图论板子整理

SPFA

void spfa(){
    queue<int> q;
    for(int i=1; i<=n; i++) dis[i]=INF; 
    q.push(s); dis[s]=0; vist[s]=1;
    while(!q.empty()){
    int u=q.front();
    q.pop();vist[u]=0;
    for(int i=head[u];i;i=edge[i].next)
        if(dis[edge[i].to]>dis[u]+edge[i].dis){
            dis[edge[i].to]=dis[u]+edge[i].dis;
            if(vist[edge[i].to]==0){vist[edge[i].to]=1;q.push(edge[i].to);}
        }   
    }
}
void spfa(int u){//DFS
    vist[u]=1;
    for(int i=head[u];i;i=edge[i].nxt){
        int g=edge[i].to;
        if(dis[g]<dis[u]+edge[i].dis){
            dis[g]=dis[u]+edge[i].dis;
            spfa(g);
        }
    }
    vist[u]=0;
}

迪杰

void dij(){
for(int i=1;i<=n;i++)dis[i]=INF;
priority_queue<int,vector<pair<int,int> >,greater<pair<int,int> > >q;
dis[s]=0;
q.push(make_pair(0,s));
while(!q.empty())
{
int tt=q.top().second;
q.pop();
if(vist[tt])continue;
vist[tt]=1;
for(int i=head[tt];i;i=edge[i].next)
if(dis[edge[i].to]>dis[tt]+edge[i].dis){dis[edge[i].to]=dis[tt]+edge[i].dis;
q.push(make_pair(dis[edge[i].to],edge[i].to));    }
}
}

DAG=拓扑配DP

int n,c,id,ne,ans,a,b,m;
struct Edge{int to,next;}edge[MAXN];
int head[MAXN],rd[MAXN],sj[MAXN],f[MAXN];
void adde(int from,int to){
    edge[++ne].next=head[from];
    edge[ne].to=to;
    head[from]=ne;
    rd[to]++;
}
void topo()
{
    queue<int> q;
    f(1,n){if(!rd[i])q.push(i);f[i]=1;}
    while(!q.empty()){
        int x=q.front();q.pop();
        for(int i=head[x];i;i=edge[i].next){
        int v=edge[i].to;
            f[v]=max(f[v],f[x]+1);
            if(!--rd[v])q.push(v);
        }
    }
}
int main(){
cin>>n>>m;
w(m){cin>>a>>b;adde(a,b);}
    topo();    
    f(1,n)cout<<f[i]<<endl;
}

krusal

int main(){
    cin>>n>>m;
    f(1,m){cin>>a>>b>>c;adde(a,b,c);adde(b,a,c);}
    f(1,ne)f[i]=i;
    sort(edge+1,edge+ne+1,cmp);
    f(1,ne){int x=find(edge[i].from),y=find(edge[i].to);
        if(x!=y){cnt++;ans+=edge[i].dis;f[x]=y;}
        if(cnt==n-1)break;
    }
    if(cnt==n-1)cout<<ans;
    else cout<<"orz";
}

PRIM

void prim(){
for(int i=1;i<=n;i++)dis[i]=0x3f3f3f3f;
priority_queue<int,vector<pair<int,int> >,greater<pair<int,int> > > q;
dis[1]=0;
q.push(make_pair(0,1));
while(!q.empty()){
int u=q.top().second;q.pop();
if(vist[u])continue;
vist[u]=1;
++cnt;
ans+=dis[u];
for(int i=head[u];i;i=edge[i].next){
int g=edge[i].to;
if(edge[i].dis<dis[g]){
dis[g]=edge[i].dis;
q.push(make_pair(dis[g],g));
}
}
if(cnt==n)break;
}
} 

二分图最大匹配

int dfs(int u) {
for(int i=head[u];i;i=edge[i].nxt) {
int g=edge[i].to;
if(!mk[g]){mk[g]=1;if(!vis[g]||dfs(vis[g])) {vis[g]=u;return 1;}}
}
return 0;
}
int main() {
cin>>n>>m>>k;
while(k--){cin>>a>>b;if(a>n||b>m)continue;adde(a,b);}
for(int i=1;i<=n;i++){
memset(mk,0,sizeof(mk));if(dfs(i))++_ans;
} 
cout<<_ans;
}