[CTS2019]田野（80分）

loj嘟嘟嘟


学完模拟退火后开始搞这道题，搞了一下午最终搞到了80分，剩下的实在不知道怎么办了……


首先肯定是把有交点的线段划分到一个集合，然后对每一个集合求一遍凸包。
然后两两合并，如果新的凸包的周长更小，那必定合并。
但有可能三个或以上合并才更优，所以上述算法肯定不行。
这时候就要模拟退火了。
每次随机合并两个，如果更优，就合并；否则有概率合并。然后我在每一次降温之前又暴力的全扫一遍尝试两两合并。
模拟退火跑到2.9秒，我又写了个一个乱搞算法，借鉴了当时rk1的写法，每次随机两个合并，直到剩一个凸包，然后取过程中的最优解。这个再跑到3.95秒。
最终搞到了80。

#include<cstdio>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<cstdlib>
#include<cctype>
#include<vector>
#include<stack>
#include<queue>
#include<assert.h>
#include<ctime>
using namespace std;
#define enter puts("")
#define space putchar(' ')
#define Mem(a, x) memset(a, x, sizeof(a))
#define In inline
typedef long long ll;
typedef double db;
const int INF = 0x3f3f3f3f;
const db eps = 1e-13;
const db DELTA = 0.99999;
const int maxn = 505;
inline ll read()
{
  ll ans = 0;
  char ch = getchar(), last = ' ';
  while(!isdigit(ch)) last = ch, ch = getchar();
  while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar();
  if(last == '-') ans = -ans;
  return ans;
}
inline void write(ll x)
{
  if(x < 0) x = -x, putchar('-');
  if(x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
In void MYFILE()
{
#ifndef mrclr
  freopen("fields.in", "r", stdin);
  freopen("fields.out", "w", stdout);
#endif
}

int n;
struct Point
{
  db x, y;
  Point operator + (const Point& oth)const
  {
    return (Point){x + oth.x, y + oth.y};
  }
  Point operator - (const Point& oth)const
  {
    return (Point){x - oth.x, y - oth.y};
  }
  db operator * (const Point& oth)const
  {
    return x * oth.y - y * oth.x;
  }
  friend In void swap(Point& A, Point& B)
  {
    swap(A.x, B.x), swap(A.y, B.y);
  }
  friend In db dis(Point& A, Point& B)
  {
    return sqrt((A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y));
  }
};
struct Line
{
  Point A, B;
  friend In bool cross(Line a, Line b)
  {
    db ret1 = ((a.B - a.A) * (b.A - a.A)) * ((a.B - a.A) * (b.B - a.A));
    db ret2 = ((b.B - b.A) * (a.A - b.A)) * ((b.B - b.A) * (a.B - b.A));
    return ret1 < 0 && ret2 < 0;
  }
}l[maxn];

int vis[maxn], cnt = 0;
vector<Point> v[maxn];
db S[maxn];

Point a[maxn], P;
int tot = 0, st[maxn], top = 0;
In bool cmp(Point A, Point B) {return (A - P) * (B - P) > 0;}
In db calc()
{
  int pos = 1;
  for(int i = 2; i <= tot; ++i)
    if(a[i].x < a[pos].x || (fabs(a[i].x - a[pos].x) < eps && a[i].y < a[pos].y)) pos = i;
  if(pos ^ 1) swap(a[1], a[pos]); P = a[1];
  sort(a + 2, a + tot + 1, cmp);
  st[top = 1] = 1;
  for(int i = 2; i <= tot; ++i)
    {
      while(top > 1 && (a[i] - a[st[top - 1]]) * (a[st[top]] - a[st[top - 1]]) > 0) --top;
      st[++top] = i;
    }
  st[top + 1] = st[1];
  db ret = 0;
  for(int i = 1; i <= top; ++i) ret += dis(a[st[i]], a[st[i + 1]]);
  return ret;
}

In db TIME() {return 1.0 * clock() / CLOCKS_PER_SEC;}

vector<Point> v2[maxn];
db S2[maxn], sum = 0, ans = 0;
int id[maxn], cnt2 = 0;
In void HIA()
{
  db T = n <= 60 ? 1000000000 : 10000000, ans2 = sum; cnt2 = 0;
  for(int i = 1; i <= cnt; ++i) if(vis[i] == i) id[++cnt2] = i;
  while(T > eps && cnt2 > 1)
    {
      if(TIME() > 2.8) return;
      int x = rand() % cnt2 + 1, y = rand() % cnt2 + 1;
      while(x == y) y = rand() % cnt2 + 1;
      if(x > y) swap(x, y);
      tot = 0;
      for(int i = 0; i < (int)v2[id[x]].size(); ++i) a[++tot] = v2[id[x]][i];
      for(int i = 0; i < (int)v2[id[y]].size(); ++i) a[++tot] = v2[id[y]][i];
      db tp = calc(), del = tp - S2[id[x]] - S2[id[y]];
      if(del < 0 || exp(-del / T) * RAND_MAX > rand())
	{
	  ans2 =  ans2 - S2[id[x]] - S2[id[y]] + tp;
	  ans = min(ans, ans2);
	  S2[id[x]] = tp;
	  for(int i = 0; i < (int)v2[id[y]].size(); ++i) v2[id[x]].push_back(v2[id[y]][i]);
	  for(int i = y + 1; i <= cnt2; ++i) id[i - 1] = id[i];
	  --cnt2;
	}
      for(int i = x + 1; i <= cnt2; ++i)
	{
	  if(TIME() > 2.8) return;
	  tot = 0;
	  for(int j = 0; j < (int)v2[id[x]].size(); ++j) a[++tot] = v2[id[x]][j];
	  for(int j = 0; j < (int)v2[id[i]].size(); ++j) a[++tot] = v2[id[i]][j];
	  db tp = calc();
	  if(tp < S2[id[x]] + S2[id[i]])
	    {
	      ans2 =  ans2 - S2[id[x]] - S2[id[i]] + tp;
	      ans = min(ans, ans2);
	      S2[id[x]] = tp;
	      for(int j = 0; j < (int)v2[id[i]].size(); ++j) v2[id[x]].push_back(v2[id[i]][j]);
	      for(int j = i + 1; j <= cnt2; ++j) id[j - 1] = id[j];
	      --cnt2;
	    }
	}
      T *= DELTA;
    }
}
In void HIA2()
{
  db ans2 = sum; cnt2 = 0;
  for(int i = 1; i <= cnt; ++i) if(vis[i] == i) id[++cnt2] = i;
  while(cnt2 > 1)
    {
      if(TIME() > 3.95) return;
      int x = rand() % cnt2 + 1, y = rand() % cnt2 + 1;
      while(x == y) y = rand() % cnt2 + 1;
      if(x > y) swap(x, y);
      tot = 0;
      for(int i = 0; i < (int)v2[id[x]].size(); ++i) a[++tot] = v2[id[x]][i];
      for(int i = 0; i < (int)v2[id[y]].size(); ++i) a[++tot] = v2[id[y]][i];
      db tp = calc();
      ans2 =  ans2 - S2[id[x]] - S2[id[y]] + tp;
      ans = min(ans, ans2);
      S2[id[x]] = tp;
      for(int i = 0; i < (int)v2[id[y]].size(); ++i) v2[id[x]].push_back(v2[id[y]][i]);
      for(int i = y + 1; i <= cnt2; ++i) id[i - 1] = id[i];
      --cnt2;
    }
}

int main()
{
  //MYFILE();
  srand(20010613);
  n = read();
  for(int i = 1; i <= n; ++i)
    {
      Point A, B;
      A.x = read(), A.y = read(), B.x = read(), B.y = read();
      l[i] = (Line){A, B};
    }
  for(int i = 1; i <= n; ++i)
    if(!vis[i])
      {
	vis[i] = 1; ++cnt;
	v[cnt].push_back(l[i].A), v[cnt].push_back(l[i].B);
	for(int j = i + 1; j <= n; ++j)
	  if(!vis[j] && cross(l[i], l[j]))
	    {
	      vis[j] = 1;
	      v[cnt].push_back(l[j].A), v[cnt].push_back(l[j].B);
	    }
      }
  for(int i = 1; i <= cnt; ++i)
    {
      tot = 0;
      for(int j = 0; j < (int)v[i].size(); ++j) a[++tot] = v[i][j];
      S[i] = calc();
    }
  Mem(vis, 0);
  for(int i = 1; i <= cnt; ++i) if(!vis[i])
    {
      vis[i] = i;
      for(int j = i + 1; j <= cnt; ++j) if(!vis[j])
	{
	  tot = 0; db tp;
	  for(int k = 0; k < (int)v[i].size(); ++k) a[++tot] = v[i][k];
	  for(int k = 0; k < (int)v[j].size(); ++k) a[++tot] = v[j][k];
	  if((tp = calc()) < S[i] + S[j])
	    {
	      S[i] = tp; vis[j] = i;
	      for(int k = 0; k < (int)v[j].size(); ++k) v[i].push_back(v[j][k]);
	    }
	}
      ans += S[i], sum += S[i];
    }
  while(TIME() < 2.9)
    {
      for(int i = 1; i <= cnt; ++i)
	{
	  v2[i].clear(); S2[i] = S[i];
	  for(int j = 0; j < (int)v[i].size(); ++j) v2[i].push_back(v[i][j]);
	}
      HIA();
    }
  while(TIME() < 3.95)
    {
      for(int i = 1; i <= cnt; ++i)
	{
	  v2[i].clear(); S2[i] = S[i];
	  for(int j = 0; j < (int)v[i].size(); ++j) v2[i].push_back(v[i][j]);
	}
      HIA2();
    }
  printf("%.8lf\n", ans);
  return 0;
}