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; }
原文:http://www.cnblogs.com/BLADEVIL/p/3714105.html