bzoj 1791 DP

　　首先对于一棵树我们可以tree_dp来解决这个问题，那么对于环上每个点为根的树我们可以求出这个树的一端为根的最长链，并且在tree_dp的过程中更新答案。那么我们对于环，从某个点断开，破环为链，然后再用DP来解决这个问题。

　　备注：很久之前的一道题，刚转的c++，然后T了，也懒得改了。

/**************************************************************
    Problem: 1791
    User: BLADEVIL
    Language: C++
    Result: Time_Limit_Exceed
****************************************************************/
 
//By BLADEVIL 
#include <cstdio> 
#include <cstring> 
#define maxn 1000010 
#define LL long long 
   
using namespace std; 
   
LL n,time,l; 
LL other[maxn<<1],last[maxn],pre[maxn<<1],dfn[maxn],low[maxn],vis[maxn],que[maxn],a[maxn],xx[maxn]; 
LL ans; 
LL len[maxn<<1],max1[maxn],max2[maxn],sum[maxn],w[maxn],yy[maxn],maxlen[maxn]; 
LL save; 
   
void getmin(LL &x,LL y) 
{if (y<x) x=y;} 
   
void connect(LL x,LL y,LL z) { 
    pre[++l]=last[x]; 
    last[x]=l; 
    other[l]=y; 
    len[l]=z; 
    //if (y>x) printf("%d %d %lld\n",x,y,z); 
} 
   
void dfs(LL x,LL fa) { 
    dfn[x]=low[x]=++time; 
    for (LL q=last[x];q;q=pre[q]) { 
        if (other[q]==fa) continue; 
        if (!low[other[q]]) { 
            dfs(other[q],x); 
            getmin(low[x],low[other[q]]); 
        } else getmin(low[x],dfn[other[q]]); 
    } 
    if (low[x]!=dfn[x]) save=low[x]; 
} 
   
void dp(LL x) { 
    memset(que,0,sizeof que); 
    LL h=0,t=1ll; 
    que[1]=x; vis[x]=1ll; 
    while (h<t) { 
        LL cur=que[++h]; 
        for (LL q=last[cur];q;q=pre[q]) { 
            if (low[other[q]]==low[x]) continue; 
            if (vis[other[q]]) continue; 
            vis[other[q]]=vis[cur]+1ll; 
            que[++t]=other[q]; 
        } 
    } 
    //for (LL i=1;i<=t;i++) printf("%d ",que[i]); printf("\n"); 
    for (LL i=t;i;i--) 
        for (LL q=last[que[i]];q;q=pre[q]) { 
            if (low[other[q]]==low[x]) continue; 
            if (vis[other[q]]!=vis[que[i]]+1) continue; 
            //printf(" %d %d\n",que[i],other[q]); 
            if (max1[other[q]]+len[q]>max1[que[i]])  
                max2[que[i]]=max1[que[i]],max1[que[i]]=max1[other[q]]+len[q]; else
            if (max1[other[q]]+len[q]>max2[que[i]]) max2[que[i]]=max1[other[q]]+len[q]; 
            if (max1[other[q]]+max2[other[q]]>maxlen[que[i]])  
                maxlen[que[i]]=max1[other[q]]+max2[other[q]]; 
            if (max1[que[i]]+max2[que[i]]>maxlen[que[i]])  
                maxlen[que[i]]=max1[que[i]]+max2[que[i]]; 
            if (maxlen[que[i]]<maxlen[other[q]]) maxlen[que[i]]=maxlen[other[q]]; 
        } 
    //for (LL i=1;i<=t;i++) printf("%d %lld %lld %lld\n",que[i],max1[que[i]],max2[que[i]],maxlen[que[i]]); 
} 
   
void solve(LL x) { 
    LL now=0ll; 
    dfs(x,-1); 
    //printf("%d",save); 
    if (save)  
        for (LL i=1;i<=n;i++) if (low[i]==save) x=i; 
    save=0; 
    /*if (xx[xx[x]]==x)  
    { 
        ans+=(yy[x]>yy[xx[x]])?yy[x]:yy[xx[x]];   
        return; 
    }*/
    LL cur; 
    for (LL i=1;i<=n;i++) if (low[i]==low[x]) dp(i),cur=i; 
    //printf(" %lld\n",max1[x]); 
    LL t=1; a[t]=cur; 
    while (1) { 
        for (LL q=last[a[t]];q;q=pre[q]) { 
            now=(maxlen[a[t]]>now)?maxlen[a[t]]:now; 
            if (low[other[q]]!=low[x]) continue; 
            if (other[q]==a[t-1]) continue; 
            a[++t]=other[q]; sum[t]=len[q]; break; 
        } 
        if (a[t]==cur) break; 
    } 
    //printf(" %d ",x); 
    //for (LL i=1;i<=t;i++) printf(" %lld %d %d\n",max1[a[i]],a[i],sum[i]); 
    t--; 
    for (LL i=2;i<=t;i++) a[i+t]=a[i],sum[i+t]=sum[i];  
    t*=2; 
    //for (LL i=1;i<=t;i++) printf(" %lld %d %d\n",max1[a[i]],a[i],sum[i]); 
    for (LL i=1;i<=t;i++) sum[i]+=sum[i-1]; 
    LL len=t>>1ll; 
    memset(que,0,sizeof que); 
    LL l=1,r=1; que[1]=1; 
    for (LL i=2;i<=t;i++) { 
        if (i-que[l]+1>len) l++; 
        w[i]=max1[a[que[l]]]+max1[a[i]]+sum[i]-sum[que[l]];  
        //printf("w[i]=%d",w[i]); printf(" %d %d\n",i,que[l]); 
        while (l<=r&&(max1[a[i]]-sum[i]>max1[a[que[r]]]-sum[que[r]])) r--; 
        que[++r]=i; 
        //for (LL i=l;i<=r;i++) printf("|%d ",que[i]); printf("\n"); 
    } 
    for (LL i=1;i<=t;i++) now=(w[i]>now)?w[i]:now; 
    //printf(" %lld ",ans); 
    ans+=now;  
} 
   
int main() { 
    scanf("%d",&n); 
    for (LL i=1;i<=n;i++) scanf("%d%lld",&xx[i],&yy[i]); 
    for (LL i=1;i<=n;i++) { 
        if (xx[i]==i) continue; 
        if (xx[xx[i]]==i&&xx[i]>i) yy[i]=(yy[xx[i]]>yy[i])?yy[xx[i]]:yy[i],yy[xx[i]]=-1ll;  
    } 
    for (LL i=1;i<=n;i++) if (yy[i]!=-1) connect(i,xx[i],yy[i]),connect(xx[i],i,yy[i]); 
    for (LL i=1;i<=n;i++) if (!low[i]) solve(i); 
    //for (LL i=1;i<=n;i++) printf(" %d %d %d\n",i,low[i],dfn[i]); 
    printf("%lld\n",ans); 
    return 0;
}