BZOJ2870 最长道路tree(并查集+LCA)
题意
(n<=50000)
题解
1 #include<iostream> 2 #include<cstring> 3 #include<cstdio> 4 #include<cmath> 5 #include<algorithm> 6 using namespace std; 7 const long long N=60000; 8 long long cnt,head[N]; 9 long long sum[N],dep[N],f[N][25]; 10 long long fa[N]; 11 long long n,a[N],b[N],book[N],ans; 12 struct edge{ 13 long long to,nxt; 14 }e[N*2]; 15 struct node{ 16 long long w,id; 17 }c[N]; 18 void add(long long u,long long v){ 19 cnt++; 20 e[cnt].nxt=head[u]; 21 e[cnt].to=v; 22 head[u]=cnt; 23 } 24 void dfs(long long u,long long ff,long long deep,long long w){ 25 sum[u]=w; 26 f[u][0]=ff; 27 dep[u]=deep; 28 for(long long i=head[u];i;i=e[i].nxt){ 29 long long v=e[i].to; 30 if(v==ff)continue; 31 dfs(v,u,deep+1,w+1); 32 } 33 } 34 bool cmp(node a,node b){ 35 return a.w>b.w; 36 } 37 long long find(long long x){ 38 if(fa[x]==x)return x; 39 else return fa[x]=find(fa[x]); 40 } 41 long long getlca(long long x,long long y){ 42 if(dep[x]<dep[y])swap(x,y); 43 for(long long i=20;i>=0;i--){ 44 if(dep[f[x][i]]>=dep[y]){ 45 x=f[x][i]; 46 } 47 } 48 if(x==y)return x; 49 for(long long i=20;i>=0;i--){ 50 if(f[x][i]!=f[y][i]){ 51 x=f[x][i];y=f[y][i]; 52 } 53 } 54 return f[x][0]; 55 } 56 long long getline(long long x,long long y){ 57 long long LCA=getlca(x,y); 58 return sum[x]+sum[y]-sum[LCA]*2+1; 59 } 60 void merge(long long x,long long y){ 61 long long tmp=0,cx,cy,len; 62 len=getline(a[x],b[x]);if(len>tmp){cx=a[x];cy=b[x];tmp=len;} 63 len=getline(a[y],b[y]);if(len>tmp){cx=a[y];cy=b[y];tmp=len;} 64 len=getline(a[x],a[y]);if(len>tmp){cx=a[x];cy=a[y];tmp=len;} 65 len=getline(b[x],b[y]);if(len>tmp){cx=b[x];cy=b[y];tmp=len;} 66 len=getline(a[x],b[y]);if(len>tmp){cx=a[x];cy=b[y];tmp=len;} 67 len=getline(a[y],b[x]);if(len>tmp){cx=a[y];cy=b[x];tmp=len;} 68 fa[y]=x; 69 a[x]=cx; 70 b[x]=cy; 71 } 72 int main(){ 73 scanf("%lld",&n); 74 for(long long i=1;i<=n;i++){ 75 scanf("%lld",&c[i].w); 76 c[i].id=i; 77 } 78 for(long long i=1;i<n;i++){ 79 long long u;long long v; 80 scanf("%lld%lld",&u,&v); 81 add(u,v); 82 add(v,u); 83 } 84 for(long long i=1;i<=n;i++){ 85 a[i]=b[i]=i;fa[i]=i; 86 } 87 dfs(1,0,1,0); 88 for(long long i=1;i<=20;i++){ 89 for(long long j=1;j<=n;j++){ 90 f[j][i]=f[f[j][i-1]][i-1]; 91 } 92 } 93 sort(c+1,c+1+n,cmp); 94 for(long long i=1;i<=n;i++){ 95 long long u=c[i].id; 96 book[u]=1; 97 for(long long j=head[u];j;j=e[j].nxt){ 98 long long v=e[j].to; 99 if(book[v]==0)continue; 100 merge(find(u),find(v)); 101 } 102 ans=max(ans,c[i].w*getline(a[u],b[u])); 103 } 104 printf("%lld",ans); 105 return 0; 106 }
