2018/finals/personal.cpp

// Personal Space
// Solution by Jacob Plachta

#define DEBUG 0

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#if DEBUG
#define GETCHAR getchar
#else
#define GETCHAR getchar_unlocked
#endif

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=GETCHAR();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define LIM 8000001

int K1,K2;
pair<PR,int> E1[LIM];
pair<PR,PR> E2[LIM];
int dyn[LIM];
set<int> S1;
set<PR> S2;
set<int>::iterator I1;
set<PR>::iterator I2,J2;

void AddRect(int x1,int y1,int x2,int y2)
{
		if ((x2<0) || (y1>INF))
			return;
	int i=K2+1;
	E2[K2++]=mp(mp(y1,1),mp(x1,i));
	E2[K2++]=mp(mp(y2,0),mp(x2,i));
}

void AddRects(int x)
{
	int i;
	int X[7];
	I1=S1.lower_bound(x);
		Fox(i,3)
			I1--;
		Fox(i,7)
			X[i]=*I1,I1++;
		Fox(i,4)
			AddRect(X[i],X[i+1],X[i+2],X[i+3]);
}

int Query(int x)
{
	I2=S2.lower_bound(mp(x+1,0));
	I2--;
	return(I2->y);
}

void Update(int x,int v)
{
	I2=S2.lower_bound(mp(x+1,0));
	I2--;
		if (v<=I2->y)
			return;
		if (I2->x<x)
			I2++;
		while ((I2!=S2.end()) && (v>=I2->y))
		{
			J2=I2,I2++;
			S2.erase(J2);
		}
	S2.insert(mp(x,v));
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int N;
	int i,j,k,x,a,b,ans;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input
			Read(N);
			K1=0;
				Fox(i,N)
				{
					Read(x),Read(a),Read(b);
					E1[K1++]=mp(mp(a,x),1);
					E1[K1++]=mp(mp(b+1,x),-1);
				}
			// bottom-up line sweep to generate all possible fish placement "rectangles"
			sort(E1,E1+K1);
			S1.clear();
				Fox1(i,4)
					S1.insert(-i),S1.insert(INF+i);
			K2=0;
				Fox(i,K1)
				{
					j=i;
						while ((j+1<K1) && (E1[j+1].x.x==E1[i].x.x))
							j++;
						FoxI(k,i,j)
							if (E1[k].y>0)
								S1.insert(E1[k].x.y);
							else
								S1.erase(E1[k].x.y);
						FoxI(k,i,j)
							AddRects(E1[k].x.y);
					i=j;
				}
			// bottom-up line sweep DP on rectangles
			sort(E2,E2+K2);
			S2.clear();
			S2.insert(mp(-INF,0));
			ans=0;
				Fox(i,K2)
				{
					x=E2[i].y.x,j=E2[i].y.y;
						if (E2[i].x.y)
							Max(ans,dyn[j]=Query(x)+1);
						else
							Update(x,dyn[j]);
				}
			// output
			printf("Case #%d: %d\n",t,ans);
		}
	return(0);
}