test/range_kth_smallest2.test.cpp

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Last update: 2024-07-28 21:04:51+08:00
Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

Code

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

#include "../default/t.cpp"
#include "../misc/compression.cpp"
#include "../segtree/persistentSegmentTree.cpp"

int id() { return 0; }
int op(const int &a, const int &b) { return a + b; }

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n, q; cin >> n >> q;
  vector<int> a(n);
  for(int &x : a)
    cin >> x;

  compression<int, true> xs(a);
  persistentSegmentTree<int, id, op> st(2 * n + n * (bit_width((unsigned)n) + 1));
  vector<int> root(n + 1);
  root[0] = st.build(0, n);
  for(int i = 1; i <= n; i++)
    root[i] = st.set(root[i - 1], 0, n, xs.ord[i - 1], 1);

  while(q--) {
    int l, r, k; cin >> l >> r >> k;
    int u = root[l], v = root[r];
    int ql = 0, qr = n;
    while(ql + 1 < qr) {
      int mid = (ql + qr) / 2;
      if (int cnt = st.data[st.lc[v]] - st.data[st.lc[u]]; cnt <= k)
        k -= cnt, u = st.rc[u], v = st.rc[v], ql = mid;
      else
        u = st.lc[u], v = st.lc[v], qr = mid;
    }
    cout << xs.val[ql] << '\n';
  }

  return 0;
}

#line 1 "test/range_kth_smallest2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"

#line 1 "default/t.cpp"
#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 <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "misc/compression.cpp"
template<class T, bool duplicate = false>
struct compression {
  vector<int> ord;
  vector<T> val;

  compression(vector<T> &init) : val(init) { precompute(); }
  compression(int size = 0) { val.reserve(size); }

  void precompute() {
    vector<T> init = val;
    ord.resize(ssize(val));
    ranges::sort(val);
    if constexpr (duplicate) {
      vector<int> cnt(ssize(init));
      iota(cnt.begin(), cnt.end(), 0);
      for(int i = 0; i < ssize(ord); i++)
        ord[i] = cnt[lower_bound(init[i])]++;
    } else {
      val.resize(unique(val.begin(), val.end()) - val.begin());
      for(int i = 0; i < ssize(ord); i++)
        ord[i] = lower_bound(init[i]);
    }
  }

  int lower_bound(T x) { return ranges::lower_bound(val, x) - val.begin(); }
  int size() { return ssize(val); }
  template<ranges::range rng, class proj = identity>
  void mapping(rng &v, proj p = {}) { for(auto &x : v) p(x) = lower_bound(p(x)); }
  template<ranges::range rng, class proj = identity>
  void insert(rng &v, proj p = {}) { for(auto &x : v) val.emplace_back(p(x)); }
};
#line 1 "segtree/persistentSegmentTree.cpp"
template<class M, M(*id)(), M(*op)(const M&, const M&)>
struct persistentSegmentTree {
  vector<int> lc, rc;
  vector<M> data, init;
  int nxt = 0;

  //sz >= (2n - 1) + q * (bit_width(n) + 1) should be satisfied
  persistentSegmentTree(int sz, vector<M> _init = vector<M>())
  : lc(sz, -1), rc(sz, -1), data(sz, id()), init(_init) {}

  int build(int l, int r) {
    int i = nxt++;
    if (l + 1 == r) {
      if (!init.empty()) data[i] = init[l];
    } else {
      int mid = (l + r) / 2;
      lc[i] = build(l, mid), rc[i] = build(mid, r);
      data[i] = op(data[lc[i]], data[rc[i]]);
    }
    return i;
  }

  int set(int v, int l, int r, int i, M x) {  
    int vv = nxt++;
    if (l + 1 == r) {
      data[vv] = x;
    } else {
      if (int mid = (l + r) / 2; i < mid)
        lc[vv] = set(lc[v], l, mid, i, x), rc[vv] = rc[v];
      else
        lc[vv] = lc[v], rc[vv] = set(rc[v], mid, r, i, x);
      data[vv] = op(data[lc[vv]], data[rc[vv]]);
    }
    return vv;
  }

  M query(int i, int l, int r, int ql, int qr) {
    if (ql == qr or i == -1 or r <= ql or l >= qr) return id();
    if (ql <= l and r <= qr) return data[i];
    return op(query(lc[i], l, (l + r) / 2, ql, qr), 
              query(rc[i], (l + r) / 2, r, ql, qr));
  }
};
#line 6 "test/range_kth_smallest2.test.cpp"

int id() { return 0; }
int op(const int &a, const int &b) { return a + b; }

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int n, q; cin >> n >> q;
  vector<int> a(n);
  for(int &x : a)
    cin >> x;

  compression<int, true> xs(a);
  persistentSegmentTree<int, id, op> st(2 * n + n * (bit_width((unsigned)n) + 1));
  vector<int> root(n + 1);
  root[0] = st.build(0, n);
  for(int i = 1; i <= n; i++)
    root[i] = st.set(root[i - 1], 0, n, xs.ord[i - 1], 1);

  while(q--) {
    int l, r, k; cin >> l >> r >> k;
    int u = root[l], v = root[r];
    int ql = 0, qr = n;
    while(ql + 1 < qr) {
      int mid = (ql + qr) / 2;
      if (int cnt = st.data[st.lc[v]] - st.data[st.lc[u]]; cnt <= k)
        k -= cnt, u = st.rc[u], v = st.rc[v], ql = mid;
      else
        u = st.lc[u], v = st.lc[v], qr = mid;
    }
    cout << xs.val[ql] << '\n';
  }

  return 0;
}