test/yosupo/static_range_inversions_query.test.cpp

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• Last update: 2021-05-01 12:56:38+09:00
• Problem: https://judge.yosupo.jp/problem/static_range_inversions_query

Depends on

• algorithm/mo.cpp
• Binary Indexed Tree (datastructure/binaryindexedtree.cpp)
• io/single.cpp
• vector/compress.cpp

Code

// verification-helper: PROBLEM https://judge.yosupo.jp/problem/static_range_inversions_query

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../../io/single.cpp"
#include "../../vector/compress.cpp"
#include "../../algorithm/mo.cpp"
#include "../../datastructure/binaryindexedtree.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,q;
  cin>>n>>q;
  auto as=read(n);
  auto dc=dict(compress(as));
  vector<int> cs(n);
  for(int i=0;i<n;i++) cs[i]=dc[as[i]];

  using ll = long long;
  ll res=0;
  vector<ll> ans(q);
  BIT<int> bit(n);
  auto expandL=[&](int i){bit.add(cs[i],+1);res+=bit.query(0,cs[i]);};
  auto expandR=[&](int i){bit.add(cs[i],+1);res+=bit.query(cs[i]+1,n);};
  auto shrinkL=[&](int i){bit.add(cs[i],-1);res-=bit.query(0,cs[i]);};
  auto shrinkR=[&](int i){bit.add(cs[i],-1);res-=bit.query(cs[i]+1,n);};

  Mo mo(n,400,expandL,expandR,shrinkL,shrinkR);
  for(int i=0;i<q;i++){
    int l,r;
    cin>>l>>r;
    mo.add(l,r);
  }
  mo.build();

  for(int i=0;i<q;i++){
    int k=mo.process();
    ans[k]=res;
  }

  for(auto a:ans) cout<<a<<'\n';
  return 0;
}

#line 1 "test/yosupo/static_range_inversions_query.test.cpp"
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/static_range_inversions_query

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#line 1 "io/single.cpp"

#line 3 "io/single.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename T=int>
vector<T> read(size_t n){
  vector<T> ts(n);
  for(size_t i=0;i<n;i++) cin>>ts[i];
  return ts;
}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 1 "vector/compress.cpp"

#line 3 "vector/compress.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename V>
V compress(V vs){
  sort(vs.begin(),vs.end());
  vs.erase(unique(vs.begin(),vs.end()),vs.end());
  return vs;
}
template<typename T>
map<T, int> dict(const vector<T> &vs){
  map<T, int> res;
  for(int i=0;i<(int)vs.size();i++)
    res[vs[i]]=i;
  return res;
}
map<char, int> dict(const string &s){
  return dict(vector<char>(s.begin(),s.end()));
}
template<typename T>
vector<T> compressed(vector<T> vs){
  auto dc=dict(compress(vs));
  for(auto &v:vs) v=dc[v];
  return vs;
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 1 "algorithm/mo.cpp"

#line 3 "algorithm/mo.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
struct Mo{
  using F = function<void(int)>;
  vector<int> ls,rs,ord;
  int n,width,nl,nr,ptr;
  F expandL,expandR;
  F shrinkL,shrinkR;

  Mo(int n,int width,F expandL,F expandR,F shrinkL,F shrinkR):
    n(n),width(width),nl(0),nr(0),ptr(0),
    expandL(expandL),expandR(expandR),
    shrinkL(shrinkL),shrinkR(shrinkR){}

  Mo(int n,int width,F expand,F shrink):
    Mo(n,width,expand,expand,shrink,shrink){}

  void add(int l,int r){
    ls.emplace_back(l);
    rs.emplace_back(r);
  }

  void build(){
    ord.resize(ls.size());
    iota(ord.begin(),ord.end(),0);
    sort(ord.begin(),ord.end(),
         [&](int a,int b){
           if(ls[a]/width!=ls[b]/width) return ls[a]<ls[b];
           if(rs[a]==rs[b]) return ls[a]<ls[b];
           return bool((rs[a]<rs[b])^((ls[a]/width)&1));
         });
  }

  int process(){
    if(ptr==(int)ord.size()) return -1;
    const int idx=ord[ptr++];
    while(nl>ls[idx]) expandL(--nl);
    while(nr<rs[idx]) expandR(nr++);
    while(nl<ls[idx]) shrinkL(nl++);
    while(nr>rs[idx]) shrinkR(--nr);
    return idx;
  }
};
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 1 "datastructure/binaryindexedtree.cpp"

#line 3 "datastructure/binaryindexedtree.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename T>
class BIT{
private:
  // \sum_{j < i}  v[j]
  T sum(int i){
    T s(0);
    for(int x=i;x>0;x-=(x&-x))
      s+=bit[x];
    return s;
  }
public:
  int n;
  vector<T> bit;
  BIT(int n_):n(n_+1),bit(n_+2,0){}

  // v[i] += a
  void add(int i,T a){
    for(int x=++i;x<=n;x+=(x&-x))
      bit[x]+=a;
  }

  // \sum_{l <= i < r} v[i]
  T query(int l,int r){return sum(r)-sum(l);}

  // min({x | sum(x) >= w})
  int lower_bound(const T w){
    if(w<=0) return 0;
    T r=w;
    int x=0,p=1;
    while(p<n) p<<=1;
    for(int k=p;k>0;k>>=1){
      if(x+k<=n and bit[x+k]<r){
        r-=bit[x+k];
        x+=k;
      }
    }
    x++;
    assert(sum(x-1)<w and sum(x)>=w);
    return x;
  }

  // min({x | sum(x) > w})
  int upper_bound(T w){return lower_bound(w+1);}
};
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 11 "test/yosupo/static_range_inversions_query.test.cpp"
#undef call_from_test

signed main(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,q;
  cin>>n>>q;
  auto as=read(n);
  auto dc=dict(compress(as));
  vector<int> cs(n);
  for(int i=0;i<n;i++) cs[i]=dc[as[i]];

  using ll = long long;
  ll res=0;
  vector<ll> ans(q);
  BIT<int> bit(n);
  auto expandL=[&](int i){bit.add(cs[i],+1);res+=bit.query(0,cs[i]);};
  auto expandR=[&](int i){bit.add(cs[i],+1);res+=bit.query(cs[i]+1,n);};
  auto shrinkL=[&](int i){bit.add(cs[i],-1);res-=bit.query(0,cs[i]);};
  auto shrinkR=[&](int i){bit.add(cs[i],-1);res-=bit.query(cs[i]+1,n);};

  Mo mo(n,400,expandL,expandR,shrinkL,shrinkR);
  for(int i=0;i<q;i++){
    int l,r;
    cin>>l>>r;
    mo.add(l,r);
  }
  mo.build();

  for(int i=0;i<q;i++){
    int k=mo.process();
    ans[k]=res;
  }

  for(auto a:ans) cout<<a<<'\n';
  return 0;
}

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