模板图论

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一、生成树

 洛谷模板最小生成树【跑的还算快的

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define N 5020
#define M 200008
using namespace std;

int n,m,ans;

int tot;

int fa[N];

struct E{
    int x,y,z;
}e[M];

bool cmp(E a,E b){
    return a.z<b.z;
}

int f(int x){
    return fa[x]==x?x:fa[x]=f(fa[x]);
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++)scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].z);
    for(int i=1;i<=n;i++)fa[i]=i;
    sort(e+1,e+m+1,cmp);
    for(int i=1;i<=m;i++){
        int x=e[i].x,y=e[i].y;
        int fx=f(x),fy=f(y);
        if(fx!=fy){
            fa[fx]=fy;
            ans+=e[i].z;
            if(++tot==n-1)break;
        }
    }
    if(tot!=n-1)cout<<"orz\\n";
    else printf("%d\\n",ans);
    return 0;
}
kruskal
#include<iostream>
#include<cstdio>
#include<cstring>
#define N 5020
#define M 200009
#define inf 10000000
using namespace std;

int n,m,sumedge,ans,dis[N],head[N];

bool vis[N];

struct Edge{
    int x,y,z,nxt;
    Edge(int x=0,int y=0,int z=0,int nxt=0):
        x(x),y(y),z(z),nxt(nxt){}
}edge[M<<1];

void add(int x,int y,int z){
    edge[++sumedge]=Edge(x,y,z,head[x]);
    head[x]=sumedge;
}

void prim(){
    memset(dis,0x3f,sizeof(dis));
    dis[1]=0;
    for(int i=1;i<=n;i++){
        int u=-1,mn=inf;
        for(int j=1;j<=n;j++){
            if(dis[j]<mn&&!vis[j]){
                u=j;mn=dis[j];
            }
        }
        if(u==-1){
            ans=-1;return;
        }
        vis[u]=true;ans+=dis[u];
        for(int x=head[u];x;x=edge[x].nxt){
            int v=edge[x].y;
            if(dis[v]>edge[x].z)dis[v]=edge[x].z;
        }
    }
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        add(x,y,z);add(y,x,z);
    }
    prim();
    if(ans==-1)cout<<"orz\\n";
    else cout<<ans;
    return 0;
}
prim

 

二、最短路

memset(dis,0x3f,sizeof(dis));
for(int i=1;i<=n;i++)dis[i][i]=0;
for(int k=1;k<=n;k++)
 for(int i=1;i<=n;i++)
  for(int j=1;j<=n;j++)
   dis[i][j]=min(dis[i][j],dis[i][k]+dis[k][j]);
floyed
#include<iostream>
#include<cstdio>
#include<cstring>
#define maxn 10009
#define inf 2147483647
using namespace std;

int n,m,s,sumedge;
int dis[maxn],vis[maxn],head[maxn];

struct Edge{
    int x,y,z,nxt;
    Edge(int x=0,int y=0,int z=0,int nxt=0):
        x(x),y(y),z(z),nxt(nxt){}
}edge[maxn*51];

void add(int x,int y,int z){
    edge[++sumedge]=Edge(x,y,z,head[x]);
    head[x]=sumedge;
}

void di(){
    for(int i=1;i<=n;i++)dis[i]=inf;
    dis[s]=0;
    for(int i=1;i<=n;i++){
        int k,mn=inf;
        for(int j=1;j<=n;j++){
            if(!vis[j]&&dis[j]<mn){
                mn=dis[j];k=j;
            }
        }
        if(mn==inf)break;
        vis[k]=true;
        for(int j=head[k];j;j=edge[j].nxt){
            int v=edge[j].y;
            if(!vis[v]&&dis[v]>dis[k]+edge[j].z)
             dis[v]=dis[k]+edge[j].z;
        }
    }
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i=1;i<=m;i++){
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        add(x,y,z);
    }
    di();
    for(int i=1;i<=n;i++)printf("%d ",dis[i]);
    return 0;
}
没有优化的dijkstra
#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#define N 100008
using namespace std;

int n,m,s;

int sumedge;

int head[N],dis[N],vis[N];

struct Edge{
    int x,y,z,nxt;
    Edge(int x=0,int y=0,int z=0,int nxt=0):
        x(x),y(y),z(z),nxt(nxt){}
}edge[N*5];

struct node{
    int x,dis;
    bool operator < (node a) const{
        return dis>a.dis;
    }
};

priority_queue<node>q;

void add(int x,int y,int z){
    edge[++sumedge]=Edge(x,y,z,head[x]);
    head[x]=sumedge;
}

void dijikstra(int x){
    while(!q.empty())q.pop();
    memset(dis,0x3f,sizeof(dis));
    dis[x]=0;
    q.push((node){x,0});
    while(!q.empty()){
        node now=q.top();q.pop();
        if(vis[now.x])continue;
        vis[now.x]=true;
        for(int i=head[now.x];i;i=edge[i].nxt){
            int v=edge[i].y;
            if(dis[v]>dis[now.x]+edge[i].z){
                dis[v]=dis[now.x]+edge[i].z;
                q.push((node){v,dis[v]}); 
            }
        }
    } 
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i=1;i<=m;i++){
        int x,y,z;
        scanf("%d%d%d",&x,&y,&z);
        add(x,y,z);
    }
    dijikstra(s);
    for(int i=1;i<=n;i++)
    if(dis[i]==0x3f3f3f3f)printf("2147483647 ");
    else 
    printf("%d ",dis[i]);
    return 0;
}
堆优化dijkstra
void spfa(){
    memset(dis,0x3f,sizeof(dis));
    memset(vis,0,sizeof(vis));
    while(!q.empty())q.pop();
    dis[1]=0;vis[1]=true;q.push(1);
    while(!q.empty()){
        int now=q.front();q.pop();vis[now]=false;
        for(int i=head[now];i;i=edge[i].nxt){
            int v=edge[i].y;
            if(dis[v]>dis[now]+edge[i].z){
                dis[v]=dis[now]+edge[i].z;
                if(!vis[v]){
                    vis[v]=true;q.push(v);
                }
            }
        }
    }
}
spfa

 

三、二分图

#include<iostream>
#include<cstdio>
#include<cstring>
#define N 1020
using namespace std;

int n,m,e,ans,sumedge;

int vis[N],match[N],head[N];

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[N*N];

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

bool dfs(int x){
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(!vis[v]){
            vis[v]=true;
            if(match[v]==0||dfs(match[v])){
                match[v]=x;return true;
            }
        }
    }
    return false;
}

int main(){
    scanf("%d%d%d",&n,&m,&e);
    for(int i=1;i<=e;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        if(y>m||x>n)continue;
        add(x,y);
    }
    for(int i=1;i<=n;i++){
        memset(vis,0,sizeof(vis));
        if(dfs(i))ans++;
    }
    cout<<ans<<endl;
    return 0;
}
洛谷模板二分图匹配

 封锁阳光大学

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#define maxn 10001
#define maxm 100009
#ifdef WIN32
#define PLL "%I64d\\n"
#else
#define PLL "%lld\\n"
#endif
using namespace std;

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[maxm*2];

int head[maxn],col[maxn],q[maxn];
int sumedge,n,m,cnt1,x,y,cnt2,ans;

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&x,&y);
        add(x,y);add(y,x);
    }
    memset(col,-1,sizeof(col));
    for(int i=1;i<=n;i++){
        if(col[i]==-1){
            int h,t;h=t=1;col[i]=1;q[h]=i;
            while(h<=t){
                int now=q[h++];
                 if(col[now]==1)cnt1++; else cnt2++;
                for(int j=head[now];j;j=edge[j].nxt){
                    int v=edge[j].y;
                    if(col[v]==-1){
                        q[++t]=v;
                        col[v]=col[now]^1;
                    }
                    if(col[v]==col[now]){
                        printf("Impossible");
                        return 0;
                    }
                }
            }
        }
        ans+=min(cnt1,cnt2);
        cnt1=cnt2=0;
    }
    printf(PLL,ans);
}
二分图判定

 

四、LCA

#include<iostream>
#include<cstdio>
#include<cstring>
#define maxn 500009
using namespace std;

int n,m,s,sumedge;
int head[maxn],deep[maxn],size[maxn],dad[maxn],top[maxn];

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[maxn<<1];

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

void dfs(int x){
    size[x]=1;deep[x]=deep[dad[x]]+1;
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(v==dad[x])continue;
        dad[v]=x;dfs(v);
        size[x]+=size[v];
    }
}

void dfs_(int x){
    int s=0;
    if(!top[x])top[x]=x;
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(v!=dad[x]&&size[v]>size[s])s=v;
    }
    if(s){
        top[s]=top[x];
        dfs_(s);
    }
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(v!=dad[x]&&v!=s)dfs_(v);
    }
}

int lca(int x,int y){
    for(;top[x]!=top[y];){
        if(deep[top[x]]>deep[top[y]])swap(x,y);
        y=dad[top[y]];
    }
    if(deep[x]>deep[y])return y;
    return x;
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i=1;i<n;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        add(x,y);add(y,x);
    }
    dfs(s);dfs_(s);
    for(int i=1;i<=m;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        printf("%d\\n",lca(x,y));
    }
    return 0;
}
树剖
#include<iostream>
#include<cstdio>
#include<cstring>
#define maxn 500009
using namespace std;

int n,m,s,sumedge;
int head[maxn],dad[maxn][25],deep[maxn];

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[maxn<<1];

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

void dfs(int x){
    deep[x]=deep[dad[x][0]]+1;
    for(int i=0;dad[x][i];i++)
     dad[x][i+1]=dad[dad[x][i]][i];
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(v==dad[x][0])continue;
        dad[v][0]=x;
        dfs(v);
    }
}

int lca(int x,int y){
    if(deep[x]>deep[y])swap(x,y);
    for(int i=20;i>=0;i--)if(deep[dad[y][i]]>=deep[x])y=dad[y][i];
    if(x==y)return x;
    for(int i=20;i>=0;i--)if(dad[x][i]!=dad[y][i])x=dad[x][i],y=dad[y][i];
    return dad[x][0];
}

int main(){
    scanf("%d%d%d",&n,&m,&s);
    for(int i=1;i<n;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        add(x,y);add(y,x);
    }
    dfs(s);
    for(int i=1;i<=m;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        printf("%d\\n",lca(x,y));
    }
    return 0;
}
倍增

 

五、tarjan

洛谷模板

#include<iostream>
#include<cstdlib>
#include<algorithm>
#include<cstdio>
#include<cstring>
#define maxn 1000006

int n,m,sumedge,root,ans,tim;
int low[maxn],dfn[maxn],iscut[maxn],head[maxn]; 

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[maxn<<1];

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

int min(int x,int y){
    return x<y?x:y;
}

void Tarjian(int x,int fa){
    dfn[x]=low[x]=++tim;int cnt=0;
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(v==fa)continue;
        if(dfn[v]==0){
            cnt++;
            Tarjian(v,x);
            low[x]=min(low[x],low[v]);
            if(low[v]>=dfn[x]&&x!=root&&iscut[x]==0)iscut[x]=true,ans++;
            if(x==root&&cnt>=2&&iscut[x]==0)iscut[x]=true,ans++;
        }else low[x]=min(low[x],dfn[v]);
    }
}

int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=m;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        add(x,y);add(y,x);
    }
    for(int i=1;i<=n;i++)
     if(!dfn[i])root=i,Tarjian(i,i);
    printf("%d\\n",ans);
    for(int i=1;i<=n;i++) if(iscut[i]) printf("%d ",i);
    return 0;
}
割点
#include<iostream>
#include<cstdio>
#include<cstring>
#define maxn 22000
using namespace std;

int n,sumedge,sumclr,top,tim,ans;
int Stack[maxn],instack[maxn],low[maxn],dfn[maxn],bel[maxn],rd[maxn],head[maxn];

struct Edge{
    int x,y,nxt;
    Edge(int x=0,int y=0,int nxt=0):
        x(x),y(y),nxt(nxt){}
}edge[maxn<<1];

void add(int x,int y){
    edge[++sumedge]=Edge(x,y,head[x]);
    head[x]=sumedge;
}

void Tarjian(int x){
    Stack[++top]=x;instack[x]=true;
    low[x]=dfn[x]=++tim;
    for(int i=head[x];i;i=edge[i].nxt){
        int v=edge[i].y;
        if(instack[v])low[x]=min(low[x],dfn[v]);
        else if(!dfn[v]){
            Tarjian(v);
            low[x]=min(low[x],low[v]);
        }
    }
    if(low[x]==dfn[x]){
        sumclr++;
        while(Stack[top+1]!=x

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