cp-library
競技プログラミング用 C++ ライブラリ
test/permutation_tree.test.cpp
test/permutation_tree.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/common_interval_decomposition_tree"
#include "../tree/permutation_tree.hpp"
#include "../components/fast_io.hpp"
int main() {
FastInput in;
FastOutput out;
int n = 0;
in.read(n);
std::vector<int> p(n);
for (int &x : p) in.read(x);
PermutationTree tree(p);
std::vector<int> id(tree.size());
for (int i = 0; i < tree.size(); ++i) id[tree.order()[i]] = i;
out.println(tree.size());
for (int v : tree.order()) {
const auto &node = tree[v];
out.write(node.parent < 0 ? -1 : id[node.parent]); out.write(' ');
out.write(node.l); out.write(' ');
out.write(node.r - 1); out.write(' ');
out.write(node.type == PermutationTree::Type::Prime ? "prime\n" : "linear\n");
}
}
#line 1 "test/permutation_tree.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/common_interval_decomposition_tree"
#line 1 "tree/permutation_tree.hpp"
#line 1 "components/static_range_min.hpp"
#line 1 "components/default_init_allocator.hpp"
#include <memory>
#include <new>
template <class T>
struct DefaultInitAllocator : std::allocator<T> {
template <class U>
struct rebind {
using other = DefaultInitAllocator<U>;
};
DefaultInitAllocator() = default;
template <class U>
DefaultInitAllocator(const DefaultInitAllocator<U> &) noexcept {}
template <class U>
void construct(U *p) { ::new (static_cast<void *>(p)) U; }
};
#line 1 "data_structure/sparse_table.hpp"
#line 5 "data_structure/sparse_table.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>
#include <vector>
template <class S, auto op, auto e = nullptr>
class SparseTable {
using Value = std::conditional_t<std::is_same_v<S, bool>, std::uint8_t, S>;
using Reference = std::conditional_t<std::is_same_v<S, bool>, bool, const S &>;
int n = 0;
std::vector<std::vector<Value, DefaultInitAllocator<Value>>> data;
static decltype(auto) combine(const Value &a, const Value &b) {
if constexpr (std::is_same_v<S, bool> || !std::is_invocable_v<decltype(op), const S &, const S &>) return S(op(S(a), S(b)));
else return op(a, b);
}
public:
SparseTable() = default;
SparseTable(const SparseTable &) = default;
SparseTable &operator=(const SparseTable &) = default;
SparseTable(SparseTable &&other) noexcept : n(std::exchange(other.n, 0)), data(std::move(other.data)) {}
SparseTable &operator=(SparseTable &&other) noexcept {
if (this != &other) {
n = std::exchange(other.n, 0);
data = std::move(other.data);
}
return *this;
}
explicit SparseTable(const std::vector<S> &a) { build(a); }
void clear() {
data.clear();
n = 0;
}
void build(const std::vector<S> &a) {
assert(a.size() <= std::size_t(std::numeric_limits<int>::max()));
build(static_cast<int>(a.size()), [&](int i) -> S { return a[i]; });
}
template <class F>
void build(int size, F value) {
assert(size >= 0);
n = size;
data.resize(std::bit_width(unsigned(n)));
if (!n) return;
if constexpr (std::is_default_constructible_v<Value>) {
data[0].resize(n);
for (int i = 0; i < n; ++i) data[0][i] = value(i);
} else {
data[0].clear();
data[0].reserve(n);
for (int i = 0; i < n; ++i) data[0].push_back(value(i));
}
for (int k = 1; k < std::bit_width(unsigned(n)); ++k) {
int length = n - (1U << k) + 1, half = 1U << (k - 1);
if constexpr (std::is_default_constructible_v<Value>) {
data[k].resize(length);
for (int i = 0; i < length; ++i) data[k][i] = combine(data[k - 1][i], data[k - 1][i + half]);
} else {
data[k].clear();
data[k].reserve(length);
for (int i = 0; i < length; ++i) data[k].push_back(combine(data[k - 1][i], data[k - 1][i + half]));
}
}
}
int size() const { return n; }
bool empty() const { return n == 0; }
Reference operator[](int i) const {
assert(0 <= i && i < n);
return data[0][i];
}
[[gnu::always_inline]] S prod(int l, int r) const {
assert(0 <= l && l <= r && r <= n);
if constexpr (std::is_same_v<decltype(e), std::nullptr_t>) assert(l < r);
else if (l == r) return e();
return prod_unchecked(l, r);
}
[[gnu::always_inline]] S prod_unchecked(int l, int r) const {
int k = std::bit_width(unsigned(r - l)) - 1;
return combine(data[k][l], data[k][r - (1U << k)]);
}
S all_prod() const { return prod(0, n); }
};
#line 7 "components/static_range_min.hpp"
#include <array>
#line 12 "components/static_range_min.hpp"
#include <span>
#line 16 "components/static_range_min.hpp"
template <class T = int, bool FastBoundaries = false> class StaticRangeMin {
static T minimum(T a, T b) { return b < a ? b : a; }
std::vector<T> values_;
std::vector<std::uint32_t, DefaultInitAllocator<std::uint32_t>> masks_;
SparseTable<T, minimum> blocks_;
struct Boundaries { std::vector<T> prefix, suffix; };
struct Empty {};
[[no_unique_address]] std::conditional_t<FastBoundaries, Boundaries, Empty> boundaries_;
T within(int l, int r) const {
auto mask = masks_[r - 1] & (~std::uint32_t(0) << (l & 31));
return values_[(l & ~31) + std::countr_zero(mask)];
}
public:
StaticRangeMin() = default;
explicit StaticRangeMin(std::vector<T> values) { build(std::move(values)); }
void build(std::vector<T> values) {
assert(values.size() <= std::size_t(std::numeric_limits<int>::max()));
values_ = std::move(values);
int n = size();
masks_.resize(n);
for (int first = 0; first < n;) {
int last = first + std::min(32, n - first);
std::uint32_t mask = 0;
for (int i = first; i < last; ++i) {
while (mask && !(values_[first + std::bit_width(mask) - 1] < values_[i]))
mask &= ~(std::uint32_t(1) << (std::bit_width(mask) - 1));
mask |= std::uint32_t(1) << (i - first);
masks_[i] = mask;
}
first = last;
}
if constexpr (FastBoundaries) {
boundaries_.prefix = values_, boundaries_.suffix = values_;
for (int first = 0; first < n;) {
int last = first + std::min(32, n - first);
for (int i = first + 1; i < last; ++i) boundaries_.prefix[i] = minimum(boundaries_.prefix[i - 1], values_[i]);
for (int i = last - 1; i > first; --i) boundaries_.suffix[i - 1] = minimum(values_[i - 1], boundaries_.suffix[i]);
first = last;
}
}
blocks_.build(n ? (n - 1) / 32 + 1 : 0, [&](int i) {
int last = i * 32 + std::min(32, n - i * 32);
if constexpr (FastBoundaries) return T(boundaries_.prefix[last - 1]);
else return within(i * 32, last);
});
}
int size() const { return static_cast<int>(values_.size()); }
bool empty() const { return values_.empty(); }
std::conditional_t<std::is_same_v<T, bool>, bool, const T &> operator[](int i) const {
assert(0 <= i && i < size());
return values_[i];
}
T prod(int l, int r) const {
assert(0 <= l && l < r && r <= size());
int a = l / 32, b = (r - 1) / 32;
if (a == b) return within(l, r);
T value = [&] {
if constexpr (FastBoundaries) return minimum(boundaries_.suffix[l], boundaries_.prefix[r - 1]);
else return minimum(within(l, (a + 1) * 32), within(b * 32, r));
}();
if (a + 1 < b) value = minimum(value, blocks_.prod_unchecked(a + 1, b));
return value;
}
std::vector<T> prod_many(std::span<const std::pair<int, int>> ranges) const {
std::vector<T> result;
result.reserve(ranges.size());
if constexpr (FastBoundaries) {
for (auto [l, r] : ranges) result.emplace_back(prod(l, r));
} else {
std::array<int, 32> left, right;
for (std::size_t first = 0; first < ranges.size(); first += 32) {
int count = int(std::min<std::size_t>(32, ranges.size() - first));
for (int i = 0; i < count; ++i) {
auto [l, r] = ranges[first + i];
assert(0 <= l && l < r && r <= size());
int a = l & ~31, b = (r - 1) & ~31;
auto mask = masks_[a == b ? r - 1 : a + 31] & (~std::uint32_t(0) << (l & 31));
left[i] = a + std::countr_zero(mask);
right[i] = a == b ? left[i] : b + std::countr_zero(masks_[r - 1]);
#if defined(__GNUC__) || defined(__clang__)
if constexpr (!std::is_same_v<T, bool>) {
__builtin_prefetch(values_.data() + left[i]);
__builtin_prefetch(values_.data() + right[i]);
}
#endif
}
for (int i = 0; i < count; ++i) {
auto [l, r] = ranges[first + i];
T value = minimum(values_[left[i]], values_[right[i]]);
int a = l / 32 + 1, b = (r - 1) / 32;
if (a < b) value = minimum(value, blocks_.prod_unchecked(a, b));
result.emplace_back(std::move(value));
}
}
}
return result;
}
T all_prod() const { return prod(0, size()); }
};
#line 11 "tree/permutation_tree.hpp"
class PermutationTree {
public:
enum class Type : unsigned char { Leaf, Increasing, Decreasing, Prime };
struct Node {
int parent, l, r, lo, hi;
Type type;
};
private:
int root_ = -1;
std::int64_t count_ = 0;
std::vector<Node> nodes_;
std::vector<int> offsets_, children_, order_;
int add_node(int l, int r, int lo, int hi, Type type) {
int id = size();
nodes_.push_back({-1, l, r, lo, hi, type});
return id;
}
void pack(int n) {
int m = size();
offsets_.assign(m + 1, 0);
for (auto &node : nodes_) if (node.parent >= 0) ++offsets_[node.parent + 1];
for (int i = 0; i < m; ++i) offsets_[i + 1] += offsets_[i];
children_.resize(m - 1);
std::vector<int> cursor = offsets_;
for (int i = 0; i < n; ++i) {
int v = i;
while (nodes_[v].parent >= 0) {
int parent = nodes_[v].parent;
children_[cursor[parent]++] = v;
if (nodes_[parent].l != i) break;
v = parent;
}
}
count_ = n;
for (int i = n; i < m; ++i) {
std::int64_t k = offsets_[i + 1] - offsets_[i];
count_ += nodes_[i].type == Type::Prime ? 1 : k * (k - 1) / 2;
}
order_.clear();
order_.reserve(m);
order_.push_back(root_);
for (int i = 0; i < m; ++i)
for (int child : children(order_[i])) order_.push_back(child);
}
public:
PermutationTree() = default;
explicit PermutationTree(std::span<const int> permutation) { build(permutation); }
void build(std::span<const int> permutation) {
assert(permutation.size() <= std::size_t(std::numeric_limits<int>::max() / 2));
int n = static_cast<int>(permutation.size());
root_ = -1;
count_ = 0;
nodes_.clear();
offsets_.clear();
children_.clear();
order_.clear();
if (!n) return;
nodes_.reserve(2 * std::size_t(n) - 1);
std::vector<int> inverse(n, -1);
for (int i = 0; i < n; ++i) {
int x = permutation[i];
assert(0 <= x && x < n && inverse[x] < 0);
inverse[x] = i;
add_node(i, i + 1, x, x + 1, Type::Leaf);
}
struct Frame { int l, lo, hi; };
struct Interval { int l, r, lo, hi; };
std::vector<Interval> intervals;
{
StaticRangeMin minimum(std::move(inverse));
std::vector<Frame> stack;
stack.reserve(n);
intervals.reserve(n - 1);
for (int r = 1; r <= n; ++r) {
int x = permutation[r - 1];
Frame current{r - 1, x, x + 1};
while (!stack.empty()) {
auto &top = stack.back();
top.lo = std::min(top.lo, current.lo);
top.hi = std::max(top.hi, current.hi);
if (top.hi - top.lo == r - top.l) {
current = top;
intervals.push_back({top.l, r, top.lo, top.hi});
stack.pop_back();
} else if (minimum.prod(top.lo, top.hi) < top.l) {
Frame removed = top;
stack.pop_back();
assert(!stack.empty());
stack.back().lo = std::min(stack.back().lo, removed.lo);
stack.back().hi = std::max(stack.back().hi, removed.hi);
} else break;
}
stack.push_back(current);
}
assert(stack.size() == 1 && stack[0].l == 0);
}
std::vector<int> at(n), next(n);
for (int i = 0; i < n; ++i) at[i] = i, next[i] = i + 1;
for (auto interval : intervals) {
int l = interval.l, r = interval.r, middle = next[l];
int first = at[l], id;
if (next[middle] == r) {
int second = at[middle];
Type type = nodes_[first].hi == nodes_[second].lo ? Type::Increasing : Type::Decreasing;
if (nodes_[first].type == type) {
id = first;
nodes_[id].r = r;
nodes_[id].lo = interval.lo;
nodes_[id].hi = interval.hi;
nodes_[second].parent = id;
} else {
id = add_node(l, r, interval.lo, interval.hi, type);
nodes_[first].parent = nodes_[second].parent = id;
}
} else {
id = add_node(l, r, interval.lo, interval.hi, Type::Prime);
for (int i = l; i < r; i = next[i]) nodes_[at[i]].parent = id;
}
at[l] = id;
next[l] = r;
}
root_ = at[0];
assert(next[0] == n);
pack(n);
}
int size() const { return static_cast<int>(nodes_.size()); }
bool empty() const { return nodes_.empty(); }
int root() const { return empty() ? -1 : root_; }
int length() const { return empty() ? 0 : nodes_[root_].r; }
int leaf(int i) const { assert(0 <= i && i < length()); return i; }
const Node &operator[](int i) const {
assert(0 <= i && i < size());
return nodes_[i];
}
const std::vector<Node> &nodes() const { return nodes_; }
std::span<const int> children(int v) const {
assert(0 <= v && v < size());
return std::span<const int>(children_).subspan(offsets_[v], offsets_[v + 1] - offsets_[v]);
}
std::span<const int> order() const { return order_; }
std::int64_t count_intervals() const { return empty() ? 0 : count_; }
};
#line 1 "components/fast_io.hpp"
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#line 14 "components/fast_io.hpp"
#include <stdexcept>
#include <string>
#include <string_view>
#line 18 "components/fast_io.hpp"
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 4 "test/permutation_tree.test.cpp"
int main() {
FastInput in;
FastOutput out;
int n = 0;
in.read(n);
std::vector<int> p(n);
for (int &x : p) in.read(x);
PermutationTree tree(p);
std::vector<int> id(tree.size());
for (int i = 0; i < tree.size(); ++i) id[tree.order()[i]] = i;
out.println(tree.size());
for (int v : tree.order()) {
const auto &node = tree[v];
out.write(node.parent < 0 ? -1 : id[node.parent]); out.write(' ');
out.write(node.l); out.write(' ');
out.write(node.r - 1); out.write(' ');
out.write(node.type == PermutationTree::Type::Prime ? "prime\n" : "linear\n");
}
}