2018/finals/citylights.cpp

// City Lights
// 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 135
#define MOD 1000000007

int W,S,K,NH;
PR PW[LIM],PS[LIM];
int H[LIM];
vector<int> ch[LIM],wh[LIM];
LL dyn[LIM][LIM][LIM]; // dyn[i][h][b] = # of combinations in i's subtree requiring b buildings, with height h still required
LL dynS[LIM][LIM][LIM]; // dynS[i][h][b] = sum of dyn[i][0..(h-1)][b]
LL tmp[LIM][LIM];

void CompSums(int i)
{
	int h,b;
		Fox(h,NH)
			Fox(b,W+1)
				dynS[i][h+1][b]=(dynS[i][h][b]+dyn[i][h][b])%MOD;
}

void Add(LL &a,LL b)
{
	a=(a+b)%MOD;
}

void rec(int i)
{
	int j,c,h,b,h2,b2,nw;
	LL pw;
	// iterate over children
	dyn[i][0][0]=1;
		Fox(j,Sz(ch[i]))
		{
			rec(c=ch[i][j]);
			// combine DP values
			CompSums(i),CompSums(c);
			Fill(tmp,0);
				Fox(h,NH)
					Fox(b,W+1)
						Fox(b2,W-b+1)
							Add(tmp[h][b+b2],dyn[i][h][b]*dynS[c][h+1][b2] + dynS[i][h][b]*dyn[c][h][b2]);
			memcpy(dyn[i],tmp,sizeof(tmp));
		}
	// consider all possible subsets of windows coming into play here
	nw=Sz(wh[i]);
	sort(All(wh[i]));
	reverse(All(wh[i]));
	Fill(tmp,0);
		Fox(j,nw+1)
		{
			h2=(j==nw ? 0 : wh[i][j]);
			pw=(1LL<<(nw-min(nw,j+1)))%MOD;
				Fox(h,NH)
					Fox(b,W+1)
						Add(tmp[max(h,h2)][b],pw*dyn[i][h][b]);
		}
	memcpy(dyn[i],tmp,sizeof(tmp));
	// place a building here when necessary
		FoxI(h,H[i],NH-1)
			Fox(b,W+1)
			{
				Add(dyn[i][0][b+1],dyn[i][h][b]);
				dyn[i][h][b]=0;
			}
	CompSums(i);
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int i,x,y,z,a,b,c;
	LL ans;
	vector<int> cy;
	set<pair<PR,int> > SI;
	set<pair<PR,int> >::iterator I;
	map<int,int> MS;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input, and compress y-coordinates
			Read(W),Read(S);
			cy.clear(),cy.pb(0);
				Fox(i,W)
					Read(PW[i].y),Read(PW[i].x),cy.pb(PW[i].x);
				Fox(i,S)
					Read(PS[i].y),Read(PS[i].x),cy.pb(PS[i].x);
			sort(All(cy));
			cy.resize(unique(All(cy))-cy.begin());
			NH=Sz(cy);
				Fox(i,W)
					PW[i].x=lower_bound(All(cy),PW[i].x)-cy.begin();
				Fox(i,S)
					PS[i].x=lower_bound(All(cy),PS[i].x)-cy.begin();
			// init tree
			Fill(H,60);
				Fox(i,K)
					ch[i].clear(),wh[i].clear();
			K=0;
			// iterate over stars in non-decreasing order of Y
			sort(PS,PS+S);
			SI.clear();
			H[0]=1,SI.insert(mp(mp(0,INF+1),K++));
			MS.clear();
				Fox(i,S)
				{
					x=PS[i].y;
					y=PS[i].x;
					// find containing interval (if any)
					I=SI.lower_bound(mp(mp(x,INF+2),0)),I--;
					a=I->x.x;
					b=I->x.y;
					c=I->y;
						if ((a<=x) && (b>=x))
						{
							// split interval at this X-coordinate
								if (a<x)
								{
									ch[c].pb(K);
									H[K]=y,SI.insert(mp(mp(a,x-1),K++));
								}
								if (b>x)
								{
									ch[c].pb(K);
									H[K]=y,SI.insert(mp(mp(x+1,b),K++));
								}
							SI.erase(I);
							MS[x]=c;
						}
				}
			// associate windows with nodes
				Fox(i,W)
				{
					x=PW[i].y;
						if (MS.count(x))
							c=MS[x];
						else
						{
							I=SI.lower_bound(mp(mp(x,INF+2),0)),I--;
							c=I->y;
						}
					wh[c].pb(PW[i].x);
				}
			// DP
			Fill(dyn,0);
			rec(0);
			ans=0;
				Fox1(i,W)
					Add(ans,i*dyn[0][0][i]);
			// output
			printf("Case #%d: %lld\n",t,ans);
		}
	return(0);
}