2021/round3/expl-ore-ation_ch3.cpp

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

const int INF = 1000000000;
const int LIM = 1000002;
const int LIM2 = 2000002;
const int LIM3 = 23;

int R, C, N, K;
int H[LIM], S[LIM];
vector<tuple<int, int, int>> A;
pair<int, int> curr;
int M;
int children[LIM2][2];
int parent[LIM2][LIM3];
int high[LIM2];

struct UnionFind {
  int N;
  vector<int> root, rank, node;

  UnionFind(int _N) : N(_N), root(_N), rank(_N, 0), node(_N) {
    for (int i = 0; i < N; i++) {
      root[i] = i;
      node[i] = M;
      children[M][0] = children[M][1] = -1;
      high[M++] = INF + 1;
    }
  }

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

  void merge(int i, int j, int e) {
    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]++;
    }
    // Make both components' tree M children of a new node.
    children[M][0] = node[i];
    children[M][1] = node[j];
    high[M] = e;
    node[j] = M++;
  }
};

struct HeavyLightTree {
  int heavy[LIM2];
  int root[LIM2], treePos[LIM2], inv[LIM2];
  int ind, L[LIM2], R[LIM2];
  multiset<int> S, S2;

  int dfs(int v) {
    L[v] = ind++;
    for (int i = 0; i < LIM3 - 1; i++) {
      int p = parent[v][i];
      if (p < 0) {
        break;
      }
      parent[v][i + 1] = parent[p][i];
    }
    int size = 1, maxSubtree = 0;
    for (int u : children[v]) {
      if (u < 0) {
        continue;
      }
      parent[u][0] = v;
      int subtree = dfs(u);
      if (subtree > maxSubtree) {
        heavy[v] = u;
        maxSubtree = subtree;
      }
      size += subtree;
    }
    R[v] = ind - 1;
    return size;
  }

  void init() {
    fill_n(heavy, M, -1);
    ind = 0;
    dfs(M - 1);
    for (int i = 0, currentPos = 0; i < M; i++) {
      if (parent[i][0] == -1 || heavy[parent[i][0]] != i) {
        for (int j = i; j != -1; j = heavy[j]) {
          root[j] = i;
          inv[currentPos] = j;
          treePos[j] = currentPos++;
        }
      }
    }
    S.clear();
    S2.clear();
    S.insert(-1);
  }

  void update(int i, bool ins) {
    if (ins) {
      S.insert(treePos[i]);
      S2.insert(L[i]);
    } else {
      S.erase(S.find(treePos[i]));
      S2.erase(S2.find(L[i]));
    }
  }

  int find_closest_ancestor_set(int i) {
    while (i >= 0) {
      int j = root[i];
      int k = *prev(S.lower_bound(treePos[i] + 1));
      if (k >= treePos[j]) {
        return inv[k];
      }
      i = parent[j][0];
    }
    return -1;
  }

  bool subtree_has_set_M(int i, bool inc) {
    auto it = S2.lower_bound(L[i] + (inc ? 0 : 1));
    return it != S2.end() && *it <= R[i];
  }
};

HeavyLightTree HLT;

void update_cell(int i, bool ins) {
  // Sample is irrelevant (impossible to collect)?
  int s = S[i];
  if (s >= H[i]) {
    return;
  }
  // Register collection.
  int d = ins ? 1 : -1;
  curr.first += d;
  // Find corresponding tree node (highest valid ancestor of leaf node).
  for (int j = LIM3 - 1; j >= 0; j--) {
    if (parent[i][j] >= 0 && high[parent[i][j]] > s) {
      i = parent[i][j];
    }
  }
  // Update HLD (if deleting).
  if (!ins) {
    HLT.update(i, ins);
  }
  // Update can only be relevant if no samples in i's subtree.
  if (!HLT.subtree_has_set_M(i, true)) {
    // Find closest ancestor with sample (if any).
    int a = HLT.find_closest_ancestor_set(i);
    // Update is relevant if a doesn't exist, or if there are other samples
    // amongst a's descendants
    if (a < 0 || HLT.subtree_has_set_M(a, false)) {
      curr.second += d;
    }
  }
  // Update HLD (if inserting).
  if (ins) {
    HLT.update(i, ins);
  }
}

pair<long long, long long> solve() {
  A.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]), i, j);
    }
    if (i % C > 0 && (j = i - 1) >= 0) {  // Left.
      A.emplace_back(-min(H[i], H[j]), i, j);
    }
  }
  for (int i = 0; i < N; i++) {
    cin >> S[i];
  }
  // Process edges in non-increasing order of elevation, and construct tree of
  // connected regions.
  M = 0;
  UnionFind U(N);
  sort(A.begin(), A.end());
  for (auto t : A) {
    U.merge(get<1>(t), get<2>(t), -get<0>(t));
  }
  memset(parent, -1, sizeof(parent[0]) * M);
  HLT.init();
  // Insert initial samples.
  curr = make_pair(0, 0);
  for (int i = 0; i < N; i++) {
    update_cell(i, 1);
  }
  // Process updates.
  cin >> K;
  pair<long long, long long> ans{0, 0};
  int prevY = 0;
  while (K--) {
    int i, j;
    cin >> i >> j;
    i = (i ^ prevY) - 1;
    j = (j ^ prevY) - 1;
    i = i * C + j;
    update_cell(i, 0);
    cin >> S[i];
    S[i] ^= prevY;
    update_cell(i, 1);
    ans.first += curr.first;
    ans.second += curr.second;
    prevY = curr.second;
  }
  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;
}