cp-library
競技プログラミング用 C++ ライブラリ
test/hld_path_sum.test.cpp
test/hld_path_sum.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include "../data_structure/fenwick_tree.hpp"
#include "../tree/hld.hpp"
#include "components/fast_io.hpp"
#include <vector>
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<long long> a(n);
for (auto &x : a) input.read(x);
HLD tree(n);
for (int i = 1, u, v; i < n; ++i) {
input.read(u), input.read(v);
tree.add_edge(u, v);
}
tree.build();
std::vector<long long> ordered(n);
for (int v = 0; v < n; ++v) ordered[tree.in[v]] = a[v];
FenwickTree<long long> seg(ordered);
while (q--) {
int type, u;
long long v;
input.read(type), input.read(u), input.read(v);
if (type == 0) seg.add(tree.in[u], v);
else {
long long result = 0;
tree.for_each_path(u, int(v), [&](int l, int r, bool) { result += seg.sum(l, r); });
output.println(result);
}
}
}
#line 1 "test/hld_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#line 1 "data_structure/fenwick_tree.hpp"
#include <cassert>
#include <cstddef>
#include <limits>
#include <type_traits>
#include <vector>
namespace fenwick_tree_detail {
template<class T, bool = std::is_integral_v<T>> struct Storage { using type = T; };
template<class T> struct Storage<T, true> { using type = std::make_unsigned_t<T>; };
#if defined(__SIZEOF_INT128__)
template<> struct Storage<__int128_t, false> { using type = __uint128_t; };
#endif
}
template<class T, bool Padded = true> class FenwickTree {
static_assert(!std::is_same_v<T, bool>);
using U = typename fenwick_tree_detail::Storage<T>::type;
std::vector<U> data_;
int n_ = 0;
static std::size_t index(unsigned i) {
if constexpr (Padded) return std::size_t(i) + (i >> 10);
else return i;
}
public:
explicit FenwickTree(int n = 0) : n_(n) {
assert(n >= 0);
data_.resize(index(unsigned(n)) + 1);
}
explicit FenwickTree(const std::vector<T> &a) {
assert(a.size() <= std::size_t(std::numeric_limits<int>::max()));
n_ = static_cast<int>(a.size());
data_.resize(index(unsigned(n_)) + 1);
for (unsigned i = 2; i <= unsigned(n_); i += 2) {
data_[index(i - 1)] += U(a[i - 2]);
data_[index(i)] += data_[index(i - 1)];
data_[index(i)] += U(a[i - 1]);
unsigned p = i + (i & -i);
if (p <= unsigned(n_)) data_[index(p)] += data_[index(i)];
}
if (n_ & 1) data_[index(unsigned(n_))] += U(a.back());
}
[[nodiscard]] int size() const { return n_; }
void add(int p, T x) {
assert(0 <= p && p < n_);
for (unsigned i = unsigned(p) + 1; i <= unsigned(n_); i += i & -i) data_[index(i)] += U(x);
}
[[nodiscard]] T sum(int r) const {
assert(0 <= r && r <= n_);
U result{};
for (unsigned i = unsigned(r); i; i &= i - 1) result += data_[index(i)];
return T(result);
}
[[nodiscard]] T sum(int l, int r) const {
assert(0 <= l && l <= r && r <= n_);
U result{};
unsigned a = unsigned(l), b = unsigned(r);
while (b > a) result += data_[index(b)], b &= b - 1;
while (a > b) result -= data_[index(a)], a &= a - 1;
return T(result);
}
};
#line 1 "tree/hld.hpp"
#include <algorithm>
#include <array>
#line 9 "tree/hld.hpp"
#include <utility>
#line 11 "tree/hld.hpp"
class HLD {
int shape_ = 0, center_ = 0;
struct Node { int position, head, parent, offset; };
std::vector<Node> nodes;
void check([[maybe_unused]] int v) const { assert(0 <= v && v < n && int(in.size()) == n); }
void initialize() {
depth.assign(n, 0);
size.assign(n, 1);
heavy.assign(n, -1);
head.resize(n), in.resize(n), out.resize(n), order.resize(n);
nodes.resize(n);
shape_ = center_ = 0;
}
void finish(int root) {
in[root] = 0, out[root] = n, head[root] = root;
for (int i = n - 2; i >= 0; --i) {
int v = order[i], p = parent[v];
depth[v] = depth[p] + 1;
if (heavy[p] == v) in[v] = in[p] + 1, head[v] = head[p];
else in[v] = out[p] -= size[v], head[v] = v;
out[v] = in[v] + size[v];
}
for (int v = 0; v < n; ++v) out[v] = in[v] + size[v], order[in[v]] = v;
parent[root] = -1;
for (int v = 0; v < n; ++v) nodes[v] = {in[v], in[head[v]], parent[head[v]], depth[v] - in[v]};
}
public:
struct Segment {
int l, r;
bool reversed;
};
int n;
std::vector<std::pair<int, int>> edges;
std::vector<int> parent, depth, size, heavy, head, in, out, order;
explicit HLD(int n = 0) : n(n) {
assert(0 <= n && n <= std::numeric_limits<int>::max() / 2);
edges.reserve(std::max(0, n - 1));
}
int add_edge(int u, int v) {
assert(0 <= u && u < n && 0 <= v && v < n);
edges.emplace_back(u, v);
return int(edges.size()) - 1;
}
void build(int root = 0) {
assert(n >= 0 && edges.size() == std::size_t(std::max(0, n - 1)));
assert(!n || (0 <= root && root < n));
parent.assign(n, -1);
initialize();
if (!n) return;
std::vector<int> degree(n), neighbors(n);
for (auto [u, v] : edges) {
++degree[u], ++degree[v];
neighbors[u] ^= v, neighbors[v] ^= u;
}
center_ = int(std::max_element(degree.begin(), degree.end()) - degree.begin());
shape_ = degree[center_] <= 2 ? 1 : degree[center_] == n - 1 ? 2 : 0;
degree[root] += 2;
int count = 0;
for (int v = 0; v < n; ++v) if (degree[v] == 1) order[count++] = v;
for (int i = 0; i < count; ++i) {
int v = order[i], p = neighbors[v];
parent[v] = p;
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
neighbors[p] ^= v;
if (--degree[p] == 1) order[count++] = p;
}
assert(count == n - 1);
finish(root);
}
void build_from_parents(std::vector<int> parents) {
assert(parents.size() <= std::size_t(std::numeric_limits<int>::max() / 2));
n = static_cast<int>(parents.size());
parent = std::move(parents);
initialize();
edges.clear();
edges.reserve(std::max(0, n - 1));
if (!n) return;
std::fill(out.begin(), out.end(), 0);
int root = -1;
bool ordered = true;
for (int v = 0; v < n; ++v) {
int p = parent[v];
assert(-1 <= p && p < n && p != v);
if (p == -1) {
assert(root == -1);
root = v;
} else {
++out[p];
edges.emplace_back(p, v);
ordered &= p < v;
}
}
assert(root != -1);
int maximum = 0;
for (int v = 0; v < n; ++v) {
int degree = out[v] + (v != root);
if (degree > maximum) maximum = degree, center_ = v;
}
shape_ = maximum <= 2 ? 1 : maximum == n - 1 ? 2 : 0;
if (ordered) {
for (int v = n - 1; v > 0; --v) {
int p = parent[v];
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
order[n - 1 - v] = v;
}
} else {
int count = 0;
for (int v = 0; v < n; ++v) if (!out[v] && v != root) order[count++] = v;
for (int i = 0; i < count; ++i) {
int v = order[i], p = parent[v];
size[p] += size[v];
if (heavy[p] == -1 || size[heavy[p]] < size[v]) heavy[p] = v;
if (!--out[p] && p != root) order[count++] = p;
}
assert(count == n - 1);
}
finish(root);
}
int lca(int u, int v) const {
check(u), check(v);
if (shape_ == 1) return head[u] != head[v] ? order[0] : in[u] < in[v] ? u : v;
if (shape_ == 2) return u == v ? u : u == order[0] || v == order[0] ? order[0] : center_;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) u = nodes[u].parent;
else v = nodes[v].parent;
}
return nodes[u].position < nodes[v].position ? u : v;
}
int dist(int u, int v) const {
int w = lca(u, v);
return depth[u] + depth[v] - 2 * depth[w];
}
bool is_ancestor(int u, int v) const {
check(u), check(v);
return in[u] <= in[v] && in[v] < out[u];
}
int ancestor(int v, int k) const {
check(v);
if (shape_) {
if (k < 0 || k > depth[v]) return -1;
if (!k) return v;
if (k == depth[v]) return order[0];
return shape_ == 2 ? parent[v] : order[in[v] - k];
}
if (k < 0) return -1;
int target = nodes[v].position + nodes[v].offset - k;
if (target < 0) return -1;
while (nodes[v].head + nodes[v].offset > target) v = nodes[v].parent;
return order[target - nodes[v].offset];
}
int jump(int u, int v, int k) const {
check(u), check(v);
if (k < 0) return -1;
if (!k) return u;
if (shape_ == 1) {
if (head[u] == head[v]) {
int delta = in[v] - in[u];
if (k > (delta < 0 ? -delta : delta)) return -1;
return order[in[u] + (delta < 0 ? -k : k)];
}
int a = depth[u], b = depth[v];
if (k > a + b) return -1;
if (k == a) return order[0];
return k < a ? order[in[u] - k] : order[in[v] - (a + b - k)];
}
if (shape_ == 2) {
int d = (u != center_) + (v != center_);
if (u == v || k > d) return -1;
return k == d ? v : center_;
}
int from = u, to = v, target = nodes[u].position + nodes[u].offset - k;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) {
if (nodes[u].head + nodes[u].offset <= target) return order[target - nodes[u].offset];
u = nodes[u].parent;
} else v = nodes[v].parent;
}
int w = nodes[u].position < nodes[v].position ? u : v;
int d = nodes[w].position + nodes[w].offset;
int length = nodes[from].position + nodes[from].offset + nodes[to].position + nodes[to].offset - 2 * d;
if (k > length) return -1;
if (target >= d) return order[target - nodes[u].offset];
return ancestor(to, length - k);
}
std::pair<int, int> subtree(int v, bool edge = false) const {
check(v);
return {in[v] + edge, out[v]};
}
int edge_vertex(int id) const {
assert(0 <= id && id < int(edges.size()));
auto [u, v] = edges[id];
check(u);
return parent[u] == v ? u : v;
}
template <class F>
void for_each_path(int u, int v, F &&f, bool edge = false) const {
check(u), check(v);
if (shape_ == 1) {
int x = in[u], y = in[v];
if (head[u] == head[v]) {
int l = std::min(x, y) + edge, r = std::max(x, y) + 1;
if (l < r) f(l, r, x > y);
} else if (head[u] == order[0]) {
if (edge < x + 1) f(int(edge), x + 1, true);
f(in[head[v]], y + 1, false);
} else {
f(in[head[u]], x + 1, true);
if (edge < y + 1) f(int(edge), y + 1, false);
}
return;
}
std::array<std::array<int, 2>, 32> right;
int count = 0;
while (nodes[u].head != nodes[v].head) {
if (nodes[u].position > nodes[v].position) {
f(nodes[u].head, nodes[u].position + 1, true);
u = nodes[u].parent;
} else {
assert(count < int(right.size()));
right[count++] = {nodes[v].head, nodes[v].position + 1};
v = nodes[v].parent;
}
}
bool reversed = nodes[u].position > nodes[v].position;
int l = std::min(nodes[u].position, nodes[v].position) + edge, r = std::max(nodes[u].position, nodes[v].position) + 1;
if (l < r) f(l, r, reversed);
while (count) {
auto [a, b] = right[--count];
f(a, b, false);
}
}
std::vector<Segment> path(int u, int v, bool edge = false) const {
std::vector<Segment> result;
for_each_path(u, v, [&](int l, int r, bool reversed) { result.push_back({l, r, reversed}); }, edge);
return result;
}
};
#line 1 "components/fast_io.hpp"
#line 6 "components/fast_io.hpp"
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 10 "components/fast_io.hpp"
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <memory>
#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 6 "test/hld_path_sum.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<long long> a(n);
for (auto &x : a) input.read(x);
HLD tree(n);
for (int i = 1, u, v; i < n; ++i) {
input.read(u), input.read(v);
tree.add_edge(u, v);
}
tree.build();
std::vector<long long> ordered(n);
for (int v = 0; v < n; ++v) ordered[tree.in[v]] = a[v];
FenwickTree<long long> seg(ordered);
while (q--) {
int type, u;
long long v;
input.read(type), input.read(u), input.read(v);
if (type == 0) seg.add(tree.in[u], v);
else {
long long result = 0;
tree.for_each_path(u, int(v), [&](int l, int r, bool) { result += seg.sum(l, r); });
output.println(result);
}
}
}