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Verify/LC_static_range_inversions_query.test.cpp

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• Last update: 2025-04-17 22:07:07+09:00
• Problem: https://judge.yosupo.jp/problem/static_range_inversions_query

Depends on

• Mo's Algorithm (Algorithm/mo.hpp)
• Binary Indexed Tree (DataStructure/bit.hpp)
• Template/template.hpp

Code

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

#include "Template/template.hpp"

#include "Algorithm/mo.hpp"

#include "DataStructure/bit.hpp"


int a[101010];
ll ret[101010],cur=0;
BIT<int> bit(101010);

int main(){
    int n,q;
    cin>>n>>q;
    using P=pair<int,int>;
    vector<P> vs(n);
    rep(i,0,n){
        cin>>vs[i].first;
        vs[i].second=i;
    }
    sort(ALL(vs));
    rep(i,0,n)a[vs[i].second]=i;

    auto addl=[&](int i){
        cur+=bit.sum(a[i]);
        bit.add(a[i],1);
    };
    auto addr=[&](int i){
        cur+=bit.all-bit.sum(a[i]);
        bit.add(a[i],1);
    };
    auto dell=[&](int i){
        bit.add(a[i],-1);
        cur-=bit.sum(a[i]);
    };
    auto delr=[&](int i){
        bit.add(a[i],-1);
        cur-=bit.all-bit.sum(a[i]);
    };
    auto out=[&](int i){
        ret[i]=cur;
    };

    Mo mo(n);
    rep(i,0,q){
        int L,R;
        cin>>L>>R;
        mo.add(L,R);
    }
    mo.run(addl,addr,dell,delr,out);
    rep(i,0,q)cout<<ret[i]<<'\n';
    return 0;
}

#line 1 "Verify/LC_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;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T, typename S = T> S SUM(const vector<T> &a) {
    return accumulate(ALL(a), S(0));
}
template <typename S, typename T = S> S POW(S a, T b) {
    S ret = 1, base = a;
    for (;;) {
        if (b & 1)
            ret *= base;
        b >>= 1;
        if (b == 0)
            break;
        base *= base;
    }
    return ret;
}
template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
    for (; a[i] != ',' && a[i] != '\0'; i++)
        cerr << a[i];
    cerr << ":" << b << " ";
    _show(i + 1, a, c...);
}
#line 2 "Algorithm/mo.hpp"

struct Mo{
    const int n;
    vector<int> L,R;
    Mo(int _n):n(_n){}
    void add(int lb,int rb){
        L.push_back(lb);
        R.push_back(rb);
    }
    template <typename AL, typename AR, typename DL, typename DR, typename OUT>
    void run(const AL& addl,const AR& addr,const DL& dell,const DR& delr,const OUT& out){
        const int q=L.size();
        const int w=max<int>(1,1.0*n/max<double>(1.0,sqrt(q*2.0/3.0)));
        vector<int> ord(q);
        iota(ALL(ord),0);
        sort(ALL(ord),[&](int i,int j){
            int a=L[i]/w,b=L[j]/w;
            if(a!=b)return a<b;
            if(a&1)return R[i]<R[j];
            else return R[i]>R[j];
        });
        int lb=0,rb=0;
        for(auto& i:ord){
            while(lb>L[i])addl(--lb);
            while(rb<R[i])addr(rb++);
            while(lb<L[i])dell(lb++);
            while(rb>R[i])delr(--rb);
            out(i);
        }
    }
};

/**
 * @brief Mo's Algorithm
 * @docs docs/mo.md
 */
#line 2 "DataStructure/bit.hpp"

template <typename T> struct BIT {
    int n;
    T all = 0;
    vector<T> val;
    BIT(int _n = 0) : n(_n), val(_n + 10) {}
    void clear() {
        val.assign(n + 10, 0);
        all = T();
    }
    void add(int i, T x) {
        for (i++; i <= n; i += (i & -i))
            val[i] = val[i] + x;
        all += x;
    }
    T sum(int i) {
        i = clamp(i, 0, n);
        T res = 0;
        for (; i; i -= (i & -i))
            res += val[i];
        return res;
    }
    // [L,R)

    T sum(int L, int R) {
        if (L > R)
            return T(0);
        return sum(R) - sum(L);
    }
    int lower_bound(T x) {
        int ret = 0, len = 1;
        while (2 * len <= n)
            len <<= 1;
        for (; len >= 1; len >>= 1) {
            if (ret + len <= n and val[ret + len] < x) {
                ret += len;
                x -= val[ret];
            }
        }
        return ret;
    }
};

/**
 * @brief Binary Indexed Tree
 */
#line 6 "Verify/LC_static_range_inversions_query.test.cpp"

int a[101010];
ll ret[101010],cur=0;
BIT<int> bit(101010);

int main(){
    int n,q;
    cin>>n>>q;
    using P=pair<int,int>;
    vector<P> vs(n);
    rep(i,0,n){
        cin>>vs[i].first;
        vs[i].second=i;
    }
    sort(ALL(vs));
    rep(i,0,n)a[vs[i].second]=i;

    auto addl=[&](int i){
        cur+=bit.sum(a[i]);
        bit.add(a[i],1);
    };
    auto addr=[&](int i){
        cur+=bit.all-bit.sum(a[i]);
        bit.add(a[i],1);
    };
    auto dell=[&](int i){
        bit.add(a[i],-1);
        cur-=bit.sum(a[i]);
    };
    auto delr=[&](int i){
        bit.add(a[i],-1);
        cur-=bit.all-bit.sum(a[i]);
    };
    auto out=[&](int i){
        ret[i]=cur;
    };

    Mo mo(n);
    rep(i,0,q){
        int L,R;
        cin>>L>>R;
        mo.add(L,R);
    }
    mo.run(addl,addr,dell,delr,out);
    rep(i,0,q)cout<<ret[i]<<'\n';
    return 0;
}

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