2021/round3/expl-ore-ation_ch2.cpp

#include <algorithm>
#include <iostream>
#include <set>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

const int INF = 1000000000;
const int LIM = 1000002;

struct UnionFind {
  int N;
  vector<int> root, rank, sidx;
  vector<set<pair<int, int>>> S;

  UnionFind(int _N) : N(_N), root(_N), rank(_N, 0), sidx(_N), S(_N) {
    for (int i = 0; i < N; i++) {
      root[i] = i;
      sidx[i] = i;
      S[i].emplace(-INF, -INF);
      S[i].emplace(INF, INF);
    }
  }

  int find(int i) {
    if (root[i] != i) {
      root[i] = find(root[i]);
    }
    return root[i];
  }

  void merge(int i, int j) {
    i = find(i);
    j = find(j);
    if (i == j) {
      return;
    }
    if (rank[i] > rank[j]) {
      swap(i, j);
    }
    root[i] = j;
    if (rank[i] == rank[j]) {
      rank[j]++;
    }
    // Merge robot interval sets (ensuring j gets the larger one, and merging the
    // other into it).
    if (S[sidx[i]].size() > S[sidx[j]].size()) {
      swap(sidx[i], sidx[j]);
    }
    auto &SA = S[sidx[i]], &SB = S[sidx[j]];
    for (auto p : SA) {
      if (p.first == -INF || p.first == INF) {
        continue;
      }
      auto it = prev(SB.lower_bound(make_pair(p.first + 1, -1)));
      if (it->second < p.first - 1) {
        it++;
      }
      while (it->first <= p.second + 1) {
        p.first = min(p.first, it->first);
        p.second = max(p.second, it->second);
        it = SB.erase(it);
      }
      SB.insert(p);
    }
    SA.clear();
  }
};

int R, C, N, K;
int H[LIM];
vector<pair<int, int>> children[LIM];
vector<tuple<int, int, int, int>> A;

pair<long long, long long> solve() {
  A.clear();
  for (int i = 0; i < LIM; i++) {
    children[i].clear();
  }
  // Input.
  cin >> R >> C;
  N = R * C;
  for (int i = 0, j; i < N; i++) {
    cin >> H[i];
    if ((j = i - C) >= 0) {  // Up.
      A.emplace_back(-min(H[i], H[j]), INF, i, j);
    }
    if (i % C > 0 && (j = i - 1) >= 0) {  // Left.
      A.emplace_back(-min(H[i], H[j]), INF, i, j);
    }
  }
  for (int i = 0; i < N; i++) {
    int s;
    cin >> s;
    children[i].emplace_back(0, s);
  }
  cin >> K;
  for (int i = 0; i < K; i++) {
    int a, b, u;
    cin >> a >> b >> u;
    a--;
    b--;
    int j = a * C + b;
    if (i == 0) {
      children[j].clear();
    }
    children[j].emplace_back(i, u);
  }
  // Determine interval of situations per original/updated S value.
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < children[i].size(); j++) {
      int a = children[i][j].first;
      int b = j < int(children[i].size()) - 1
        ? children[i][j + 1].first - 1
        : K - 1;
      A.emplace_back(-children[i][j].second, i, a, b);
    }
  }
  // Process edges/samples in non-increasing order of elevation.
  UnionFind U(N);
  sort(A.begin(), A.end());
  pair<long long, long long> ans{0, 0};
  for (const auto &t : A) {
    int h = -get<0>(t), i = get<1>(t), a = get<2>(t), b = get<3>(t);
    if (i < INF) {  // Sample.
      if (H[i] <= h) {  // Impossible to collect.
        continue;
      }
      ans.first += b - a + 1;  // Collect it in each relevant situation.
      auto &S = U.S[U.sidx[U.find(i)]];
      // Add new robots to relevant situations as necessary.
      auto it = prev(S.lower_bound(make_pair(a + 1, -1)));
      if (it->second < a - 1) {
        it++;
      }
      while (it->first <= b + 1) {
        a = min(a, it->first);
        b = max(b, it->second);
        ans.second -= it->second - it->first + 1;
        it = S.erase(it);
      }
      S.emplace(a, b);
      ans.second += b - a + 1;
      continue;
    }
    U.merge(a, b);  // Edge.
  }
  return ans;
}

int main() {
  int T;
  cin >> T;
  for (int t = 1; t <= T; t++) {
    auto ans = solve();
    cout << "Case #" << t << ": " << ans.first << " " << ans.second << endl;
  }
  return 0;
}