static_range_distinct.hpp¶
Count distinct values in every offline half-open range [l, r).
Verified by static_range_count_distinct.
回答静态数组任意区间内不同值的个数；适合大量不带修改的区间去重计数。
Implementation¶
#ifndef NOYA_STATIC_RANGE_DISTINCT_HPP
#define NOYA_STATIC_RANGE_DISTINCT_HPP 1
/// @complexity Time: O((n + q) log n).
/// Space: O(n + q).
#include "noya/point_add_range_sum.hpp"
#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>
namespace noya {
/// @brief Count distinct values in every offline half-open range [l, r).
template <class T>
std::vector<int>
static_range_distinct(const std::vector<T> &values,
const std::vector<std::pair<int, int>> &queries) {
const int n = int(values.size());
std::vector<T> coordinates = values;
std::sort(coordinates.begin(), coordinates.end());
coordinates.erase(std::unique(coordinates.begin(), coordinates.end()),
coordinates.end());
std::vector<std::vector<std::pair<int, int>>> by_right(n + 1);
for (int id = 0; id < int(queries.size()); id++) {
auto [left, right] = queries[id];
assert(0 <= left && left <= right && right <= n);
by_right[right].emplace_back(id, left);
}
fenwick<int> active(n);
std::vector<int> last(coordinates.size(), -1);
std::vector<int> answer(queries.size());
for (int right = 0; right <= n; right++) {
if (right > 0) {
int position = right - 1;
int value = int(std::lower_bound(coordinates.begin(), coordinates.end(),
values[position]) -
coordinates.begin());
if (last[value] != -1) {
active.add(last[value], -1);
}
active.add(position, 1);
last[value] = position;
}
for (auto [id, left] : by_right[right]) {
answer[id] = active.prod(left, right);
}
}
return answer;
}
} // namespace noya
#endif // NOYA_STATIC_RANGE_DISTINCT_HPP
#include <algorithm>
#include <cassert>
#include <cmath>
#include <numeric>
#include <type_traits>
#include <utility>
#include <vector>
/// @complexity Time: O((n + q) log n).
/// Space: O(n + q).
/// @complexity Time: O(log n) point update or range sum.
/// Space: O(n).
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
// Reference: https://en.wikipedia.org/wiki/Fenwick_tree
template <class T> struct fenwick_tree {
using U = internal::to_unsigned_t<T>;
public:
fenwick_tree() : _n(0) {}
explicit fenwick_tree(int n) : _n(n), data(n) {}
void add(int p, T x) {
assert(0 <= p && p < _n);
p++;
while (p <= _n) {
data[p - 1] += U(x);
p += p & -p;
}
}
T sum(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
return sum(r) - sum(l);
}
private:
int _n;
std::vector<U> data;
U sum(int r) {
U s = 0;
while (r > 0) {
s += data[r - 1];
r -= r & -r;
}
return s;
}
};
} // namespace atcoder
namespace noya {
template <class T> struct block {
int V, sqrtV;
block() {}
block(const int &_V) {
if (_V > 0) {
build(_V);
}
}
std::vector<T> point, blo;
void build(const int &_V) {
V = _V;
sqrtV = sqrt(V);
point.assign(V, 0);
blo.assign(V / sqrtV + 1, 0);
}
void add(int x, T v) {
assert(0 <= x && x < V);
int bel = x / sqrtV;
blo[bel] += v;
point[x] += v;
}
T query(int x) const {
assert(0 <= x && x <= V);
T res = 0;
int bel = x / sqrtV;
for (int i = 0; i < bel; i++)
res += blo[i];
int start = bel * sqrtV;
int end = x;
for (int i = start; i < end; i++)
res += point[i];
return res;
}
/// @brief Sum of [l, r).
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= V);
return query(r) - query(l);
}
};
template <class T> struct fenwick : atcoder::fenwick_tree<T> {
using atcoder::fenwick_tree<T>::fenwick_tree;
using atcoder::fenwick_tree<T>::add;
T query(int x) { return this->sum(0, x); }
T prod(int l, int r) { return this->sum(l, r); }
};
} // namespace noya
namespace noya {
/// @brief Count distinct values in every offline half-open range [l, r).
template <class T>
std::vector<int>
static_range_distinct(const std::vector<T> &values,
const std::vector<std::pair<int, int>> &queries) {
const int n = int(values.size());
std::vector<T> coordinates = values;
std::sort(coordinates.begin(), coordinates.end());
coordinates.erase(std::unique(coordinates.begin(), coordinates.end()),
coordinates.end());
std::vector<std::vector<std::pair<int, int>>> by_right(n + 1);
for (int id = 0; id < int(queries.size()); id++) {
auto [left, right] = queries[id];
assert(0 <= left && left <= right && right <= n);
by_right[right].emplace_back(id, left);
}
fenwick<int> active(n);
std::vector<int> last(coordinates.size(), -1);
std::vector<int> answer(queries.size());
for (int right = 0; right <= n; right++) {
if (right > 0) {
int position = right - 1;
int value = int(std::lower_bound(coordinates.begin(), coordinates.end(),
values[position]) -
coordinates.begin());
if (last[value] != -1) {
active.add(last[value], -1);
}
active.add(position, 1);
last[value] = position;
}
for (auto [id, left] : by_right[right]) {
answer[id] = active.prod(left, right);
}
}
return answer;
}
} // namespace noya