2020/round3/mail_security.cpp

// Mail Security
// Solution by 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 <unordered_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);

#define GETCHAR getchar_unlocked

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 1000000

int N, M, K, X;
int S[LIM], P[LIM];

void ReadSeq(int* V, int N, int K)
{
  int i, A, B, C, D;
  Fox(i, K)
    Read(V[i]);
  Read(A), Read(B), Read(C), Read(D);
  FoxI(i, K, N - 1)
    V[i] = ((LL)A * V[i - 2] + (LL)B * V[i - 1] + C) % D + 1;
}

bool Valid(int np)
{
  int i;
  // assemble list of relevant objects
  vector<PR> O;
  FoxR(i, N) // largest np mailboxes, plus any large enough for a key
    if (O.size() < np || S[i] >= X)
      O.pb(mp(S[i], 1));
  int nb = Sz(O);
  Fox(i, np) // smallest np packages
    O.pb(mp(P[i], 0));
  sort(All(O), std::greater<>());
  // iterate over objects by non-increasing capacity/size
  multiset<PR> AC; // available pairs of (capacity % X, capacity)
  LL nk = 0;
  for (auto o : O)
  {
    // mailbox?
    if (o.y)
    {
      nk += o.x / X;
      AC.insert(mp(o.x % X, o.x));
      continue;
    }
    // package
    if (AC.empty())
      return(0);
    auto I = AC.lower_bound(mp(o.x % X, 0));
    if (I == AC.end())
      I = AC.begin();
    int c = I->y;
    AC.erase(I);
    nk += (c - o.x) / X - c / X;
  }
  return(nk >= nb - 1);
}

int ProcessCase()
{
  // input
  Read(N), Read(M), Read(K), Read(X);
  ReadSeq(S, N, K);
  ReadSeq(P, M, K);
  // sort objects by capacity/size
  sort(S, S + N);
  sort(P, P + M);
  // binary search
  int r1 = 0, r2 = min(N, M);
  while (r1 < r2)
  {
    int m = (r1 + r2 + 1) / 2;
    if (Valid(m))
      r1 = m;
    else
      r2 = m - 1;
  }
  return(r1);
}

int main()
{
  int T, t;
  Read(T);
  Fox1(t, T)
    printf("Case #%d: %d\n", t, ProcessCase());
  return(0);
}