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: \(O((m + q) \log (m + 2))\) with linear stable-sort workspace. Space: \(O(1 + m + q)\), where \(m\) is the span of all nonempty queries.
AC 记录：static_range_count_distinct。
Implementation¶
当前头文件，省略 include guard；依赖见 #include。
/// @complexity Time: O((m+q) log(m+2)) with linear stable-sort workspace.
/// Space: O(1+m+q), where m is the span of all nonempty queries.
#include "noya/ds/point_add_range_sum.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <numeric>
#include <utility>
#include <vector>
namespace noya {
/// @brief Count distinct values in every offline half-open range [l, r).
/// Values are grouped by ordering equivalence; bounds assume O(1) comparisons.
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<int> ans(qs.size());
int first = n, end = 0;
for (auto [l, r] : qs) {
assert(0 <= l && l <= r && r <= n);
if (l < r) {
first = std::min(first, l);
end = std::max(end, r);
}
}
if (first >= end) return ans;
const int m = end - first;
std::vector<int> prev(m, -1);
{
std::vector<int> order(m);
std::iota(order.begin(), order.end(), 0);
// Stable ties retain position order, so adjacent equals give predecessors.
std::stable_sort(order.begin(), order.end(),
[&](int i, int j) { return a[first + i] < a[first + j]; });
for (int i = 1; i < m; ++i) {
if (!(a[first + order[i - 1]] < a[first + order[i]]))
prev[order[i]] = order[i - 1];
}
}
std::vector<int> head(std::size_t(m) + 1, -1), next(qs.size());
for (int id = 0; id < int(qs.size()); ++id) {
auto [l, r] = qs[id];
if (l == r) continue;
r -= first;
next[id] = head[r];
head[r] = id;
}
fenwick<int> covered(m);
int distinct = 0;
for (int pos = 0; pos < m; ++pos) {
if (prev[pos] == -1) ++distinct;
else covered.add(prev[pos], 1);
// At r=pos+1, there are r-distinct covered positions in the prefix.
// Remove those in [l,r) from its length: distinct-l+covered.query(l).
for (int id = head[pos + 1]; id != -1; id = next[id]) {
int l = qs[id].first - first;
ans[id] = distinct - l + covered.query(l);
}
}
return ans;
}
} // namespace noya
// NOYA_STATIC_RANGE_DISTINCT_HPP
#ifndef NOYA_STATIC_RANGE_DISTINCT_HPP
#define NOYA_STATIC_RANGE_DISTINCT_HPP 1
/// @complexity Time: O((m+q) log(m+2)) with linear stable-sort workspace.
/// Space: O(1+m+q), where m is the span of all nonempty queries.
#include "noya/ds/point_add_range_sum.hpp"
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <numeric>
#include <utility>
#include <vector>
namespace noya {
/// @brief Count distinct values in every offline half-open range [l, r).
/// Values are grouped by ordering equivalence; bounds assume O(1) comparisons.
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<int> ans(qs.size());
int first = n, end = 0;
for (auto [l, r] : qs) {
assert(0 <= l && l <= r && r <= n);
if (l < r) {
first = std::min(first, l);
end = std::max(end, r);
}
}
if (first >= end) return ans;
const int m = end - first;
std::vector<int> prev(m, -1);
{
std::vector<int> order(m);
std::iota(order.begin(), order.end(), 0);
// Stable ties retain position order, so adjacent equals give predecessors.
std::stable_sort(order.begin(), order.end(),
[&](int i, int j) { return a[first + i] < a[first + j]; });
for (int i = 1; i < m; ++i) {
if (!(a[first + order[i - 1]] < a[first + order[i]]))
prev[order[i]] = order[i - 1];
}
}
std::vector<int> head(std::size_t(m) + 1, -1), next(qs.size());
for (int id = 0; id < int(qs.size()); ++id) {
auto [l, r] = qs[id];
if (l == r) continue;
r -= first;
next[id] = head[r];
head[r] = id;
}
fenwick<int> covered(m);
int distinct = 0;
for (int pos = 0; pos < m; ++pos) {
if (prev[pos] == -1) ++distinct;
else covered.add(prev[pos], 1);
// At r=pos+1, there are r-distinct covered positions in the prefix.
// Remove those in [l,r) from its length: distinct-l+covered.query(l).
for (int id = head[pos + 1]; id != -1; id = next[id]) {
int l = qs[id].first - first;
ans[id] = distinct - l + covered.query(l);
}
}
return ans;
}
} // namespace noya
#endif // NOYA_STATIC_RANGE_DISTINCT_HPP
/// @complexity Time: O((m+q) log(m+2)) with linear stable-sort workspace.
/// Space: O(1+m+q), where m is the span of all nonempty queries.
/// @complexity Time: fenwick O(log n) update/query; block O(1) update and
/// O(sqrt(n)) query. Both initialize in O(n).
/// Space: O(n).
#include <cassert>
#include <vector>
#include <cassert>
#include <numeric>
#include <type_traits>
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
#include <algorithm>
#include <cassert>
#include <cmath>
#include <vector>
namespace noya {
/// @brief Square-root decomposition for point additions and range sums.
template <class T> struct block {
int V = 0, B = 1;
block() = default;
block(const int &_V) { build(_V); }
std::vector<T> pt, blo;
void build(const int &_V) {
assert(_V >= 0);
V = _V;
B = std::max(1, int(std::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);
if (l == 0) {
return query(r);
}
int lb = l / B, rb = r / B;
T res = 0;
if (lb == rb) {
for (int i = l; i < r; ++i)
res += pt[i];
return res;
}
if (l == lb * B) {
res += blo[lb];
} else {
for (int i = l; i < (lb + 1) * B; ++i)
res += pt[i];
}
for (int i = lb + 1; i < rb; ++i)
res += blo[i];
for (int i = rb * B; i < r; ++i)
res += pt[i];
return res;
}
};
/// @brief Fenwick-tree wrapper with prefix query and half-open prod aliases.
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
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <numeric>
#include <utility>
#include <vector>
namespace noya {
/// @brief Count distinct values in every offline half-open range [l, r).
/// Values are grouped by ordering equivalence; bounds assume O(1) comparisons.
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<int> ans(qs.size());
int first = n, end = 0;
for (auto [l, r] : qs) {
assert(0 <= l && l <= r && r <= n);
if (l < r) {
first = std::min(first, l);
end = std::max(end, r);
}
}
if (first >= end) return ans;
const int m = end - first;
std::vector<int> prev(m, -1);
{
std::vector<int> order(m);
std::iota(order.begin(), order.end(), 0);
// Stable ties retain position order, so adjacent equals give predecessors.
std::stable_sort(order.begin(), order.end(),
[&](int i, int j) { return a[first + i] < a[first + j]; });
for (int i = 1; i < m; ++i) {
if (!(a[first + order[i - 1]] < a[first + order[i]]))
prev[order[i]] = order[i - 1];
}
}
std::vector<int> head(std::size_t(m) + 1, -1), next(qs.size());
for (int id = 0; id < int(qs.size()); ++id) {
auto [l, r] = qs[id];
if (l == r) continue;
r -= first;
next[id] = head[r];
head[r] = id;
}
fenwick<int> covered(m);
int distinct = 0;
for (int pos = 0; pos < m; ++pos) {
if (prev[pos] == -1) ++distinct;
else covered.add(prev[pos], 1);
// At r=pos+1, there are r-distinct covered positions in the prefix.
// Remove those in [l,r) from its length: distinct-l+covered.query(l).
for (int id = head[pos + 1]; id != -1; id = next[id]) {
int l = qs[id].first - first;
ans[id] = distinct - l + covered.query(l);
}
}
return ans;
}
} // namespace noya
// NOYA_STATIC_RANGE_DISTINCT_HPP