結果

問題 No.1526 Sum of Mex 2
ユーザー 👑 emthrmemthrm
提出日時 2021-06-08 19:22:23
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 209 ms / 3,000 ms
コード長 9,709 bytes
コンパイル時間 2,251 ms
コンパイル使用メモリ 218,104 KB
実行使用メモリ 17,172 KB
最終ジャッジ日時 2024-05-05 05:24:11
合計ジャッジ時間 7,176 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 1 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 1 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 23 ms
5,376 KB
testcase_14 AC 28 ms
6,016 KB
testcase_15 AC 33 ms
6,400 KB
testcase_16 AC 197 ms
16,640 KB
testcase_17 AC 129 ms
14,144 KB
testcase_18 AC 13 ms
5,376 KB
testcase_19 AC 11 ms
5,376 KB
testcase_20 AC 73 ms
9,596 KB
testcase_21 AC 186 ms
16,448 KB
testcase_22 AC 98 ms
10,624 KB
testcase_23 AC 195 ms
16,704 KB
testcase_24 AC 209 ms
17,008 KB
testcase_25 AC 189 ms
16,540 KB
testcase_26 AC 204 ms
16,816 KB
testcase_27 AC 205 ms
16,984 KB
testcase_28 AC 209 ms
17,088 KB
testcase_29 AC 206 ms
16,988 KB
testcase_30 AC 207 ms
17,172 KB
testcase_31 AC 199 ms
17,168 KB
testcase_32 AC 195 ms
16,616 KB
testcase_33 AC 108 ms
15,328 KB
evil_largest AC 368 ms
44,984 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <typename T>
struct LazySegmentTree {
  using Monoid = typename T::Monoid;
  using OperatorMonoid = typename T::OperatorMonoid;

  LazySegmentTree(int n) : LazySegmentTree(std::vector<Monoid>(n, T::m_id())) {}

  LazySegmentTree(const std::vector<Monoid> &a) : n(a.size()) {
    while ((1 << height) < n) ++height;
    p2 = 1 << height;
    lazy.assign(p2, T::o_id());
    dat.assign(p2 << 1, T::m_id());
    for (int i = 0; i < n; ++i) dat[i + p2] = a[i];
    for (int i = p2 - 1; i > 0; --i) dat[i] = T::m_merge(dat[i << 1], dat[(i << 1) + 1]);
  }

  void set(int idx, const Monoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) propagate(idx >> i);
    dat[idx] = val;
    for (int i = 1; i <= height; ++i) {
      int current_idx = idx >> i;
      dat[current_idx] = T::m_merge(dat[current_idx << 1], dat[(current_idx << 1) + 1]);
    }
  }

  void apply(int idx, const OperatorMonoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) propagate(idx >> i);
    dat[idx] = T::apply(dat[idx], val);
    for (int i = 1; i <= height; ++i) {
      int current_idx = idx >> i;
      dat[current_idx] = T::m_merge(dat[current_idx << 1], dat[(current_idx << 1) + 1]);
    }
  }

  void apply(int left, int right, const OperatorMonoid val) {
    if (right <= left) return;
    left += p2;
    right += p2;
    int left_ctz = __builtin_ctz(left);
    for (int i = height; i > left_ctz; --i) propagate(left >> i);
    int right_ctz = __builtin_ctz(right);
    for (int i = height; i > right_ctz; --i) propagate(right >> i);
    for (int l = left, r = right; l < r; l >>= 1, r >>= 1) {
      if (l & 1) sub_apply(l++, val);
      if (r & 1) sub_apply(--r, val);
    }
    for (int i = left >> (left_ctz + 1); i > 0; i >>= 1) dat[i] = T::m_merge(dat[i << 1], dat[(i << 1) + 1]);
    for (int i = right >> (right_ctz + 1); i > 0; i >>= 1) dat[i] = T::m_merge(dat[i << 1], dat[(i << 1) + 1]);
  }

  Monoid get(int left, int right) {
    if (right <= left) return T::m_id();
    left += p2;
    right += p2;
    int left_ctz = __builtin_ctz(left);
    for (int i = height; i > left_ctz; --i) propagate(left >> i);
    int right_ctz = __builtin_ctz(right);
    for (int i = height; i > right_ctz; --i) propagate(right >> i);
    Monoid l_res = T::m_id(), r_res = T::m_id();
    for (; left < right; left >>= 1, right >>= 1) {
      if (left & 1) l_res = T::m_merge(l_res, dat[left++]);
      if (right & 1) r_res = T::m_merge(dat[--right], r_res);
    }
    return T::m_merge(l_res, r_res);
  }

  Monoid operator[](const int idx) {
    int node = idx + p2;
    for (int i = height; i > 0; --i) propagate(node >> i);
    return dat[node];
  }

  template <typename G>
  int find_right(int left, G g) {
    if (left >= n) return n;
    left += p2;
    for (int i = height; i > 0; --i) propagate(left >> i);
    Monoid val = T::m_id();
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nx = T::m_merge(val, dat[left]);
      if (!g(nx)) {
        while (left < p2) {
          propagate(left);
          left <<= 1;
          nx = T::m_merge(val, dat[left]);
          if (g(nx)) {
            val = nx;
            ++left;
          }
        }
        return left - p2;
      }
      val = nx;
      ++left;
    } while (__builtin_popcount(left) > 1);
    return n;
  }

  template <typename G>
  int find_left(int right, G g) {
    if (right <= 0) return -1;
    right += p2;
    for (int i = height; i > 0; --i) propagate((right - 1) >> i);
    Monoid val = T::m_id();
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nx = T::m_merge(dat[right], val);
      if (!g(nx)) {
        while (right < p2) {
          propagate(right);
          right = (right << 1) + 1;
          nx = T::m_merge(dat[right], val);
          if (g(nx)) {
            val = nx;
            --right;
          }
        }
        return right - p2;
      }
      val = nx;
    } while (__builtin_popcount(right) > 1);
    return -1;
  }

private:
  int n, p2, height = 0;
  std::vector<Monoid> dat;
  std::vector<OperatorMonoid> lazy;

  void sub_apply(int idx, const OperatorMonoid &val) {
    dat[idx] = T::apply(dat[idx], val);
    if (idx < p2) lazy[idx] = T::o_merge(lazy[idx], val);
  }

  void propagate(int idx) {
    // assert(1 <= idx && idx < p2);
    sub_apply(idx << 1, lazy[idx]);
    sub_apply((idx << 1) + 1, lazy[idx]);
    lazy[idx] = T::o_id();
  }
};

namespace monoid {
template <typename T>
struct RangeMinimumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return std::numeric_limits<Monoid>::max(); }
  static constexpr OperatorMonoid o_id() { return std::numeric_limits<OperatorMonoid>::max(); }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return std::min(a, b); }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return b == o_id() ? a : b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return b == o_id()? a : b; }
};

template <typename T>
struct RangeMaximumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return std::numeric_limits<Monoid>::lowest(); }
  static constexpr OperatorMonoid o_id() { return std::numeric_limits<OperatorMonoid>::lowest(); }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return std::max(a, b); }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return b == o_id() ? a : b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return b == o_id()? a : b; }
};

template <typename T, T Inf>
struct RangeMinimumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return std::min(a, b); }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return a + b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return a + b; }
};

template <typename T, T Inf>
struct RangeMaximumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return -Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return std::max(a, b); }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return a + b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return a + b; }
};

template <typename T>
struct RangeSumAndUpdateQuery {
  using Monoid = struct {
    T sum;
    int len;
  };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(int n) { return std::vector<Monoid>(n, Monoid{0, 1}); }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() { return std::numeric_limits<OperatorMonoid>::max(); }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return Monoid{a.sum + b.sum, a.len + b.len}; }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return b == o_id() ? a : b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return Monoid{b == o_id() ? a.sum : b * a.len, a.len}; }
};

template <typename T>
struct RangeSumAndAddQuery {
  using Monoid = struct {
    T sum;
    int len;
  };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(int n) { return std::vector<Monoid>(n, Monoid{0, 1}); }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid &a, const Monoid &b) { return Monoid{a.sum + b.sum, a.len + b.len}; }
  static OperatorMonoid o_merge(const OperatorMonoid &a, const OperatorMonoid &b) { return a + b; }
  static Monoid apply(const Monoid &a, const OperatorMonoid &b) { return Monoid{a.sum + b * a.len, a.len}; }
};
}  // monoid

int main() {
  int n; cin >> n;
  vector<int> a(n); REP(i, n) cin >> a[i], --a[i];
  vector<vector<int>> p(n);
  for (int i = n - 1; i >= 0; --i) p[a[i]].emplace_back(i);
  auto mex = monoid::RangeSumAndUpdateQuery<ll>::init(n);
  unordered_set<int> s;
  REP(i, n) {
    s.emplace(a[i]);
    mex[i].sum = (i == 0 ? 0 : mex[i - 1].sum);
    while (s.count(mex[i].sum) == 1) ++mex[i].sum;
  }
  LazySegmentTree<monoid::RangeSumAndUpdateQuery<ll>> seg(mex);
  ll ans = 0;
  REP(i, n) {
    ans += seg.get(i, n).sum;
    p[a[i]].pop_back();
    int l = i - 1, r = (p[a[i]].empty() ? n : p[a[i]].back());
    while (r - l > 1) {
      int m = (l + r) / 2;
      (seg[m].sum > a[i] ? r : l) = m;
    }
    seg.apply(r, p[a[i]].empty() ? n : p[a[i]].back(), a[i]);
  }
  assert(seg.get(0, n).sum == 0);
  cout << ans + n * (n + 1LL) / 2 << '\n';
  return 0;
}
0