i].to] = dis[p] + edge[i].w;
                   if(!vis[edge[i].to])
                   {
                       q.push(edge[i].to);
                       vis[edge[i].to] = 1;
                   }
               }
           }
       }
}

int s;
int main()
{
    memset(head,-1,sizeof(head));
    cin >> n >> m >> s;
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        cin >> a >> b >> c;
        add(a,b,c);
    }
    SPFA(s);
    for(int i=1; i<=n; i++)
    {
        cout << dis[i] << ' ';
    }
    return 0;
}

Floyd

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#include <iostream>
#include <algorithm>
#include <cstdio>
#include <string.h>
#include <queue>

using namespace std;

const int INF = 0x3f3f3f3f;
const int maxn = 1005;
int Map[maxn][maxn],n,m;

int main()
{
    memset(Map,INF,sizeof(Map));
    cin >> n >> m;
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        cin >> a >> b >> c;
        Map[a][b] = c;
    }
    for(int k=1; k<=n; k++)
        for(int i=1; i<=n; i++)
            for(int j=1; j<=n; j++)
                if(k!=i && i!=j && k!=j)
                    Map[i][j] = min(Map[i][j],Map[i][k]+Map[k][j]);
    cout << Map[1][n];
    return 0;
}

Second Shortest Path

C++Luogu P2865
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#include <iostream>
#include <string.h>
#include <cstdio>
#include <algorithm>
#include <queue>

using namespace std;

int read()
{
    char c = ' ';
    while(c<'0' || c>'9') c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v * 10 + c - '0';
        c = getchar();
    }
    return v;
}

const int maxn = 100010;
int head[maxn],cur,vis[maxn],dis1[maxn],dis2[maxn],n,m;

struct hzw
{
    int next,to,w;
}edge[maxn<<1];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}

struct heapnode
{
    int d,u;
    bool operator < (const heapnode & h) const
    {
        return d > h.d;
    }
};


void dijkstra(int s, int dis[])
{
    priority_queue <heapnode> q;
    dis[s] = 0;
    q.push((heapnode){dis[s],s});
    int u;
    while(!q.empty())
    {
        heapnode p = q.top();
        q.pop();
        u = p.u;
        if(vis[u]) continue;
        vis[u] = 1;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            if( dis[edge[i].to] > dis[u] + edge[i].w)
                dis[edge[i].to] = dis[u] + edge[i].w;
            q.push((heapnode){dis[edge[i].to],edge[i].to});
        }
    }
}

int main()
{
    memset(dis1,0x3f,sizeof(dis1));
    memset(dis2,0x3f,sizeof(dis2));
    memset(head,-1,sizeof(head));
    n = read(), m = read();
    for(int i=1; i<=m; i++) 
    {
        int a,b,c;
        a = read(), b = read(), c = read();
        add(a,b,c);
        add(b,a,c);
    }
    dijkstra(1,dis1);
    memset(vis,0,sizeof(vis));
    dijkstra(n,dis2);
    int ans = 0x3f3f3f3f;
    for(int u=1; u<=n; u++)
    {
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            int cmp = dis1[u] + dis2[edge[i].to] + edge[i].w;
            if(cmp > dis1[n] && cmp < ans) ans = cmp;
        }
    }
    cout << ans;
    return 0;
}

Layered Graph

C++Luogu P2939
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#include <iostream>
#include <string.h>
#include <algorithm>
#include <cstdio>
#include <queue>

using namespace std;
int read()
{
    char c = ' ';
    while(c<'0' || c>'9') c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v * 10 + c - '0';
        c = getchar();
    }
    return v;
}

const int maxn = 100100;
int head[maxn],cur,n,m,k,dis[maxn][21],vis[maxn][21];

struct hzw
{
    int next,to,w;
}edge[maxn<<1];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}

struct heapnode
{
    int d,u,h;
    bool operator < (const heapnode & h) const
    {
        return d > h.d;
    }
};

void dijkstra(int s)
{
    priority_queue <heapnode> q;
    memset(dis,0x3f,sizeof(dis));
    dis[1][0] = 0;
    q.push((heapnode){0,1,0});
    while(!q.empty())
    {
        heapnode p = q.top();
        q.pop();
        int u = p.u;
        int h = p.h;
        if(vis[u][h]) continue;
        vis[u][h] = 1;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            if(dis[edge[i].to][h] > dis[u][h] + edge[i].w)
            {
                dis[edge[i].to][h] = dis[u][h] + edge[i].w;
                q.push((heapnode){dis[edge[i].to][h],edge[i].to,h});
            }    
            if(h < k)
            {
                if(dis[edge[i].to][h+1] > dis[u][h])
                {
                    dis[edge[i].to][h+1] = dis[u][h];
                    q.push((heapnode){dis[edge[i].to][h+1],edge[i].to,h+1});
                }
            }
        }
    }
}

int main()
{
    memset(head,-1,sizeof(head));
    n = read(), m = read(), k = read();
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        a = read(), b = read(), c = read();
        add(a,b,c);
        add(b,a,c);
    }
    dijkstra(1);
    cout << dis[n][k];
    return 0;
}

HLD (Heavy-Light Decomposition)

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#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string.h>
#include<queue>
#define nqp main

using namespace std;

const int maxn = 300030;
int head[maxn],cur,n,m,r,p,top[maxn],son[maxn],tid[maxn],rnk[maxn],size[maxn],val[maxn];
int deep[maxn],f[maxn];

int read()
{
    char c = ' ';
    int f = 1;
    while(c<'0' || c>'9')
    {
        if(c == '-') f = -1;
        c = getchar();
    }
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v*10 + c -'0';
        c = getchar();
    }
    return v * f;
}

struct hzw
{
    int next,to;
}edge[maxn];

void add(int u, int v)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    head[u] = cur;
}

struct ljm
{
    int sum,tag,lc,rc;
}a[maxn];

void update(int rt)
{
    a[rt].sum = a[a[rt].lc].sum + a[a[rt].rc].sum;
}

int tot = 1;
void build(int l, int r, int rt)
{
    if(l == r)
    {
        a[rt].sum = rnk[l];
        return;
    }
    int mid = (l+r) >> 1;
    a[rt].lc = ++tot;
    build(l,mid,a[rt].lc);
    a[rt].rc = ++tot;
    build(mid+1,r,a[rt].rc);
    update(rt);
}

void pushdown(int l, int r, int rt)
{
//    printf("%d %d\n",l,r);
    int mid = (l+r) / 2;
    a[a[rt].lc].sum += (mid-l+1) * a[rt].tag;
    a[a[rt].lc].tag += a[rt].tag;
    a[a[rt].rc].sum += (r-mid) * a[rt].tag;
    a[a[rt].rc].tag += a[rt].tag;
    a[rt].tag = 0;
}

int query(int l, int r, int rt, int nowl, int nowr)
{
    int ans = 0;
    if(l == nowl && r == nowr)
    {
        return a[rt].sum;
    }
    int mid = (l+r) >> 1;
    pushdown(l,r,rt);
    if(nowr <= mid) ans += query(l,mid,a[rt].lc,nowl,nowr);
    else if(nowl > mid) ans += query(mid+1,r,a[rt].rc,nowl,nowr);
    else
    {
        ans += query(l,mid,a[rt].lc,nowl,mid);
        ans += query(mid+1,r,a[rt].rc,mid+1,nowr);
    }
    return ans;
}


void modify(int l, int r, int rt, int nowl, int nowr, int w)
{
    if(l == nowl && r == nowr)
    {
        a[rt].sum += (r-l+1) * w;
        a[rt].tag += w;
        return;
    }
    int mid = (l+r) >> 1;
    pushdown(l,r,rt);
    if(nowr <= mid) modify(l,mid,a[rt].lc,nowl,nowr,w);
    else if(nowl > mid) modify(mid+1,r,a[rt].rc,nowl,nowr,w);
    else
    {
        modify(l,mid,a[rt].lc,nowl,mid,w);
        modify(mid+1,r,a[rt].rc,mid+1,nowr,w);
    }
    update(rt);
}



//-----------------------------------------------------build tree

void dfs1(int u, int fa, int dep)
{
    size[u] = 1;
    deep[u] = dep;
    f[u] = fa;
    for(int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(v == fa) continue;
        dfs1(v,u,dep+1);
        size[u] += size[v];
        if(son[u] == -1 || size[v] > size[son[u]]) son[u] = v;
    }
}

int cnt = 1;
void dfs2(int u, int t)
{
    top[u] = t;
    tid[u] = cnt;
    rnk[cnt] = val[u];
    cnt++;
    if(son[u] == -1) return;
    dfs2(son[u],t);
    for(int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(!tid[v]) dfs2(v,v);
    }
}

int query_path(int x, int y)
{
    int ans = 0;
    while(top[x] != top[y])
    {
        if(deep[top[x]] < deep[top[y]]) swap(x,y);
        ans += query(1,n,1,tid[top[x]],tid[x]);
        x = f[top[x]];
    } 
    if(deep[x] > deep[y]) swap(x,y);
    ans += query(1,n,1,tid[x],tid[y]);        
    return ans;
}

void modify_path(int x, int y, int w)
{
    while(top[x] != top[y])
    {
        if(deep[top[x]] < deep[top[y]]) swap(x,y);
        modify(1,n,1,tid[top[x]],tid[x],w);
        x = f[top[x]];
    }
    if(deep[x] > deep[y]) swap(x,y);
    modify(1,n,1,tid[x],tid[y],w);
}

int nqp()
{
    memset(head,-1,sizeof(head));
    memset(son,-1,sizeof(size));
    cin >> n >> m >> r >> p;
    for(int i=1; i<=n; i++)
    {
        cin >> val[i];
    }
    for(int i=1; i<=n-1; i++)
    {
        int a,b;
        cin >> a >> b;
        add(a,b);
        add(b,a);
    }
    dfs1(r,r,1);
    dfs2(r,r);
    build(1,n,1);
    for(int i=1; i<=m; i++)
    {
        int x;
        x = read();
        if(x == 1) 
        {
            int y,z,k;
            y = read(), z = read(), k = read();
            modify_path(y,z,k);
        }
        else if(x == 2)
        {
            int y,z;
            y = read(), z = read();
            int ans = query_path(y,z);
            cout << ans << endl;
        }
        else if(x == 3)
        {
            int y,z;
            y = read(), z = read();
            modify(1,n,1,tid[y],tid[y]+size[y]-1,z);
        }
        else
        {
            int y;
            y = read();
            cout << query(1,n,1,tid[y],tid[y]+size[y]-1) << endl;
        }
    }
    return 0;
}

Tree Diff

C++Luogu P3128
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#include <iostream>
#include <algorithm>
#include <string.h>
#include <cstdio>
#include <queue>

using namespace std;

const int maxn = 500050;
int head[maxn],cur,f[maxn][21],deep[maxn],faa[maxn];
int d[maxn];
int maxx = -0x3f3f3f3f;

struct hzw
{
    int next,to,w;
}edge[maxn<<1];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    head[u] = cur;
}

void dfs(int u, int fa)
{
    faa[u] = fa;
    f[u][0] = fa;
    deep[u] = deep[fa] + 1;
    for(int i=head[u]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(fa == v) continue;
        dfs(v,u);
    }
}

int LCA(int a, int b)
{
    if(deep[a] > deep[b]) swap(a,b);
    for(int i=20; i>=0; i--)
    {
        if(deep[a] <= deep[b] - (1<<i))
        {
            b = f[b][i];
        }
    }
    if(a == b) return a;
    for(int i=20; i>=0; i--)
    {
        if(f[a][i] == f[b][i]) continue;
        a = f[a][i];
        b = f[b][i];
    }
    return f[a][0];
}

void dfs1(int a, int fa)
{
    for(int i=head[a]; i!=-1; i=edge[i].next)
    {
        int v = edge[i].to;
        if(v == fa) continue;
        dfs1(v,a);
        d[a] += d[v];
    }
    maxx = max(d[a],maxx);
}

int n,m;

int read()
{
    char c = ' ';
    while(c<'0' || c>'9') c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v * 10 + c - '0';
        c = getchar();
    }
    return v;
}

int main()
{
    memset(head,-1,sizeof(head));
    n = read(), m = read();
    for(int i=1; i<=n-1; i++)
    {
        int a,b;
        a = read(), b = read();
        add(a,b,0);
        add(b,a,0);
    }
    dfs(1,0);
    for(int i=1; i<=20; i++)
    {
        for(int j=1; j<=n; j++)
        {
            f[j][i] = f[f[j][i-1]][i-1];
        }
    }
    for(int i=1; i<=m; i++)
    {
        int a,b;
        a = read(), b = read();
        d[a]++;d[b]++;d[LCA(a,b)]--;d[f[LCA(a,b)][0]]--;
    }
    dfs1(1,0);
    cout << maxx;
    return 0;
}

Diff Constraints

我们可以用松弛来理解一下差分约束.

对于松弛来说 dis[v] > dis[u] + edge[i].w;
我们可以认为 v > u + c. 移项可得 v – u > w 所以我们就可以建一条从u->v的边,边权为c

例如:

a + b >= c 即 add(b,a,c);
a – b <= c 即 add(b,a,-c);
a – b == 0 即 add(a,b,0) add(b,a,0);

用差分约束建图即可

  • 注: 一定要用SPFA判负环!!!!!!

Bipartite Graph Match

Hungary Algorithm

社会主义分老婆

C++Luogu P3386
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#include <iostream>
#include <algorithm>
#include <string.h>
#include <cstdio>
#include <queue>

using namespace std;

int read()
{
    char c = ' ';
    while(c<'0' || c>'9') c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v * 10 + c -'0';
        c = getchar();
    }
    return v;
}

const int maxn = 1005;
int flag[maxn][maxn],vis[maxn],n,m,e,cx[maxn],cy[maxn];

int dfs(int x)
{
    for(int y=1; y<=m; y++)
    {
        if(flag[x][y] && !vis[y])
        {
            vis[y] = 1;
            if(!cy[y] || dfs(cy[y]))
            {
                cx[x] = y;
                cy[y] = x;
                return 1;
            }
        }
    }
    return 0;
}

int main()
{
    n = read(), m = read(), e = read();
    for(int i=1; i<=e; i++)
    {
        int x,y;
        x = read(), y = read();
        flag[x][y] = 1;
    }
    int ans = 0;
    for(int i=1; i<=n; i++)
    {
        memset(vis,0,sizeof(vis));
        ans += dfs(i);
    }
    cout << ans;
    return 0;
}

MST (Minimum Spanning Tree)

Kruskal

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#include<iostream>
#include<algorithm>
#include<cstdio>
#include<string.h>
#define nqp main

using namespace std;

int getint()
{
    char c = ' ';
    while(c<'0' || c>'9')
        c = getchar();
    int v = 0;
    while(c>='0' && c<='9')
    {
        v = v*10 + c - '0';
        c = getchar();
    }
    return v;
}

const int maxn = 600000;
int cur,head[maxn],n,m,vis[maxn],ans,f[maxn];

struct hzw
{
    int to,next,w,u;
    bool operator < (const hzw &h) const
    {
        return w < h.w;
    }
}edge[maxn];

void add(int u, int v, int w)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    edge[cur].w = w;
    edge[cur].u = u;
    head[u] = cur;
}

int find(int x)
{
    if(f[x]!=x)
        f[x] = find(f[x]);
    return f[x];
}

void un(int x, int y)
{
    f[find(x)] = find(y);
}

bool query(int x, int y)
{
    return find(x) == find(y);
}

int num;
void kru()
{ 
    sort(edge+1,edge+m+1);
    for(int i=1; i<=m; i++)
    {
        if(!query(edge[i].u,edge[i].to))
        {
            un(edge[i].to,edge[i].u);
            num++;
            ans += edge[i].w;
        }
        if(num == n-1) break;
    }
}

int nqp()
{
    cin >> n >> m;
    for(int i=1; i<=m; i++)
    {
        int a,b,c;
        a = getint(),b = getint(),c = getint();
        add(a,b,c);
    }
    for(int i=1; i<=m; i++)
    {
        f[i] = i;
    } 
    kru();
    cout << ans << endl;
    return 0; 
}

SCC (Strongly Connected Components)

Tarjan

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#include<iostream>
#include<cstdio>
#include<algorithm>
#include<string.h>
#include<stack>

using namespace std;

const int maxn = 100010;
int head[maxn],cur,m,vis[maxn],dfn[maxn],low[maxn],n,belong[maxn];

struct hzw
{
    int to,next;
}edge[maxn];

void add(int u, int v)
{
    edge[++cur].next = head[u];
    edge[cur].to = v;
    head[u] = cur;
}

int tot,col;
stack <int> s; 

void tarjan(int u)
{
//    cout<<"now "<<u<<endl;
    dfn[u] = low[u] = ++tot;
    s.push(u);
    vis[u] = 1;
    for(int i=head[u]; i!=-1; i=edge[i].next)    
    {
        if(!dfn[edge[i].to])
        {
            tarjan(edge[i].to);
            low[u] = min(low[u],low[edge[i].to]);
        }
        else if(vis[edge[i].to])
        {
            low[u] = min(low[u],dfn[edge[i].to]);
        }
    }
    if(low[u] == dfn[u])
    {
        col++;    
        while(s.top() != u)
        {
            int front = s.top();
            belong[front] = col;
            s.pop();
            vis[front] = 0;
        }
        int front = s.top();
        belong[front] = col;
        s.pop();
        vis[front] = 0;
    }
}

struct ljm
{
    int val,color;
    bool operator < (const ljm & j) const
    {
        return val > j.val;
    }
}size[maxn];

int main()
{
    memset(head,-1,sizeof(head));
    cin >> n >> m;
    for(int i=1; i<=m; i++)
    {
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        if(z==1) add(x,y);
        else add(x,y),add(y,x);
    }
    for(int i=1; i<=n; i++)
        if(!dfn[i]) tarjan(i);
    for(int i=1; i<=n; i++)
    {
        size[belong[i]].val++;//记录环的长度
        size[belong[i]].color = belong[i];//记录环的颜色 
    }
    sort(size+1,size+1+n);
    cout << size[1].val << "\n";
    for(int i=1; i<=n; i++)
    {
        if(belong[i] == size[1].color) cout << i << " ";
    }
    return 0;
}