#define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query" #include "../../template/template.hpp" #include "../../data-structure/binary-indexed-tree.hpp" #include "../../misc/compress.hpp" #include "../../misc/fastio.hpp" #include "../../misc/mo.hpp" using namespace Nyaan; void Nyaan::solve() { int N, Q; rd(N); rd(Q); vi a(N); rep(i, N) rd(a[i]); Mo mo(N, Q); rep(i, Q) { int l, r; rd(l); rd(r); mo.insert(l, r); } compress<int> zip(a); BinaryIndexedTree<int> bit(zip.size() + 1); rep(i, N) a[i] = zip.get(a[i]); ll cnt = 0; vl ans(Q); auto addleft = [&](int idx) { cnt += bit.sum(0, a[idx] - 1); bit.add(a[idx], 1); }; auto addright = [&](int idx) { cnt += bit.sum(a[idx] + 1, zip.size()); bit.add(a[idx], 1); }; auto delleft = [&](int idx) { cnt -= bit.sum(0, a[idx] - 1); bit.add(a[idx], -1); }; auto delright = [&](int idx) { cnt -= bit.sum(a[idx] + 1, zip.size()); bit.add(a[idx], -1); }; auto rem = [&](int idx) { ans[idx] = cnt; }; mo.run(addleft,addright,delleft,delright,rem); each(x, ans) { wt(x); wt('\n'); } }
#line 1 "verify/verify-yosupo-ds/yosupo-static-range-inversions-query.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/static_range_inversions_query" #line 2 "template/template.hpp" using namespace std; // intrinstic #include <immintrin.h> #include <algorithm> #include <array> #include <bitset> #include <cassert> #include <cctype> #include <cfenv> #include <cfloat> #include <chrono> #include <cinttypes> #include <climits> #include <cmath> #include <complex> #include <cstdarg> #include <cstddef> #include <cstdint> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <fstream> #include <functional> #include <initializer_list> #include <iomanip> #include <ios> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <new> #include <numeric> #include <ostream> #include <queue> #include <random> #include <set> #include <sstream> #include <stack> #include <streambuf> #include <string> #include <tuple> #include <type_traits> #include <typeinfo> #include <unordered_map> #include <unordered_set> #include <utility> #include <vector> // utility #line 1 "template/util.hpp" namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; using vi = vector<int>; using vl = vector<long long>; using vd = V<double>; using vs = V<string>; using vvi = vector<vector<int>>; using vvl = vector<vector<long long>>; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <typename T, typename U> struct P : pair<T, U> { template <typename... Args> P(Args... args) : pair<T, U>(args...) {} using pair<T, U>::first; using pair<T, U>::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template <typename S> P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template <typename S> P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P<ll, ll>; using pi = P<int, int>; using vp = V<pl>; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template <typename T> int sz(const T &t) { return t.size(); } template <typename T, typename U> inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template <typename T> inline T Max(const vector<T> &v) { return *max_element(begin(v), end(v)); } template <typename T> inline T Min(const vector<T> &v) { return *min_element(begin(v), end(v)); } template <typename T> inline long long Sum(const vector<T> &v) { return accumulate(begin(v), end(v), 0LL); } template <typename T> int lb(const vector<T> &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template <typename T> int ub(const vector<T> &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template <typename T, typename U> pair<T, U> mkp(const T &t, const U &u) { return make_pair(t, u); } template <typename T> vector<T> mkrui(const vector<T> &v, bool rev = false) { vector<T> ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template <typename T> vector<T> mkuni(const vector<T> &v) { vector<T> ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template <typename F> vector<int> mkord(int N, F f) { vector<int> ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template <typename T> vector<int> mkinv(vector<T> &v) { int max_val = *max_element(begin(v), end(v)); vector<int> inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector<int> mkiota(int n) { vector<int> ret(n); iota(begin(ret), end(ret), 0); return ret; } template <typename T> T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template <typename T> bool nxp(vector<T> &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template <typename T> vector<vector<T>> product(const vector<T> &a) { vector<vector<T>> ret; vector<T> v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I, const function<void(T &)> &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template <typename T> T Power(T a, long long n, const T &I) { return Power(a, n, I, function<void(T &)>{[](T &) -> void {}}); } } // namespace Nyaan #line 58 "template/template.hpp" // bit operation #line 1 "template/bitop.hpp" namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template <typename T> inline int gbit(const T &a, int i) { return (a >> i) & 1; } template <typename T> inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan #line 61 "template/template.hpp" // inout #line 1 "template/inout.hpp" namespace Nyaan { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template <typename T, class... U> void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan #line 64 "template/template.hpp" // debug #line 1 "template/debug.hpp" namespace DebugImpl { template <typename U, typename = void> struct is_specialize : false_type {}; template <typename U> struct is_specialize< U, typename conditional<false, typename U::iterator, void>::type> : true_type {}; template <typename U> struct is_specialize< U, typename conditional<false, decltype(U::first), void>::type> : true_type {}; template <typename U> struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type { }; void dump(const char& t) { cerr << t; } void dump(const string& t) { cerr << t; } void dump(const bool& t) { cerr << (t ? "true" : "false"); } void dump(__int128_t t) { if (t == 0) cerr << 0; if (t < 0) cerr << '-', t = -t; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } void dump(__uint128_t t) { if (t == 0) cerr << 0; string S; while (t) S.push_back('0' + t % 10), t /= 10; reverse(begin(S), end(S)); cerr << S; } template <typename U, enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr> void dump(const U& t) { cerr << t; } template <typename T> void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) { string res; if (t == Nyaan::inf) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::inf) res = "-inf"; } if constexpr (sizeof(T) == 8) { if (t == Nyaan::infLL) res = "inf"; if constexpr (is_signed<T>::value) { if (t == -Nyaan::infLL) res = "-inf"; } } if (res.empty()) res = to_string(t); cerr << res; } template <typename T, typename U> void dump(const pair<T, U>&); template <typename T> void dump(const pair<T*, int>&); template <typename T> void dump(const T& t, enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) { cerr << "[ "; for (auto it = t.begin(); it != t.end();) { dump(*it); cerr << (++it == t.end() ? "" : ", "); } cerr << " ]"; } template <typename T, typename U> void dump(const pair<T, U>& t) { cerr << "( "; dump(t.first); cerr << ", "; dump(t.second); cerr << " )"; } template <typename T> void dump(const pair<T*, int>& t) { cerr << "[ "; for (int i = 0; i < t.second; i++) { dump(t.first[i]); cerr << (i == t.second - 1 ? "" : ", "); } cerr << " ]"; } void trace() { cerr << endl; } template <typename Head, typename... Tail> void trace(Head&& head, Tail&&... tail) { cerr << " "; dump(head); if (sizeof...(tail) != 0) cerr << ","; trace(forward<Tail>(tail)...); } } // namespace DebugImpl #ifdef NyaanDebug #define trc(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) \ do { \ cerr << "## " << #__VA_ARGS__ << " = "; \ DebugImpl::trace(__VA_ARGS__); \ } while (0) #else #define trc2(...) (void(0)) #endif #line 67 "template/template.hpp" // macro #line 1 "template/macro.hpp" #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) #line 70 "template/template.hpp" namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } #line 2 "data-structure/binary-indexed-tree.hpp" template <typename T> struct BinaryIndexedTree { int N; vector<T> data; BinaryIndexedTree() = default; BinaryIndexedTree(int size) { init(size); } void init(int size) { N = size + 2; data.assign(N + 1, {}); } // get sum of [0,k] T sum(int k) const { if (k < 0) return T{}; // return 0 if k < 0 T ret{}; for (++k; k > 0; k -= k & -k) ret += data[k]; return ret; } // getsum of [l,r] inline T sum(int l, int r) const { return sum(r) - sum(l - 1); } // get value of k inline T operator[](int k) const { return sum(k) - sum(k - 1); } // data[k] += x void add(int k, T x) { for (++k; k < N; k += k & -k) data[k] += x; } // range add x to [l,r] void imos(int l, int r, T x) { add(l, x); add(r + 1, -x); } // minimize i s.t. sum(i) >= w int lower_bound(T w) { if (w <= 0) return 0; int x = 0; for (int k = 1 << __lg(N); k; k >>= 1) { if (x + k <= N - 1 && data[x + k] < w) { w -= data[x + k]; x += k; } } return x; } // minimize i s.t. sum(i) > w int upper_bound(T w) { if (w < 0) return 0; int x = 0; for (int k = 1 << __lg(N); k; k >>= 1) { if (x + k <= N - 1 && data[x + k] <= w) { w -= data[x + k]; x += k; } } return x; } }; /** * @brief Binary Indexed Tree(Fenwick Tree) * @docs docs/data-structure/binary-indexed-tree.md */ #line 2 "misc/compress.hpp" template <class T> struct compress { vector<T> xs; compress(const vector<T>& v) { xs.reserve(v.size()); for (T x : v) xs.push_back(x); sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end()); } int get(const T& x) const { return lower_bound(xs.begin(), xs.end(), x) - xs.begin(); } inline int operator()(const T& x) const { return get(x); } T operator[](int i) { return xs[i]; } int size() const { return xs.size(); } }; /** * 座標圧縮 */ #line 2 "misc/fastio.hpp" #line 8 "misc/fastio.hpp" using namespace std; #line 2 "internal/internal-type-traits.hpp" #line 4 "internal/internal-type-traits.hpp" using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 12 "misc/fastio.hpp" namespace fastio { static constexpr int SZ = 1 << 17; static constexpr int offset = 64; char inbuf[SZ], outbuf[SZ]; int in_left = 0, in_right = 0, out_right = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; void load() { int len = in_right - in_left; memmove(inbuf, inbuf + in_left, len); in_right = len + fread(inbuf + len, 1, SZ - len, stdin); in_left = 0; } void flush() { fwrite(outbuf, 1, out_right, stdout); out_right = 0; } void skip_space() { if (in_left + offset > in_right) load(); while (inbuf[in_left] <= ' ') in_left++; } void single_read(char& c) { if (in_left + offset > in_right) load(); skip_space(); c = inbuf[in_left++]; } void single_read(string& S) { skip_space(); while (true) { if (in_left == in_right) load(); int i = in_left; for (; i != in_right; i++) { if (inbuf[i] <= ' ') break; } copy(inbuf + in_left, inbuf + i, back_inserter(S)); in_left = i; if (i != in_right) break; } } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_read(T& x) { if (in_left + offset > in_right) load(); skip_space(); char c = inbuf[in_left++]; [[maybe_unused]] bool minus = false; if constexpr (internal::is_broadly_signed_v<T>) { if (c == '-') minus = true, c = inbuf[in_left++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = inbuf[in_left++]; } if constexpr (internal::is_broadly_signed_v<T>) { if (minus) x = -x; } } void rd() {} template <typename Head, typename... Tail> void rd(Head& head, Tail&... tail) { single_read(head); rd(tail...); } void single_write(const char& c) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = c; } void single_write(const bool& b) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = b ? '1' : '0'; } void single_write(const string& S) { flush(), fwrite(S.data(), 1, S.size(), stdout); } void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_write(const T& _x) { if (out_right > SZ - offset) flush(); if (_x == 0) { outbuf[out_right++] = '0'; return; } T x = _x; if constexpr (internal::is_broadly_signed_v<T>) { if (x < 0) outbuf[out_right++] = '-', x = -x; } constexpr int buffer_size = sizeof(T) * 10 / 4; char buf[buffer_size]; int i = buffer_size; while (x >= 10000) { i -= 4; memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; } if (x < 100) { if (x < 10) { outbuf[out_right] = '0' + x; ++out_right; } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; outbuf[out_right] = '0' + q; outbuf[out_right + 1] = '0' + r; out_right += 2; } } else { if (x < 1000) { memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3); out_right += 3; } else { memcpy(outbuf + out_right, pre.num + (x << 2), 4); out_right += 4; } } memcpy(outbuf + out_right, buf + i, buffer_size - i); out_right += buffer_size - i; } void wt() {} template <typename Head, typename... Tail> void wt(const Head& head, const Tail&... tail) { single_write(head); wt(forward<const Tail>(tail)...); } template <typename... Args> void wtn(const Args&... x) { wt(forward<const Args>(x)...); wt('\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::skip_space; using fastio::wt; using fastio::wtn; #line 2 "misc/mo.hpp" struct Mo { int width; vector<int> left, right, order; Mo(int N, int Q) : order(Q) { width = max<int>(1, 1.0 * N / max<double>(1.0, sqrt(Q * 2.0 / 3.0))); iota(begin(order), end(order), 0); } void insert(int l, int r) { /* [l, r) */ left.emplace_back(l); right.emplace_back(r); } template <typename AL, typename AR, typename DL, typename DR, typename REM> void run(const AL &add_left, const AR &add_right, const DL &delete_left, const DR &delete_right, const REM &rem) { assert(left.size() == order.size()); sort(begin(order), end(order), [&](int a, int b) { int ablock = left[a] / width, bblock = left[b] / width; if (ablock != bblock) return ablock < bblock; if (ablock & 1) return right[a] < right[b]; return right[a] > right[b]; }); int nl = 0, nr = 0; for (auto idx : order) { while (nl > left[idx]) add_left(--nl); while (nr < right[idx]) add_right(nr++); while (nl < left[idx]) delete_left(nl++); while (nr > right[idx]) delete_right(--nr); rem(idx); } } }; /** * @brief Mo's algorithm * @docs docs/misc/mo.md */ #line 8 "verify/verify-yosupo-ds/yosupo-static-range-inversions-query.test.cpp" using namespace Nyaan; void Nyaan::solve() { int N, Q; rd(N); rd(Q); vi a(N); rep(i, N) rd(a[i]); Mo mo(N, Q); rep(i, Q) { int l, r; rd(l); rd(r); mo.insert(l, r); } compress<int> zip(a); BinaryIndexedTree<int> bit(zip.size() + 1); rep(i, N) a[i] = zip.get(a[i]); ll cnt = 0; vl ans(Q); auto addleft = [&](int idx) { cnt += bit.sum(0, a[idx] - 1); bit.add(a[idx], 1); }; auto addright = [&](int idx) { cnt += bit.sum(a[idx] + 1, zip.size()); bit.add(a[idx], 1); }; auto delleft = [&](int idx) { cnt -= bit.sum(0, a[idx] - 1); bit.add(a[idx], -1); }; auto delright = [&](int idx) { cnt -= bit.sum(a[idx] + 1, zip.size()); bit.add(a[idx], -1); }; auto rem = [&](int idx) { ans[idx] = cnt; }; mo.run(addleft,addright,delleft,delright,rem); each(x, ans) { wt(x); wt('\n'); } }