static_range_distinct.hpp¶
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。
Complexity: Time: O((n + q) log n). Space: O(n + q).
AC 记录：static_range_count_distinct。
Implementation¶
当前头文件，省略 include guard；依赖见 #include。
/// @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> &a,
const std::vector<std::pair<int, int>> &qs) {
const int n = int(a.size());
std::vector<T> xs = a;
std::sort(xs.begin(), xs.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
std::vector<std::vector<std::pair<int, int>>> by(n + 1);
for (int id = 0; id < int(qs.size()); id++) {
auto [l, r] = qs[id];
assert(0 <= l && l <= r && r <= n);
by[r].emplace_back(id, l);
}
fenwick<int> on(n);
std::vector<int> lst(xs.size(), -1);
std::vector<int> ans(qs.size());
for (int r = 0; r <= n; r++) {
if (r > 0) {
int pos = r - 1;
int val =
int(std::lower_bound(xs.begin(), xs.end(), a[pos]) - xs.begin());
if (lst[val] != -1) {
on.add(lst[val], -1);
}
on.add(pos, 1);
lst[val] = pos;
}
for (auto [id, l] : by[r]) {
ans[id] = on.prod(l, r);
}
}
return ans;
}
} // namespace noya
#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> &a,
const std::vector<std::pair<int, int>> &qs) {
const int n = int(a.size());
std::vector<T> xs = a;
std::sort(xs.begin(), xs.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
std::vector<std::vector<std::pair<int, int>>> by(n + 1);
for (int id = 0; id < int(qs.size()); id++) {
auto [l, r] = qs[id];
assert(0 <= l && l <= r && r <= n);
by[r].emplace_back(id, l);
}
fenwick<int> on(n);
std::vector<int> lst(xs.size(), -1);
std::vector<int> ans(qs.size());
for (int r = 0; r <= n; r++) {
if (r > 0) {
int pos = r - 1;
int val =
int(std::lower_bound(xs.begin(), xs.end(), a[pos]) - xs.begin());
if (lst[val] != -1) {
on.add(lst[val], -1);
}
on.add(pos, 1);
lst[val] = pos;
}
for (auto [id, l] : by[r]) {
ans[id] = on.prod(l, r);
}
}
return ans;
}
} // 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, B;
block() {}
block(const int &_V) {
if (_V > 0) {
build(_V);
}
}
std::vector<T> pt, blo;
void build(const int &_V) {
V = _V;
B = sqrt(V);
pt.assign(V, 0);
blo.assign(V / B + 1, 0);
}
void add(int x, T v) {
assert(0 <= x && x < V);
int bel = x / B;
blo[bel] += v;
pt[x] += v;
}
T query(int x) const {
assert(0 <= x && x <= V);
T res = 0;
int bel = x / B;
for (int i = 0; i < bel; i++)
res += blo[i];
int st = bel * B;
int end = x;
for (int i = st; i < end; i++)
res += pt[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> &a,
const std::vector<std::pair<int, int>> &qs) {
const int n = int(a.size());
std::vector<T> xs = a;
std::sort(xs.begin(), xs.end());
xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
std::vector<std::vector<std::pair<int, int>>> by(n + 1);
for (int id = 0; id < int(qs.size()); id++) {
auto [l, r] = qs[id];
assert(0 <= l && l <= r && r <= n);
by[r].emplace_back(id, l);
}
fenwick<int> on(n);
std::vector<int> lst(xs.size(), -1);
std::vector<int> ans(qs.size());
for (int r = 0; r <= n; r++) {
if (r > 0) {
int pos = r - 1;
int val =
int(std::lower_bound(xs.begin(), xs.end(), a[pos]) - xs.begin());
if (lst[val] != -1) {
on.add(lst[val], -1);
}
on.add(pos, 1);
lst[val] = pos;
}
for (auto [id, l] : by[r]) {
ans[id] = on.prod(l, r);
}
}
return ans;
}
} // namespace noya