test/verify/yosupo-static-range-inversions-query.test.cpp

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Last update: 2026-08-10 14:24:31+00:00
Problem: https://judge.yosupo.jp/problem/static_range_inversions_query

Depends on

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/static_range_inversions_query
// clang-format on

#include <algorithm>
#include <iostream>
#include <vector>

#include "../../other/mo.hpp"
#include "../../structure/others/binary-indexed-tree.hpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  Mo mo(N, Q);
  for (int i = 0; i < Q; i++) {
    int l, r;
    cin >> l >> r;
    mo.add_query(l, r);
  }
  vector<int> xs = A;
  sort(xs.begin(), xs.end());
  xs.erase(unique(xs.begin(), xs.end()), xs.end());
  for (auto& a : A) {
    a = lower_bound(xs.begin(), xs.end(), a) - xs.begin();
  }
  BinaryIndexedTree<int> bit(xs.size());
  long long inv = 0, all = 0;
  vector<long long> ans(Q);
  auto add_left = [&](int idx) {
    inv += bit.prod(A[idx]);
    bit.apply(A[idx], 1);
    all++;
  };
  auto add_right = [&](int idx) {
    inv += all - bit.prod(A[idx] + 1);
    bit.apply(A[idx], 1);
    ++all;
  };
  auto erase_left = [&](int idx) {
    inv -= bit.prod(A[idx]);
    bit.apply(A[idx], -1);
    --all;
  };
  auto erase_right = [&](int idx) {
    inv -= all - bit.prod(A[idx] + 1);
    bit.apply(A[idx], -1);
    --all;
  };
  auto query = [&](int idx) { ans[idx] = inv; };
  mo.calclate_queries(add_left, add_right, erase_left, erase_right, query);
  for (auto& p : ans) cout << p << "\n";
}

#line 1 "test/verify/yosupo-static-range-inversions-query.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/static_range_inversions_query
// clang-format on

#include <algorithm>
#include <iostream>
#include <vector>

#line 2 "other/mo.hpp"

#line 4 "other/mo.hpp"
#include <cassert>
#include <cmath>
#include <iterator>
#include <numeric>
#include <utility>
#line 10 "other/mo.hpp"

struct Mo {
 private:
  int n, w;
  std::vector<int> ord;
  std::vector<std::pair<int, int> > lr;

 public:
  Mo(int n, int q) : n(n), ord(q) {
    w = std::max<int>(1, n / std::max(1.0, std::sqrt(q * 2.0 / 3.0)));
    std::iota(ord.begin(), ord.end(), 0);
    lr.reserve(q);
  }

  void add_query(int l, int r) {
    assert(0 <= l and l < r and r <= n);
    lr.emplace_back(l, r);
  }

  template <typename AL, typename AR, typename EL, typename ER, typename Q>
  void calclate_queries(const AL& add_left, const AR& add_right,
                        const EL& erase_left, const ER& erase_right,
                        const Q& query) {
    assert(lr.size() == ord.size());
    std::vector<int> bs(n);
    for (int i = 0, cnt = 0, b = 0; i < n; i++) {
      bs[i] = b;
      if (++cnt == w) {
        ++b;
        cnt = 0;
      }
    }
    std::sort(ord.begin(), ord.end(), [&](int a, int b) {
      int a_block = bs[lr[a].first];
      int b_block = bs[lr[b].first];
      if (a_block != b_block) return a_block < b_block;
      if (a_block & 1)
        return lr[a].second < lr[b].second;
      else
        return lr[a].second > lr[b].second;
    });
    int l = 0, r = 0;
    for (auto idx : ord) {
      while (l > lr[idx].first) add_left(--l);
      while (r < lr[idx].second) add_right(r++);
      while (l < lr[idx].first) erase_left(l++);
      while (r > lr[idx].second) erase_right(--r);
      query(idx);
    }
  }

  template <typename A, typename E, typename Q>
  void calclate_queries(const A& add, const E& erase, const Q& query) {
    calclate_queries(add, add, erase, erase, query);
  }
};
#line 2 "structure/others/binary-indexed-tree.hpp"

#line 5 "structure/others/binary-indexed-tree.hpp"

template <typename T>
struct BinaryIndexedTree {
 private:
  int n;
  std::vector<T> data;

 public:
  BinaryIndexedTree() = default;

  explicit BinaryIndexedTree(int n) : n(n) { data.assign(n + 1, T()); }

  explicit BinaryIndexedTree(const std::vector<T>& v)
      : BinaryIndexedTree((int)v.size()) {
    build(v);
  }

  void build(const std::vector<T>& v) {
    assert(n == (int)v.size());
    for (int i = 1; i <= n; i++) data[i] = v[i - 1];
    for (int i = 1; i <= n; i++) {
      int j = i + (i & -i);
      if (j <= n) data[j] += data[i];
    }
  }

  void apply(int k, const T& x) {
    for (++k; k <= n; k += k & -k) data[k] += x;
  }

  T prod(int r) const {
    T ret = T();
    for (; r > 0; r -= r & -r) ret += data[r];
    return ret;
  }

  T prod(int l, int r) const { return prod(r) - prod(l); }

  int lower_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] < x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }

  int upper_bound(T x) const {
    int i = 0;
    for (int k = 1 << (32 - __builtin_clz(n)); k > 0; k >>= 1) {
      if (i + k <= n && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};
#line 11 "test/verify/yosupo-static-range-inversions-query.test.cpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (auto& a : A) cin >> a;
  Mo mo(N, Q);
  for (int i = 0; i < Q; i++) {
    int l, r;
    cin >> l >> r;
    mo.add_query(l, r);
  }
  vector<int> xs = A;
  sort(xs.begin(), xs.end());
  xs.erase(unique(xs.begin(), xs.end()), xs.end());
  for (auto& a : A) {
    a = lower_bound(xs.begin(), xs.end(), a) - xs.begin();
  }
  BinaryIndexedTree<int> bit(xs.size());
  long long inv = 0, all = 0;
  vector<long long> ans(Q);
  auto add_left = [&](int idx) {
    inv += bit.prod(A[idx]);
    bit.apply(A[idx], 1);
    all++;
  };
  auto add_right = [&](int idx) {
    inv += all - bit.prod(A[idx] + 1);
    bit.apply(A[idx], 1);
    ++all;
  };
  auto erase_left = [&](int idx) {
    inv -= bit.prod(A[idx]);
    bit.apply(A[idx], -1);
    --all;
  };
  auto erase_right = [&](int idx) {
    inv -= all - bit.prod(A[idx] + 1);
    bit.apply(A[idx], -1);
    --all;
  };
  auto query = [&](int idx) { ans[idx] = inv; };
  mo.calclate_queries(add_left, add_right, erase_left, erase_right, query);
  for (auto& p : ans) cout << p << "\n";
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	3 ms	4 MB
g++	max_00	AC	838 ms	7 MB
g++	max_01	AC	726 ms	7 MB
g++	max_02	AC	713 ms	7 MB
g++	random_00	AC	120 ms	5 MB
g++	random_01	AC	217 ms	5 MB
g++	random_02	AC	268 ms	5 MB
g++	small_a_00	AC	388 ms	6 MB
g++	small_n_00	AC	8 ms	4 MB
g++	small_n_01	AC	23 ms	5 MB
g++	small_n_02	AC	19 ms	4 MB
g++	small_n_03	AC	14 ms	4 MB
g++	small_n_04	AC	7 ms	4 MB
clang++	example_00	AC	3 ms	4 MB
clang++	max_00	AC	706 ms	7 MB
clang++	max_01	AC	728 ms	7 MB
clang++	max_02	AC	724 ms	7 MB
clang++	random_00	AC	133 ms	5 MB
clang++	random_01	AC	226 ms	5 MB
clang++	random_02	AC	293 ms	5 MB
clang++	small_a_00	AC	437 ms	6 MB
clang++	small_n_00	AC	7 ms	4 MB
clang++	small_n_01	AC	23 ms	5 MB
clang++	small_n_02	AC	18 ms	4 MB
clang++	small_n_03	AC	14 ms	4 MB
clang++	small_n_04	AC	7 ms	4 MB