2017/finals/tolls.cpp

// Hacker Cup 2017
// Final Round
// Fox Tolls
// Jacob Plachta

#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); }

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

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 500000
#define LIM2 2100000
#define MOD 1000000007

int ind;
int L[2][LIM],R[2][LIM],S[2][LIM];
vector<int> con[LIM];

int sz;
vector<int> lst[LIM2];

void rec(int z,int i,int p)
{
	int j,k;
	L[z][i]=ind++;
		Fox(j,Sz(con[i]))
			if ((k=con[i][j])!=p)
				rec(z,k,i);
	R[z][i]=ind-1;
	S[z][i]=R[z][i]-L[z][i];
}

int Query(int i,int r1,int r2,int a,int b,int v1,int v2)
{
		if ((a<=r1) && (r2<=b))
		{
			return(
				lower_bound(lst[i].begin(),lst[i].end(),v2+1) -
				lower_bound(lst[i].begin(),lst[i].end(),v1)
			);
		}
	i<<=1;
	int m=(r1+r2)>>1,s=0;
		if (a<=m)
			s+=Query(i,r1,m,a,b,v1,v2);
		if (b>m)
			s+=Query(i+1,m+1,r2,a,b,v1,v2);
	return(s);
}

int main()
{
	// vars
	int T,t;
	int N,M;
	int i,j,k,a,b,z,z1,z2;
	int ans,tot;
	char c1,c2;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input
			Read(N),Read(M);
				Fox(z,2)
				{
					// clear graph
						Fox(i,N)
							con[i].clear();
					// input tree
						Fox(i,N-1)
						{
							Read(j),Read(k),j--,k--;
							con[j].pb(k);
							con[k].pb(j);
						}
					// calculate DFS ordering for this tree
					ind=0;
					rec(z,0,0);
				}
			// construct segment tree
				for(sz=1;sz<N;sz<<=1);
				Fox(i,sz<<1)
					lst[i].clear();
				Fox(i,N)
					lst[sz+L[0][i]].pb(L[1][i]);
				FoxR1(i,sz-1)
				{
					j=i<<1,k=j+1;
					a=b=0;
						while ((a<Sz(lst[j])) && (b<Sz(lst[k])))
							if (lst[j][a]<lst[k][b])
								lst[i].pb(lst[j][a++]);
							else
								lst[i].pb(lst[k][b++]);
						while (a<Sz(lst[j]))
							lst[i].pb(lst[j][a++]);
						while (b<Sz(lst[k]))
							lst[i].pb(lst[k][b++]);
				}
			// handle days
			tot=0;
				while (M--)
				{
					// input
					Read(i),Read(j),i--,j--;
					scanf("%c %c",&c1,&c2);
					z1=c1=='T' ? 0 : 1;
					z2=c2=='T' ? 0 : 1;
					// same tree?
						if (z1==z2)
						{
							z=z1;
								if (L[z][i]>L[z][j])
									swap(i,j);
							// nested subtrees?
								if (L[z][j]<=R[z][i])
								{
									ans=2*S[z][i] + S[z][j];
									goto Done;
								}
							// disjoint subtrees
							ans=2*(S[z][i] + S[z][j]);
							goto Done;
						}
					// different trees
						if (z1)
							swap(i,j);
					ans=2*(S[0][i] + S[1][j]);
						if ((S[0][i]) && (S[1][j]))
							ans-=Query(1,0,sz-1,L[0][i]+1,R[0][i],L[1][j]+1,R[1][j]);
					// update total
Done:;
					tot=((LL)tot*12345+ans)%MOD;
				}
			//output
			printf("Case #%d: %d\n",t,tot);
		}
	return(0);
}