UOJ276 [清华集训2016] 汽水 【二分答案】【点分治】【树状数组】

  1 #include<bits/stdc++.h>
  2 using namespace std;
  3 
  4 typedef long long ll;
  5 
  6 const int maxn = 50100;
  7 
  8 ll k,md; int flag = 0,num,n,rnum;
  9 vector <pair<int,ll> > g[maxn];
 10 int arr[maxn],sz[maxn],imp[maxn],cnt[maxn];
 11 struct node{ll A;int B,pla;}op[maxn];
 12 
 13 int cmp(node X,node Y){
 14     return -X.A-md*X.B < -Y.A-md*Y.B;
 15 }
 16 
 17 struct Fenwick{
 18     int C[maxn];
 19     void Add(int now){
 20     while(now <= rnum){C[now] ++; now += (now&-now);}
 21     }
 22     int query(int now){
 23     int ans = 0;
 24     while(now){ans += C[now]; now -= (now&-now);}
 25     return ans;
 26     }
 27 }T1;
 28 
 29 void read(){
 30     scanf("%d%lld",&n,&k);
 31     for(int i=1;i<n;i++){
 32     int x,y;long long v; scanf("%d%d%lld",&x,&y,&v); v -= k;
 33     g[x].push_back(make_pair(y,v)); g[y].push_back(make_pair(x,v));
 34     }
 35 }
 36 
 37 void dfs1(int now,int fa,int dp){
 38     sz[now] = 1;imp[now] = 0;
 39     for(auto it : g[now]){
 40     if((arr[it.first] && arr[it.first] < dp) || fa == it.first) continue;
 41     dfs1(it.first,now,dp); sz[now] += sz[it.first];
 42     }
 43 }
 44 
 45 int dfs2(int now,int fa,int dp,int ssz){
 46     int ans = 0;
 47     for(auto it : g[now]){
 48     if((arr[it.first] && arr[it.first] < dp) || fa == it.first) continue;
 49     int data = dfs2(it.first,now,dp,ssz);
 50     if(ans==0 || imp[ans] > imp[data])ans = data;
 51     imp[now] = max(sz[it.first],imp[now]);
 52     }
 53     imp[now] = max(imp[now],ssz-sz[now]);
 54     if(ans==0 || imp[ans] > imp[now]) ans = now;
 55     return ans;
 56 }
 57 
 58 void dfs3(int now,int fa,int dp,int A,int B){
 59     for(auto it : g[now]){
 60     if(it.first == fa || (arr[it.first] && arr[it.first] < dp)) continue;
 61     op[++num] = (node){A+it.second,B+1,it.first};
 62     dfs3(it.first,now,dp,A+it.second,B+1);
 63     }
 64 }
 65 
 66 long long lisan[maxn];
 67 void solve(int dr){
 68     rnum = num;
 69     for(int i=1;i<=num;i++){lisan[i] = -op[i].A+md*op[i].B;}
 70     sort(lisan+1,lisan+num+1);rnum = unique(lisan+1,lisan+num+1)-lisan-1;
 71     for(int i=1;i<=rnum;i++) T1.C[i]=0;
 72     for(int i=num,j=1;i>=1;i--){
 73     while(j <= num && (-op[j].A-md*op[j].B < op[i].A+md*op[i].B)){
 74         T1.Add(lower_bound(lisan+1,lisan+rnum+1,-op[j].A+md*op[j].B)-lisan);
 75         j++;
 76     }
 77     int ans=j-1-T1.query(upper_bound(lisan+1,lisan+rnum+1,op[i].A-md*op[i].B)-lisan-1);
 78     if(op[i].A-md*op[i].B < -op[i].A+md*op[i].B && j > i)ans--;
 79     if(dr == 1){
 80         if(ans - cnt[op[i].pla]){flag = 1;return;}
 81     }else{cnt[op[i].pla] = ans;}
 82     }
 83 }
 84 
 85 void divide(int now,int dp,int lst,long long AA){
 86     dfs1(now,0,dp); int heavy = dfs2(now,0,dp,sz[now]);arr[heavy] = dp;
 87     for(auto it : g[heavy]){
 88     if(arr[it.first]&&arr[it.first]<dp) continue;
 89     divide(it.first,dp+1,heavy,it.second);
 90     if(flag == 1) return;
 91     }
 92     num = 0; dfs3(heavy,0,dp,0,0); sort(op+1,op+num+1,cmp);
 93     solve(1); num = 0;
 94     if(lst) {
 95     num = 0;dfs3(now,0,dp,AA,1);
 96     sort(op+1,op+num+1,cmp);
 97     for(int i=1;i<=num;i++) cnt[op[i].pla] = 0;
 98     solve(0);
 99     }
100 }
101 
102 void work(){
103     long long l = 0,r = 1e13;
104     while(l < r){
105     md = (l+r)/2; flag = 0;
106     memset(arr,0,sizeof(arr));
107     divide(1,1,0,0);
108     if(flag) r = md; else l = md+1;
109     }
110     printf("%lld",l-1);
111 }
112 
113 int main(){
114     read();
115     work();
116     return 0;
117 }