2019/round2/seafood.cpp

// Seafood
// 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 800001

int N,K;
int G[2][LIM];
char O[LIM];
pair< int, pair<char,int> > P[LIM];
int C[LIM],B[LIM];
int sufCB[LIM],sufCH[LIM];
int ss,nfr;
PR st[LIM],fr[LIM];

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int i,j,a,b,c,d,p;
	LL ans;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input, and generate values
			Read(N);
				Fox(i,2)
				{
					Read(G[i][0]),Read(G[i][1]),Read(a),Read(b),Read(c),Read(d);
						FoxI(j,2,N-1)
							G[i][j]=((LL)a*G[i][j-2] + (LL)b*G[i][j-1] + c)%d+1;
				}
			scanf("%s",&O);
				Fox(i,N)
					P[i]=mp(G[0][i],mp(O[i],G[1][i]));
			// sort objects by position
			sort(P,P+N);
			// get list of clams
			K=0;
				Fox(i,N)
					if (P[i].y.x=='C')
						C[K++]=i;
			// get list of useful rocks up to final clam
			ss=0;
				FoxR(i,C[K-1])
					if ((P[i].y.x=='R') && ((!ss) || (P[i].y.y>st[ss-1].x)))
						st[ss++]=mp(P[i].y.y,P[i].x);
			// get clams' backtrack positions
			Fill(B,-1);
				Fox(i,K)
				{
					j=lower_bound(st,st+ss,mp(P[C[i]].y.y+1,0))-st;
						if (j==ss)
							break;
					B[i]=st[j].y;
				}
			// precompute suffix mins/maxes of clams' backtrack positions/hardnesses
			sufCB[K]=INF,sufCH[K]=0;
				FoxR(i,K)
				{
					sufCB[i]=min(sufCB[i+1],B[i]);
					sufCH[i]=max(sufCH[i+1],P[C[i]].y.y);
				}
			// get list of useful rocks past final clam
			nfr=0;
				FoxI(i,C[K-1]+1,N-1)
					if ((!nfr) || (P[i].y.y>fr[nfr-1].x))
						fr[nfr++]=mp(P[i].y.y,P[i].x);
			// DP
			ans=2*INF;
			ss=0;
				Fox(i,K)
				{
					// perform optional transition from an earlier clam
						if (!i)
							d=0;
						else
						{
							p=P[C[i-1]].x;
								while (ss>1)
								{
									a=st[ss-1].y;
									b=min(a,st[ss-2].y);
										if ((LL)st[ss-1].x+2*max(0,p-a)<(LL)st[ss-2].x+2*max(0,p-b))
											break;
									st[ss-2].y=b;
									ss--;
								}
							d=st[ss-1].x+2*max(0,p-st[ss-1].y);
						}
					st[ss++]=mp(d,B[i]);
					// consider concluding with transition to final clam
					p=P[C[K-1]].x;
						if (sufCB[i]>=0)
							Min(ans,(LL)d+max(0,p-sufCB[i]));
					a=lower_bound(fr,fr+nfr,mp(sufCH[i]+1,0))-fr;
						if (a<nfr)
							Min(ans,(LL)d+(fr[a].y-p));
						if (B[i]<0)
							break;
				}
				if (ans==2*INF)
					ans=-1;
				else
					ans+=P[C[K-1]].x;
			// output
			printf("Case #%d: %lld\n",t,ans);
		}
	return(0);
}