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

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• Last update: 2022-09-11 00:53:50+09:00
• Problem: https://judge.yosupo.jp/problem/static_range_inversions_query

Depends on

• Mo's Algorithm (other/mo.hpp)
• Binary-Indexed-Tree(BIT) (structure/others/binary-indexed-tree.hpp)
• template/template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query"

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

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

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > A(N);
  for(auto &a : A) cin >> a;
  Mo mo(N);
  for(int i = 0; i < Q; i++) {
    int l, r;
    cin >> l >> r;
    mo.add(l, r);
  }
  vector< int > xs{A};
  sort(begin(xs), end(xs));
  xs.erase(unique(begin(xs), end(xs)), end(xs));
  for(auto &a : A) a = lower_bound(begin(xs), end(xs), a) - begin(xs);
  BinaryIndexedTree< int > bit(xs.size());
  int64_t inv = 0, all = 0;
  vector< int64_t > 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 out = [&](int idx) {
    ans[idx] = inv;
  };
  mo.build(add_left, add_right, erase_left, erase_right, out);
  for(auto &p : ans) cout << p << "\n";
}

#line 1 "test/verify/yosupo-static-range-inversions-query.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query"

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

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

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-static-range-inversions-query.test.cpp"

#line 1 "other/mo.hpp"
/**
 * @brief Mo's Algorithm
 */
struct Mo {
  int n;
  vector< pair< int, int > > lr;

  explicit Mo(int n) : n(n) {}

  void add(int l, int r) { /* [l, r) */
    lr.emplace_back(l, r);
  }

  template< typename AL, typename AR, typename EL, typename ER, typename O >
  void build(const AL &add_left, const AR &add_right, const EL &erase_left, const ER &erase_right, const O &out) {
    int q = (int) lr.size();
    int bs = n / min< int >(n, sqrt(q));
    vector< int > ord(q);
    iota(begin(ord), end(ord), 0);
    sort(begin(ord), end(ord), [&](int a, int b) {
      int ablock = lr[a].first / bs, bblock = lr[b].first / bs;
      if(ablock != bblock) return ablock < bblock;
      return (ablock & 1) ? lr[a].second > lr[b].second : 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);
      out(idx);
    }
  }

  template< typename A, typename E, typename O >
  void build(const A &add, const E &erase, const O &out) {
    build(add, add, erase, erase, out);
  }
};
#line 1 "structure/others/binary-indexed-tree.hpp"
/**
 * @brief Binary-Indexed-Tree(BIT)
 * @docs docs/binary-indexed-tree.md
 */
template< typename T >
struct BinaryIndexedTree {
private:
  int n;
  vector< T > data;

public:
  BinaryIndexedTree() = default;

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

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

  void build(const 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 << (__lg(n) + 1); 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 << (__lg(n) + 1); k > 0; k >>= 1) {
      if(i + k <= n && data[i + k] <= x) {
        x -= data[i + k];
        i += k;
      }
    }
    return i;
  }
};
#line 7 "test/verify/yosupo-static-range-inversions-query.test.cpp"

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > A(N);
  for(auto &a : A) cin >> a;
  Mo mo(N);
  for(int i = 0; i < Q; i++) {
    int l, r;
    cin >> l >> r;
    mo.add(l, r);
  }
  vector< int > xs{A};
  sort(begin(xs), end(xs));
  xs.erase(unique(begin(xs), end(xs)), end(xs));
  for(auto &a : A) a = lower_bound(begin(xs), end(xs), a) - begin(xs);
  BinaryIndexedTree< int > bit(xs.size());
  int64_t inv = 0, all = 0;
  vector< int64_t > 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 out = [&](int idx) {
    ans[idx] = inv;
  };
  mo.build(add_left, add_right, erase_left, erase_right, out);
  for(auto &p : ans) cout << p << "\n";
}

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