2020/finals/spider_spring.cpp

// Spider Spring
// 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_map>
#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);
}

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;
}

#define MOD 1000000007
#define LIM 1000001

#define TVAL LL
#define TLAZY pair<LL,LL> // (set, increase)
#define TLIM 2100000

TVAL ZERO_VAL = 0;
TLAZY ZERO_LAZY = mp(0, 0);

struct SegTree
{
  void UpdateValForUpdateOrLazy(TVAL& a, TLAZY v)
  {
    if (v.x)
      a = v.x;
    if (v.y)
      a += v.y;
  }

  void UpdateLazyForUpdateOrLazy(TLAZY& a, TLAZY v)
  {
    if (v.x)
      a.x = v.x;
    if (v.y)
      a.y += v.y;
  }

  TVAL CombVals(TVAL v1, TVAL v2)
  {
    return(v1 + v2);
  }

  int N, sz;
  TVAL tree[TLIM];
  TLAZY lazy[TLIM];

  SegTree() {}

  SegTree(int _N)
  {
    Init(_N);
  }

  void Init(int _N)
  {
    N = _N;
    for (sz = 1; sz < N; sz <<= 1);
    Clear();
  }

  void Clear()
  {
    int i;
    Fox(i, sz << 1)
      tree[i] = ZERO_VAL;
    Fox(i, sz << 1)
      lazy[i] = ZERO_LAZY;
  }

  void Prop(int i)
  {
    TLAZY v = lazy[i];
    lazy[i] = ZERO_LAZY;
    UpdateValForUpdateOrLazy(tree[i], v);
    if (i < sz)
    {
      int c1 = i << 1, c2 = c1 + 1;
      UpdateLazyForUpdateOrLazy(lazy[c1], v);
      UpdateLazyForUpdateOrLazy(lazy[c2], v);
    }
  }

  void Comp(int i)
  {
    int c1 = i << 1, c2 = c1 + 1;
    tree[i] = CombVals(tree[c1], tree[c2]);
  }

  TVAL Query(
    int a, int b,
    int i = 1, int r1 = 0, int r2 = -1
  ) {
    if (r2 < 0)
      r2 = sz - 1;
    Prop(i);
    if (a <= r1 && r2 <= b)
      return(tree[i]);
    int m = (r1 + r2) >> 1, c = i << 1;
    TVAL ret = ZERO_VAL;
    if (a <= m)
      ret = CombVals(ret, Query(a, b, c, r1, m));
    if (b > m)
      ret = CombVals(ret, Query(a, b, c + 1, m + 1, r2));
    return(ret);
  }

  void Update(
    int a, int b,
    TLAZY v,
    int i = 1, int r1 = 0, int r2 = -1
  ) {
    if (r2 < 0)
      r2 = sz - 1;
    Prop(i);
    if (a <= r1 && r2 <= b)
    {
      UpdateLazyForUpdateOrLazy(lazy[i], v);
      Prop(i);
      return;
    }
    int m = (r1 + r2) >> 1, c = i << 1;
    if (a <= m)
      Update(a, b, v, c, r1, m);
    if (b > m)
      Update(a, b, v, c + 1, m + 1, r2);
    Prop(c), Prop(c + 1), Comp(i);
  }

  void UpdateOne(int i, TLAZY v) {
    i += sz;
    UpdateValForUpdateOrLazy(tree[i], v);
    while (i > 1)
    {
      i >>= 1;
      Comp(i);
    }
  }
};

int N, M, K;
int H[LIM], X[LIM], Y[LIM], Z[LIM], W[LIM];
set<int> LS;

// 0: height of column i
// 1: sum of A endpoint weights with endpoint value i
// 2: sum of A endpoint weighted values with endpoint value i
// 3: sum of B endpoint weights with endpoint value i
// 4: sum of B endpoint weighted values with endpoint value i
SegTree ST[5];

void UpdateHeights(int a, int b, int h)
{
  ST[0].Update(a, b, mp(h, 0));
}

void UpdateLineSegment(int i, int d) // d = 1 (add) / -1 (remove)
{
  if (i < 0 || i + 1 >= N)
    return;
  int a = ST[0].Query(i, i), b = ST[0].Query(i + 1, i + 1);
  if (a > b)
    swap(a, b);
  LL w = (LL)(i + 1) * (N - i - 1);
  ST[1].UpdateOne(a, mp(0, w % MOD * d));
  ST[2].UpdateOne(a, mp(0, a * w % MOD * d));
  ST[3].UpdateOne(b, mp(0, w % MOD * d));
  ST[4].UpdateOne(b, mp(0, b * w % MOD * d));
  if (d > 0)
    LS.insert(i);
  else
    LS.erase(i);
}

int ProcessCase()
{
  int i;
  // input
  Read(N), Read(M), Read(K);
  ReadSeq(H, N, K);
  ReadSeq(X, M, K);
  ReadSeq(Y, M, K);
  ReadSeq(Z, M, K);
  ReadSeq(W, M, K);
  // init segment trees, line segment set, and horizontal sum
  Fox(i, 5)
    ST[i].Init(!i ? N : LIM);
  LS.clear();
  LL horiz = 0;
  Fox(i, N)
  {
    UpdateHeights(i, i, H[i]);
    UpdateLineSegment(i - 1, 1);
    horiz = (horiz + (LL)i * (N - i)) % MOD;
  }
  // process events
  int ans = 1;
  Fox(i, M)
  {
    // update
    int x = X[i] - 1;
    int y = min(x + Y[i], N) - 1;
    int z = Z[i];
    auto I = LS.lower_bound(x - 1);
    while (I != LS.end() && *I <= y)
    {
      int k = *I;
      I++;
      UpdateLineSegment(k, -1);
    }
    UpdateHeights(x, y, z);
    UpdateLineSegment(x - 1, 1);
    UpdateLineSegment(y, 1);
    // query
    int w = W[i];
    LL d1 = ST[4].Query(w + 1, LIM - 1) - ST[2].Query(w + 1, LIM - 1);
    LL d2 = ST[3].Query(w + 1, LIM - 1) - ST[1].Query(w + 1, LIM - 1);
    LL vert = ((d1 - d2 % MOD * w) % MOD + MOD) % MOD;
    ans = (LL)ans * (horiz + vert) * 2 % MOD;
  }
  return(ans);
}

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