test/verify/yosupo-rectangle-sum.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/rectangle_sum

Depends on

• Succinct Indexable Dictionary(完備辞書) (structure/wavelet/succinct-indexable-dictionary.hpp)
• Wavelet Matrix Rectangle Sum (structure/wavelet/wavelet-matrix-rectangle-sum.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/rectangle_sum

#include "../../template/template.hpp"

#include "../../structure/wavelet/succinct-indexable-dictionary.hpp"
#include "../../structure/wavelet/wavelet-matrix-rectangle-sum.hpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > x(N), y(N), w(N);
  vector< pair< int, int > > xs(N);
  for(int i = 0; i < N; i++) {
    cin >> x[i] >> y[i] >> w[i];
    xs[i] = {x[i], i};
  }
  sort(begin(xs), end(xs));
  vector< int > ys(N);
  vector< int64 > ws(N);
  for(int i = 0; i < N; i++) {
    x[i] = lower_bound(begin(xs), end(xs), make_pair(x[i], i)) - begin(xs);
    ys[x[i]] = y[i];
    ws[x[i]] = w[i];
  }
  CompressedWaveletMatrixRectangleSum< int, 18, int64 > mat(ys, ws);
  while(Q--) {
    int l, r, d, u;
    cin >> l >> d >> r >> u;
    l = lower_bound(begin(xs), end(xs), make_pair(l, -1)) - begin(xs);
    r = lower_bound(begin(xs), end(xs), make_pair(r, -1)) - begin(xs);
    cout << mat.rect_sum(l, r, d, u) << "\n";
  }
}

#line 1 "test/verify/yosupo-rectangle-sum.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/rectangle_sum

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-rectangle-sum.test.cpp"

#line 1 "structure/wavelet/succinct-indexable-dictionary.hpp"
/**
 * @brief Succinct Indexable Dictionary(完備辞書)
 */
struct SuccinctIndexableDictionary {
  size_t length;
  size_t blocks;
  vector<unsigned> bit, sum;

  SuccinctIndexableDictionary() = default;

  SuccinctIndexableDictionary(size_t length)
      : length(length), blocks((length + 31) >> 5) {
    bit.assign(blocks, 0U);
    sum.assign(blocks, 0U);
  }

  void set(int k) { bit[k >> 5] |= 1U << (k & 31); }

  void build() {
    sum[0] = 0U;
    for (int i = 1; i < blocks; i++) {
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }

  bool operator[](int k) { return (bool((bit[k >> 5] >> (k & 31)) & 1)); }

  int rank(int k) {
    return (sum[k >> 5] +
            __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
  }

  int rank(bool val, int k) { return (val ? rank(k) : k - rank(k)); }
};
#line 1 "structure/wavelet/wavelet-matrix-rectangle-sum.hpp"
/*
 * @brief Wavelet Matrix Rectangle Sum
 *
 */
template <typename T, int MAXLOG, typename D>
struct WaveletMatrixRectangleSum {
  size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  vector<D> ds[MAXLOG];
  int mid[MAXLOG];

  WaveletMatrixRectangleSum() = default;

  WaveletMatrixRectangleSum(const vector<T> &v, const vector<D> &d)
      : length(v.size()) {
    assert(v.size() == d.size());
    vector<int> l(length), r(length), ord(length);
    iota(begin(ord), end(ord), 0);
    for (int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for (int i = 0; i < length; i++) {
        if (((v[ord[i]] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = ord[i];
        } else {
          l[left++] = ord[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      ord.swap(l);
      for (int i = 0; i < right; i++) {
        ord[left + i] = r[i];
      }
      ds[level].resize(length + 1);
      ds[level][0] = D();
      for (int i = 0; i < length; i++) {
        ds[level][i + 1] = ds[level][i] + d[ord[i]];
      }
    }
  }

  pair<int, int> succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f,
            matrix[level].rank(f, r) + mid[level] * f};
  }

  // count d[i] s.t. (l <= i < r) && (v[i] < upper)
  D rect_sum(int l, int r, T upper) {
    D ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((upper >> level) & 1);
      if (f)
        ret += ds[level][matrix[level].rank(false, r)] -
               ds[level][matrix[level].rank(false, l)];
      tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  D rect_sum(int l, int r, T lower, T upper) {
    return rect_sum(l, r, upper) - rect_sum(l, r, lower);
  }
};

template <typename T, int MAXLOG, typename D>
struct CompressedWaveletMatrixRectangleSum {
  WaveletMatrixRectangleSum<int, MAXLOG, D> mat;
  vector<T> ys;

  CompressedWaveletMatrixRectangleSum(const vector<T> &v, const vector<D> &d)
      : ys(v) {
    sort(begin(ys), end(ys));
    ys.erase(unique(begin(ys), end(ys)), end(ys));
    vector<int> t(v.size());
    for (int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletMatrixRectangleSum<int, MAXLOG, D>(t, d);
  }

  inline int get(const T &x) {
    return lower_bound(begin(ys), end(ys), x) - begin(ys);
  }

  D rect_sum(int l, int r, T upper) { return mat.rect_sum(l, r, get(upper)); }

  D rect_sum(int l, int r, T lower, T upper) {
    return mat.rect_sum(l, r, get(lower), get(upper));
  }
};
#line 7 "test/verify/yosupo-rectangle-sum.test.cpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > x(N), y(N), w(N);
  vector< pair< int, int > > xs(N);
  for(int i = 0; i < N; i++) {
    cin >> x[i] >> y[i] >> w[i];
    xs[i] = {x[i], i};
  }
  sort(begin(xs), end(xs));
  vector< int > ys(N);
  vector< int64 > ws(N);
  for(int i = 0; i < N; i++) {
    x[i] = lower_bound(begin(xs), end(xs), make_pair(x[i], i)) - begin(xs);
    ys[x[i]] = y[i];
    ws[x[i]] = w[i];
  }
  CompressedWaveletMatrixRectangleSum< int, 18, int64 > mat(ys, ws);
  while(Q--) {
    int l, r, d, u;
    cin >> l >> d >> r >> u;
    l = lower_bound(begin(xs), end(xs), make_pair(l, -1)) - begin(xs);
    r = lower_bound(begin(xs), end(xs), make_pair(r, -1)) - begin(xs);
    cout << mat.rect_sum(l, r, d, u) << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	7 ms	4 MB
g++	max_random_00	AC	683 ms	42 MB
g++	max_random_01	AC	687 ms	42 MB
g++	max_random_02	AC	684 ms	42 MB
g++	n_131072_00	AC	368 ms	29 MB
g++	random_00	AC	457 ms	28 MB
g++	random_01	AC	493 ms	33 MB
g++	random_02	AC	258 ms	14 MB
g++	small_00	AC	8 ms	4 MB
g++	small_01	AC	7 ms	4 MB
g++	small_02	AC	8 ms	4 MB
g++	xy_concentrate_00	AC	637 ms	42 MB
g++	xy_concentrate_01	AC	639 ms	42 MB
g++	xy_concentrate_02	AC	628 ms	42 MB
clang++	example_00	AC	7 ms	4 MB
clang++	max_random_00	AC	737 ms	42 MB
clang++	max_random_01	AC	738 ms	42 MB
clang++	max_random_02	AC	745 ms	42 MB
clang++	n_131072_00	AC	389 ms	29 MB
clang++	random_00	AC	486 ms	28 MB
clang++	random_01	AC	520 ms	33 MB
clang++	random_02	AC	259 ms	14 MB
clang++	small_00	AC	9 ms	4 MB
clang++	small_01	AC	8 ms	4 MB
clang++	small_02	AC	8 ms	4 MB
clang++	xy_concentrate_00	AC	646 ms	42 MB
clang++	xy_concentrate_01	AC	670 ms	42 MB
clang++	xy_concentrate_02	AC	671 ms	42 MB

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