OJ-Problems-Source/HDOJ/4575_autoAC.cpp

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#include <iostream>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <vector>
#include <map>
using namespace std;
#define inf 9e99
#define eps 1e-9
#define x first
#define y second
#define pb push_back
#define sz(a) int(a.size())
#define rep(i,a,b) for(int i=a;i<=b;i++)
template<class T> inline void gmin(T&a,T b) {if(a>b)a=b;}
template<class T> inline T sqr(T a) {return a*a;}
#define N 20020
vector<int> to[N],len[N];
int col[N],n;
double sum[N],L;
#define is_leaf(x) sz(to[x])==1 && sum[to[x][0]]<sum[x]
void pre_dfs(int x) {
rep(i,0,sz(to[x])-1) {
int y=to[x][i];
if (sum[y]<0) {
col[y]=x==1?y:col[x];
sum[y]=sum[x]+len[x][i];
pre_dfs(y);
}
}
}
vector<int> path,tmp[N];
double dp1[N],ans1[N];
double dp2[N],ans2[N];
double Y1(int j) {return dp1[j]+sqrt(dp1[j])+sqr(sum[j])+2.0*sum[j]*L;}
double Y2(int j) {return dp2[j]+sqrt(dp2[j])+sqr(sum[j])-2.0*sum[j]*L;}
double slope1(int j,int k) {return (Y1(j)-Y1(k))/(sum[j]-sum[k]);}
double slope2(int j,int k) {return (Y2(j)-Y2(k))/(sum[j]-sum[k]);}
double calc(double Ej,double sum) {return Ej+sqrt(Ej)+sum*sum;}
struct Queue {
map<double,int> q;
void clear() {q.clear();}
int size() {return q.size();}
int front() {return sz(q)?q.begin()->y:0;}
int front2() {return sz(q)?(++q.begin())->y:0;}
int back() {return sz(q)?q.rbegin()->y:0;}
int back2() {return sz(q)?(++q.rbegin())->y:0;}
void pop_front() {q.erase(q.begin());}
void pop_back() {q.erase(--q.end());}
void insert(int x,int y) {q[x]=y;}
void merge(Queue *b) {
while (b->size()) {
int cur=b->front();
b->pop_front();
if (q.find(sum[cur])!=q.end()) {
int j=cur,k=q[sum[cur]];
if (Y2(j)>=Y2(k)) continue;
}
q[sum[cur]]=cur;
if (sz(q)<=2) continue;
map<double,int>::iterator i=q.find(sum[cur]),l1,l2,r1,r2;
if (i!=q.begin() && i!=(--q.end())) {
l1=i, l1--;
r1=i, r1++;
if (slope2(l1->y,i->y)>=slope2(i->y,r1->y)) {
q.erase(i);
continue;
}
}
while (i!=q.begin() && i!=(++q.begin())) {
l1=i, l1--;
l2=l1, l2--;
if (slope2(l2->y,l1->y)<=slope2(l1->y,i->y)) break;
q.erase(l1);
}
while (i!=(--q.end()) && i!=(--(--q.end()))) {
r1=i, r1++;
r2=r1, r2++;
if (slope2(i->y,r1->y)<=slope2(r1->y,r2->y)) break;
q.erase(r1);
}
}
}
} q1,*q2[N];
void first_run(int x) {
rep(i,0,sz(to[x])-1) {
int y=to[x][i];
if (sum[y]<=sum[x]) continue;
path.pb(y);
tmp[x].clear();
while (sz(q1)>=2 && slope1(q1.front(),q1.front2())<=2.0*sum[y] ) {
tmp[x].pb(q1.front());
q1.pop_front();
}
dp1[y]=calc(dp1[q1.front()],sum[y]-sum[q1.front()]-L);
while (sz(q1)>=2 && slope1(q1.back2(),q1.back())>=slope1(q1.back(),y) ) {
tmp[x].pb(q1.back());
q1.pop_back();
}
q1.insert(sum[y],y);
first_run(y);
q1.pop_back();
rep(i,0,sz(tmp[x])-1)
q1.insert(sum[tmp[x][i]],tmp[x][i]);
path.pop_back();
}
if (is_leaf(x)) {
gmin(ans1[col[x]],dp1[x]);
}
}
void merge(Queue *&a,Queue *&b) {
if (b->size() < a->size()) {
a->merge(b);
} else {
b->merge(a);
a=b;
}
}
double get_val(Queue *q,int x) {
while (q->size()>=2 && slope2(q->back(),q->back2())>=2.0*sum[x]) q->pop_back();
dp2[x]=calc(dp2[q->back()],sum[q->back()]-sum[x]-L);
while (q->size()>=2 && slope2(q->front2(),q->front())<=slope2(q->front(),x) ) q->pop_front();
return dp2[x];
}
void second_run(int x) {
q2[x]=new Queue;
rep(i,0,sz(to[x])-1){
int y=to[x][i];
if (sum[y]<=sum[x]) continue;
second_run(y);
if (x==1) {
gmin(ans2[y],get_val(q2[y],x));
} else {
merge(q2[x],q2[y]);
}
}
if (x!=1) {
dp2[x]=is_leaf(x)?0:get_val(q2[x],x);
q2[x]->insert(sum[x],x);
}
}
double get_answer() {
vector<int> part;
rep(i,2,n) if (col[i]==i) part.pb(i);
double min1=inf,min2=inf;
int pos1;
rep(i,0,sz(part)-1) {
if (min1>ans2[part[i]]) {
min2=min1;
min1=ans2[part[i]];
pos1=i;
} else
if (min2>ans2[part[i]]) {
min2=ans2[part[i]];
}
}
double res=inf;
rep(i,0,sz(part)-1)
gmin(res,ans1[part[i]]+(pos1==i?min2:min1));
return res;
}
int main() {
while (~scanf("%d%lf",&n,&L)) {
rep(i,1,n) {
to[i].clear();
len[i].clear();
}
rep(i,1,n-1) {
int u,v,w;
scanf("%d%d%d",&u,&v,&w);
to[u].pb(v);
to[v].pb(u);
len[u].pb(w);
len[v].pb(w);
}
if (sz(to[1])<2) {
puts("-1");
continue;
}
fill(sum+2,sum+n+1,-1);
pre_dfs(1);
fill(dp1+2,dp1+n+1,inf);
fill(dp2+1,dp2+n+1,inf);
fill(ans1,ans1+n+1,inf);
fill(ans2,ans2+n+1,inf);
path.clear();
path.pb(1);
q1.clear();
q1.insert(0,1);
first_run(1);
second_run(1);
printf("%.2lf\n",get_answer());
}
return 0;
}