data-structure/segtree.cpp

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• Last update: 2020-05-26 19:55:50+09:00

Depends on

• template.cpp
• util/function-objects.cpp

Required by

• string/hash-monoid.cpp

Verified with

• verify/aoj/0355.test.cpp
• verify/aoj/0367.test.cpp

Code

#pragma once

#include "template.cpp"
#include "util/function-objects.cpp"

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wshadow"
template <typename T, typename Combine, typename Action>
class SegmentTree {
 private:
  const size_t n;
  const T unit;
  const Combine combine;
  const Action action;
  vector<T> data;

 public:
  SegmentTree(size_t n = 0, T unit = {}, Combine combine = {},
              Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1, unit) {
    build();
  }

  template <
      typename Iter,
      enable_if_t<is_same<typename Iter::value_type, T>::value>* = nullptr>
  SegmentTree(Iter first, Iter last, size_t n, T unit = {},
              Combine combine = {}, Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1) {
    copy(first, last, data.begin() + n);
    build();
  }

  template <
      typename Iter,
      enable_if_t<!is_same<typename Iter::value_type, T>::value>* = nullptr>
  [[deprecated]] SegmentTree(Iter first, Iter last, size_t n, T unit = {},
                             Combine combine = {}, Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1) {
    copy(first, last, data.begin() + n);
    build();
  }

  template <typename Iter>
  SegmentTree(Iter first, Iter last, T unit = {}, Combine combine = {},
              Action action = {})
      : SegmentTree(first, last, distance(first, last), unit, combine, action) {
  }

 private:
  void build() { repr(i, n) data[i] = combine(data[i << 1], data[i << 1 | 1]); }

 public:
  void modify(int l, T v) {
    l += n;
    data[l] = action(data[l], v);
    for (; l > 1; l >>= 1) data[l >> 1] = combine(data[l & (~1)], data[l | 1]);
  }

  T fold(int l, int r) const {
    if (l == r) return unit;
    if (l + 1 == r) return data[l + n];
    T resl = data[l += n], resr = data[(r += n) - 1];
    for (l++, r--; l < r; l >>= 1, r >>= 1) {
      if (l & 1) resl = combine(resl, data[l++]);
      if (r & 1) resr = combine(data[--r], resr);
    }
    return combine(resl, resr);
  }
  // min r s.t. fold(l, r) >= v -- or n+1 if failed
  template <typename Compare = less<T>>
  int lower_bound(T v, int l = 0, Compare comp = {}) {
    if (not comp(unit, v)) return l;
    int r = n;
    VI rootL, rootR;
    for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
      if (l & 1) rootL.push_back(l++);
      if (r & 1) rootR.push_back(--r);
    }
    VI roots = move(rootL); roots.insert(roots.end(), rall(rootR));
    T accL = unit;
    for (int root : roots) {
      T tmpL = combine(accL, data[root]);
      if (comp(tmpL, v)) {
        accL = tmpL;
        continue;
      }
      while (root < n) {
        tmpL = combine(accL, data[root << 1]);
        if (comp(tmpL, v)) accL = tmpL, root = root << 1 | 1;
        else root = root << 1;
      }
      return root - n + 1;
    }
    return n + 1;
  }
};
#pragma GCC diagnostic pop

#line 2 "data-structure/segtree.cpp"

#line 2 "template.cpp"

#ifndef LOCAL
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx")
#endif
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VLL = vector<ll>;
using VVLL = vector<vector<ll>>;
using VB = vector<bool>;
using PII = pair<int, int>;
using PLL = pair<ll, ll>;
constexpr int INF = 1000000007;
constexpr ll INF_LL = 1'000'000'000'000'000'007;
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define newl '\n'

// loops rep(until) / rep(var, until) / rep(var, from, until) / repr (reversed order)
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define rep(...) OVERLOAD3(__VA_ARGS__, REPEAT_FROM_UNTIL, REPEAT_UNTIL, REPEAT)(__VA_ARGS__)
#define REPEAT(times) REPEAT_CNT(_repeat, __COUNTER__, times)
#define REPEAT_CNT(_repeat, cnt, times) REPEAT_CNT_CAT(_repeat, cnt, times)
#define REPEAT_CNT_CAT(_repeat, cnt, times) REPEAT_FROM_UNTIL(_repeat ## cnt, 0, times)
#define REPEAT_UNTIL(name, times) REPEAT_FROM_UNTIL(name, 0, times)
#define REPEAT_FROM_UNTIL(name, from, until) for (int name = from, name ## __until = (until); name < name ## __until; name++)
#define repr(...) OVERLOAD3(__VA_ARGS__, REPR_FROM_UNTIL, REPR_UNTIL, REPEAT)(__VA_ARGS__)
#define REPR_UNTIL(name, times) REPR_FROM_UNTIL(name, 0, times)
#define REPR_FROM_UNTIL(name, from, until) for (int name = (until)-1, name ## __from = (from); name >= name ## __from; name--)

template <typename T, typename U>
bool chmin(T& var, U x) { if (var > x) { var = x; return true; } else return false; }
template <typename T, typename U>
bool chmax(T& var, U x) { if (var < x) { var = x; return true; } else return false; }
ll power(ll e, ll t, ll mod = INF_LL) {
  ll res = 1; for (; t; t >>= 1, (e *= e) %= mod) if (t & 1) (res *= e) %= mod; return res;
}
ll choose(ll n, int r) {
  chmin(r, n-r); if (r < 0) return 0; ll res = 1; rep(i, r) res *= n-i, res /= i+1; return res;
}
template <typename T, typename U> T divceil(T m, U d) { return (m + d - 1) / d; }
template <typename T> vector<T> make_v(size_t a, T b) { return vector<T>(a, b); }
template <typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v(ts...))>(a, make_v(ts...));
}

// debugging stuff
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wmisleading-indentation"
#define repi(it, ds) for (auto it = ds.begin(); it != ds.end(); it++)
class DebugPrint { public: template <typename T> DebugPrint& operator <<(const T& v) {
#ifdef LOCAL
    cerr << v;
#endif
return *this; } } debugos; template <typename T> DebugPrint& operator<<(DebugPrint& 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> DebugPrint&
operator<<(DebugPrint& os, const map<T, U>& map_var) { os << "{"; repi(itr, map_var) { os << *
itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template <
typename T> DebugPrint& operator<<(DebugPrint& os, const set<T>& set_var) { os << "{"; repi(
itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}";
return os; } template <typename T, typename U> DebugPrint& operator<<(DebugPrint& os, const
pair<T, U>& p) { os << "(" << p.first << ", " << p.second << ")"; return os; } void dump_func(
) { debugos << newl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail
&&... tail) { debugos << head; if (sizeof...(Tail) > 0) { debugos << ", "; } dump_func(forward
<Tail>(tail)...); }
#ifdef LOCAL
#define dump(...) debugos << "  " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) \
<< ":" << __FUNCTION__ << "]" << newl << "    ", dump_func(__VA_ARGS__)
#else
#define dump(...) ({})
#endif
#pragma GCC diagnostic pop


#line 2 "util/function-objects.cpp"

#line 4 "util/function-objects.cpp"

struct minT {
  template <typename T>
  T operator()(T a, T b) const {
    return min(a, b);
  }
};

struct maxT {
  template <typename T>
  T operator()(T a, T b) const {
    return max(a, b);
  }
};

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-parameter"
struct assignT {
  template <typename T>
  T operator()(T a, T b, int k = 0) const { return b; }
};
#pragma GCC diagnostic pop

struct plusT {
  template <typename T>
  T operator()(T a, T b, int k = 1) const { return a + b * k; }
};
#line 5 "data-structure/segtree.cpp"

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wshadow"
template <typename T, typename Combine, typename Action>
class SegmentTree {
 private:
  const size_t n;
  const T unit;
  const Combine combine;
  const Action action;
  vector<T> data;

 public:
  SegmentTree(size_t n = 0, T unit = {}, Combine combine = {},
              Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1, unit) {
    build();
  }

  template <
      typename Iter,
      enable_if_t<is_same<typename Iter::value_type, T>::value>* = nullptr>
  SegmentTree(Iter first, Iter last, size_t n, T unit = {},
              Combine combine = {}, Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1) {
    copy(first, last, data.begin() + n);
    build();
  }

  template <
      typename Iter,
      enable_if_t<!is_same<typename Iter::value_type, T>::value>* = nullptr>
  [[deprecated]] SegmentTree(Iter first, Iter last, size_t n, T unit = {},
                             Combine combine = {}, Action action = {})
      : n(n), unit(unit), combine(combine), action(action), data(n << 1) {
    copy(first, last, data.begin() + n);
    build();
  }

  template <typename Iter>
  SegmentTree(Iter first, Iter last, T unit = {}, Combine combine = {},
              Action action = {})
      : SegmentTree(first, last, distance(first, last), unit, combine, action) {
  }

 private:
  void build() { repr(i, n) data[i] = combine(data[i << 1], data[i << 1 | 1]); }

 public:
  void modify(int l, T v) {
    l += n;
    data[l] = action(data[l], v);
    for (; l > 1; l >>= 1) data[l >> 1] = combine(data[l & (~1)], data[l | 1]);
  }

  T fold(int l, int r) const {
    if (l == r) return unit;
    if (l + 1 == r) return data[l + n];
    T resl = data[l += n], resr = data[(r += n) - 1];
    for (l++, r--; l < r; l >>= 1, r >>= 1) {
      if (l & 1) resl = combine(resl, data[l++]);
      if (r & 1) resr = combine(data[--r], resr);
    }
    return combine(resl, resr);
  }
  // min r s.t. fold(l, r) >= v -- or n+1 if failed
  template <typename Compare = less<T>>
  int lower_bound(T v, int l = 0, Compare comp = {}) {
    if (not comp(unit, v)) return l;
    int r = n;
    VI rootL, rootR;
    for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
      if (l & 1) rootL.push_back(l++);
      if (r & 1) rootR.push_back(--r);
    }
    VI roots = move(rootL); roots.insert(roots.end(), rall(rootR));
    T accL = unit;
    for (int root : roots) {
      T tmpL = combine(accL, data[root]);
      if (comp(tmpL, v)) {
        accL = tmpL;
        continue;
      }
      while (root < n) {
        tmpL = combine(accL, data[root << 1]);
        if (comp(tmpL, v)) accL = tmpL, root = root << 1 | 1;
        else root = root << 1;
      }
      return root - n + 1;
    }
    return n + 1;
  }
};
#pragma GCC diagnostic pop

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