結果

問題 No.925 紲星 Extra
ユーザー maspy
提出日時 2022-05-01 04:42:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5,914 ms / 10,000 ms
コード長 18,927 bytes
コンパイル時間 2,757 ms
コンパイル使用メモリ 223,556 KB
最終ジャッジ日時 2025-01-29 01:15:39
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 19
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ソースコード

diff #
プレゼンテーションモードにする

#line 1 "/home/maspy/compro/library/my_template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i))
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
#define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i))
#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
template <typename T>
T SUM(vector<T> &A) {
  T sum = T(0);
  for (auto &&a: A) sum += a;
  return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}
ll binary_search(function<bool(ll)> check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    if (check(x))
      ok = x;
    else
      ng = x;
  }
  return ok;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}
vi s_to_vi(const string& S, char first_char) {
  vi A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}
template <typename T>
vector<T> cumsum(vector<T> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}
template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}
template <typename T>
vector<int> argsort(const vector<T> &A) {
  // stable
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  int n = len(A);
  assert(len(I) == n);
  vc<T> B(n);
  FOR(i, n) B[i] = A[I[i]];
  return B;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }
  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a), write(' '), write(b), write(' '), write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d);
  }
  template <class A, class B, class C, class D, class E>
  void write(const tuple<A, B, C, D, E> &val) {
    auto &[a, b, c, d, e] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e);
  }
  template <class A, class B, class C, class D, class E, class F>
  void write(const tuple<A, B, C, D, E, F> &val) {
    auto &[a, b, c, d, e, f] = val;
    write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if(val < 0){
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if(negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)      \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)
#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "/home/maspy/compro/library/alg/group_add.hpp"
template <class X>
struct Group_Add {
  using value_type = X;
  static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
  static constexpr X inverse(const X &x) noexcept { return -x; }
  static constexpr X power(const X &x, ll n) noexcept { return n * x; }
  static constexpr X unit() { return X(0); }
  static constexpr bool commute = true;
};
#line 3 "/home/maspy/compro/library/ds/fenwick.hpp"
template <typename AbelGroup>
struct FenwickTree {
  using E = typename AbelGroup::value_type;
  int n;
  vector<E> dat;
  E total;
  FenwickTree() : FenwickTree(0) {}
  FenwickTree(int n) : n(n), total(AbelGroup::unit()) {
    assert(AbelGroup::commute);
    dat.assign(n, AbelGroup::unit());
  }
  FenwickTree(vc<E> v) : n(len(v)), total(AbelGroup::unit()) {
    assert(AbelGroup::commute);
    FOR(i, n) total = AbelGroup::op(total, v[i]);
    dat = v;
    FOR3(i, 1, n + 1) {
      int j = i + (i & -i);
      if (j <= n) dat[j - 1] = AbelGroup::op(dat[i - 1], dat[j - 1]);
    }
  }
  void reset(){
    total = AbelGroup::unit();
    dat.assign(n, AbelGroup::unit());
  }
  E sum(int k) {
    E ret = AbelGroup::unit();
    for (; k > 0; k -= k & -k) ret = AbelGroup::op(ret, dat[k - 1]);
    return ret;
  }
  E sum(int L, int R) {
    E pos = AbelGroup::unit();
    while (L < R) {
      pos = AbelGroup::op(pos, dat[R - 1]);
      R -= R & -R;
    }
    E neg = AbelGroup::unit();
    while (R < L) {
      neg = AbelGroup::op(neg, dat[L - 1]);
      L -= L & -L;
    }
    return AbelGroup::op(pos, AbelGroup::inverse(neg));
  }
  E sum_all() { return total; }
  void add(int k, E x) {
    total = AbelGroup::op(total, x);
    for (++k; k <= n; k += k & -k) dat[k - 1] = AbelGroup::op(dat[k - 1], x);
  }
  template <class F>
  int max_right(F& check) {
    assert(check(E(0)));
    ll i = 0;
    E s = AbelGroup::unit();
    int k = 1;
    int N = len(dat) + 1;
    while (2 * k < N) k *= 2;
    while (k) {
      if (i + k < N && check(AbelGroup::op(s, dat[i + k - 1]))) {
        i += k;
        s = AbelGroup::op(s, dat[i - 1]);
      }
      k >>= 1;
    }
    return i;
  }
  int find_kth(E k) {
    auto check = [&](E x) -> bool { return x <= k; };
    return max_right(check);
  }
  void debug() { print("fenwick", dat); }
};
#line 1 "/home/maspy/compro/library/ds/binarytrie.hpp"
template <int LOG = 30>
struct BinaryTrie {
  struct Node {
    ll cnt = 0;
    int ch[2] = {-1, -1};
  };
  vector<Node> ns;
  BinaryTrie() : ns(1) {}
  ll size() const { return ns[0].cnt; }
  ll operator[](int k) const { return find_kth(k, 0); }
  ll find_kth(ll k, ll xor_add = 0) const {
    assert(0 <= k && k < size());
    ll idx = 0;
    ll val = 0;
    FOR_R(i, LOG) {
      ll c = xor_add >> i & 1;
      ll low_ch = ns[idx].ch[c];
      ll low_cnt = (low_ch >= 0 ? ns[low_ch].cnt : 0);
      if (k < low_cnt) {
        idx = low_ch;
      } else {
        k -= low_cnt;
        idx = ns[idx].ch[c ^ 1];
        val ^= 1LL << i;
      }
      assert(idx >= 0);
    }
    return val;
  }
  void add(ll val, ll cnt = 1) {
    assert(0 <= val && val < (1LL << LOG));
    int idx = 0;
    FOR_R(i, LOG) {
      ns[idx].cnt += cnt;
      assert(ns[idx].cnt >= 0);
      int &nxt = ns[idx].ch[val >> i & 1];
      if (nxt == -1) {
        idx = nxt = ns.size();
        ns.emplace_back();
      } else {
        idx = nxt;
      }
    }
    ns[idx].cnt += cnt;
    assert(ns[idx].cnt >= 0);
    return;
  }
  ll lower_bound(ll val, ll xor_add = 0) {
    assert(0 <= val);
    if (val >= (1LL << LOG)) return size();
    int idx = 0;
    ll cnt = 0;
    FOR_R(i, LOG) {
      int b = val >> i & 1, c = xor_add >> i & 1;
      int ch = ns[idx].ch[c];
      cnt += (b & (ch >= 0) ? ns[ch].cnt : 0);
      idx = ns[idx].ch[b ^ c];
      if (idx < 0 or ns[idx].cnt == 0) break;
    }
    return cnt;
  }
  ll count(ll val) const {
    assert(0 <= val && val < (1LL << LOG));
    int idx = 0;
    FOR_R(i, LOG) {
      idx = ns[idx].ch[val >> i & 1];
      if (idx < 0 or ns[idx].cnt == 0) return 0;
    }
    return ns[idx].cnt;
  }
  ll count(ll L, ll R, ll xor_add = 0) {
    assert(0 <= L && L <= R && R <= (1LL << LOG));
    return lower_bound(R, xor_add) - lower_bound(L, xor_add);
  }
  ll min(ll xor_add = 0) { return find_kth(0, xor_add); }
  ll max(ll xor_add = 0) { return find_kth(size() - 1, xor_add); }
  void debug() {
    FOR(i, len(ns)) print(i, "cnt", ns[i].cnt, "ch", ns[i].ch[0], ns[i].ch[1]);
  }
};
#line 5 "main.cpp"
void solve() {
  LL(N, Q);
  VEC(ll, A, N);
  FenwickTree<Group_Add<ll>> bit(A);
  BinaryTrie<40> BT;
  for (auto&& a: A) BT.add(a);
  ll b_sz = 1;
  while (b_sz * b_sz <= 10 * N) ++b_sz;
  ll b_num = ceil(N, b_sz);
  while (N < b_sz * b_num) {
    ++N;
    A.eb(0);
  }
  /*
  バケットごとに
  ・ソート列
  ・累積和
  を持つ
  */
  vv(ll, B, b_num, b_sz);
  vv(ll, Bc, b_num, b_sz + 1);
  auto build = [&](ll b) -> void {
    ll L = b * b_sz;
    ll R = L + b_sz;
    B[b] = {A.begin() + L, A.begin() + R};
    sort(all(B[b]));
    Bc[b] = cumsum(B[b]);
  };
  auto calc = [&](ll L, ll R, ll x) -> pi {
    // x 以下の要素について、個数と和を求める
    ll l0 = -b_sz, r0 = 0;
    ll cnt = 0, sum = 0;
    FOR(b, b_num) {
      l0 += b_sz, r0 += b_sz;
      ll l = max(L, l0);
      ll r = min(R, r0);
      if (l >= r) continue;
      if (r - l == b_sz) {
        ll k = UB(B[b], x);
        cnt += k;
        sum += Bc[b][k];
      } else {
        FOR3(i, l, r) {
          if (A[i] <= x) {
            ++cnt;
            sum += A[i];
          }
        }
      }
    }
    return {cnt, sum};
  };
  FOR(b, b_num) build(b);
  ll s = 0;
  ll MASK16 = (1LL << 16) - 1;
  ll MASK40 = (1LL << 40) - 1;
  const ll INF = 1LL << 60;
  FOR_(Q) {
    LL(t);
    if (t == 1) {
      LL(X, Y);
      X = X ^ (s & MASK16);
      Y = Y ^ (s & MASK40);
      assert(1 <= X && X <= N);
      assert(0 <= Y && Y <= MASK40);
      --X;
      bit.add(X, Y - A[X]);
      A[X] = Y;
      BT.add(Y);
      build(X / b_sz);
    }
    if (t == 2) {
      LL(L, R);
      L = L ^ (s & MASK16);
      R = R ^ (s & MASK16);
      if (L > R) swap(L, R);
      assert(1 <= L && L <= R && R <= N);
      --L;
      ll ANS = INF;
      ll full = bit.sum(L, R);
      ll n = (R - L);
      auto check = [&](ll k) -> bool {
        ll x = BT.find_kth(k);
        // x 以下の要素が (n+1)/2 個以上あれば ok
        auto [cnt, sum] = calc(L, R, x);
        ll sum_lo = x * cnt - sum;
        ll sum_hi = (full - sum) - x * (n - cnt);
        chmin(ANS, sum_lo + sum_hi);
        return cnt >= (n + 1) / 2;
      };
      binary_search(check, BT.size() - 1, -1);
      print(ANS);
      s ^= ANS;
    }
  }
}
signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(15);
  ll T = 1;
  // LL(T);
  FOR(_, T) solve();
  return 0;
}
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