cp-library
競技プログラミング用 C++ ライブラリ
test/lca_path_sum.test.cpp
test/lca_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 "tree/lca.hpp"
#include "components/fenwick_sum.hpp"
#include "components/fast_io_bulk.hpp"
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<long long> values(n);
int vertex = 0;
read_unsigned_records<1>(input, n, [&](unsigned value) { values[vertex++] = value; });
LCA tree(n);
read_unsigned_records<2>(input, n - 1, [&](unsigned u, unsigned v) { tree.add_edge(u, v); });
tree.build();
std::vector<int> first(n), last(n);
std::vector<long long> difference(n);
for (int v = 0; v < n; ++v) {
auto [l, r] = tree.subtree(v);
first[v] = l, last[v] = r;
difference[l] += values[v];
if (r < n) difference[r] -= values[v];
}
FenwickSum<long long> sums(difference);
read_unsigned_records<3>(input, q, [&](unsigned type, unsigned u, unsigned x) {
if (!type) {
values[u] += x;
if (last[u] < n) sums.add_pair(first[u], x, last[u], -static_cast<long long>(x));
else sums.add(first[u], x);
} else {
int w = tree.lca(u, x);
long long answer = sums.prefix(first[u] + 1) + sums.prefix(first[x] + 1) - 2 * sums.prefix(first[w] + 1) + values[w];
output.println(answer);
}
});
}
#line 1 "test/lca_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#line 1 "tree/lca.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/lca.hpp"
class LCA {
std::vector<int> in, out, order;
bool ordered_ = false;
StaticRangeMin<int, true> table;
void check([[maybe_unused]] int v) const { assert(0 <= v && v < n && static_cast<int>(in.size()) == n); }
void finish(int root) {
in[root] = n;
ordered_ = root == 0;
for (int i = n - 2; i >= 0; --i) {
int v = order[i], p = parent[v];
depth[v] = depth[p] + 1;
in[v] = in[p];
in[p] -= out[v];
}
for (int v = 0; v < n; ++v) {
--in[v];
out[v] += in[v];
order[in[v]] = v;
ordered_ &= parent[v] < v;
}
std::vector<int> values(n);
for (int i = 1; i < n; ++i) values[i] = ordered_ ? parent[order[i]] : in[parent[order[i]]];
table.build(std::move(values));
parent[root] = -1;
}
public:
int n;
std::vector<std::pair<int, int>> edges;
std::vector<int> parent, depth;
explicit LCA(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 static_cast<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));
in.resize(n);
out.resize(n);
order.resize(n);
parent.assign(n, -1);
depth.assign(n, 0);
table = StaticRangeMin<int, true>();
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;
}
degree[root] += 2;
std::fill(out.begin(), out.end(), 1);
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;
out[p] += out[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);
in.resize(n);
out.assign(n, 1);
order.resize(n);
depth.assign(n, 0);
table = StaticRangeMin<int, true>();
edges.clear();
edges.reserve(std::max(0, n - 1));
if (!n) return;
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 {
edges.emplace_back(p, v);
ordered &= p < v;
}
}
assert(root != -1);
if (ordered) {
for (int v = n - 1; v > 0; --v) {
out[parent[v]] += out[v];
order[n - 1 - v] = v;
}
} else {
std::fill(in.begin(), in.end(), 0);
for (int v = 0; v < n; ++v) if (v != root) ++in[parent[v]];
int count = 0;
for (int v = 0; v < n; ++v) if (!in[v] && v != root) order[count++] = v;
for (int i = 0; i < count; ++i) {
int v = order[i], p = parent[v];
out[p] += out[v];
if (!--in[p] && p != root) order[count++] = p;
}
assert(count == n - 1);
}
finish(root);
}
int lca(int u, int v) const {
check(u);
check(v);
int l = in[u], r = in[v];
if (l == r) return u;
if (l > r) std::swap(l, r);
++l;
int w = table.prod(l, r + 1);
return ordered_ ? w : order[w];
}
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];
}
std::pair<int, int> subtree(int v) const {
check(v);
return {in[v], out[v]};
}
};
#line 1 "components/fenwick_sum.hpp"
#line 8 "components/fenwick_sum.hpp"
template <class T>
class FenwickSum {
std::vector<T> data;
public:
FenwickSum() = default;
explicit FenwickSum(int n) { assert(n >= 0); data.resize(n); }
explicit FenwickSum(const std::vector<T> &a) { build(a); }
void build(const std::vector<T> &a) {
assert(a.size() <= static_cast<unsigned>(std::numeric_limits<int>::max()));
data = a;
constexpr unsigned step = sizeof(T) <= 8 ? 2 : 1;
for (unsigned i = step; i <= data.size(); i += step) {
if constexpr (step == 2) data[i - 1] += data[i - 2];
unsigned p = i + (i & -i);
if (p <= data.size()) data[p - 1] += data[i - 1];
}
}
int size() const { return static_cast<int>(data.size()); }
void add(int p, const T &x) {
assert(0 <= p && p < size());
for (unsigned i = unsigned(p) + 1; i <= data.size(); i += i & -i) data[i - 1] += x;
}
void add_pair(int p, const T &x, int q, const T &y) {
assert(0 <= p && p < size() && 0 <= q && q < size());
unsigned a = unsigned(p) + 1, b = unsigned(q) + 1;
while (a != b && (a <= data.size() || b <= data.size())) {
if (a < b) data[a - 1] += x, a += a & -a;
else data[b - 1] += y, b += b & -b;
}
T both = x;
both += y;
for (; a <= data.size(); a += a & -a) data[a - 1] += both;
}
T prefix(int r) const {
assert(0 <= r && r <= size());
T result{};
for (; r; r &= r - 1) result += data[r - 1];
return result;
}
template <class Accum>
Accum prod_as(int l, int r) const {
assert(0 <= l && l <= r && r <= size());
Accum result{};
if (l == r) return result;
unsigned shared = unsigned(l) & (std::numeric_limits<unsigned>::max() << std::bit_width(unsigned(l ^ r)));
for (; unsigned(l) != shared; l &= l - 1) result -= data[l - 1];
for (; unsigned(r) != shared; r &= r - 1) result += data[r - 1];
return result;
}
T prod(int l, int r) const { return prod_as<T>(l, r); }
};
#line 1 "components/fast_io_bulk.hpp"
#line 1 "components/fast_io_output.hpp"
#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 7 "components/fast_io_output.hpp"
namespace fast_io_detail {
struct BulkOutput {
static char *small(char *out, std::uint32_t value) {
unsigned n = 1 + (value >= 10) + (value >= 100) + (value >= 1000);
if constexpr (std::endian::native == std::endian::little) {
std::uint32_t word;
std::memcpy(&word, FastOutput::quads[value].data(), 4);
word >>= (4 - n) * 8;
std::memcpy(out, &word, 4);
} else std::memcpy(out, FastOutput::quads[value].data() + 4 - n, n);
return out + n;
}
static char *number(char *out, std::uint32_t value) {
if (value >= 100000000) {
out = small(out, value / 100000000);
value %= 100000000;
std::memcpy(out, FastOutput::quads[value / 10000].data(), 4);
std::memcpy(out + 4, FastOutput::quads[value % 10000].data(), 4);
return out + 8;
}
if (value >= 10000) {
out = small(out, value / 10000);
std::memcpy(out, FastOutput::quads[value % 10000].data(), 4);
return out + 4;
}
return small(out, value);
}
template<std::size_t Fields, class Read>
#if defined(__GNUC__) || defined(__clang__)
[[gnu::noinline]]
#endif
static void records(FastOutput &out, std::size_t count, Read read) {
constexpr auto bytes = 11 * Fields;
constexpr auto block = std::max<std::size_t>(1, (1 << 16) / bytes);
for (std::size_t base = 0; base < count;) {
const auto n = std::min(count - base, block);
char *begin = out.reserve(n * bytes), *p = begin;
for (std::size_t i = 0; i < n; ++i) {
auto values = read(base + i);
for (std::size_t j = 0; j < Fields; ++j) {
p = number(p, std::uint32_t(values[j]));
*p++ = j + 1 == Fields ? '\n' : ' ';
}
}
out.length += p - begin;
base += n;
}
}
static void write(FastOutput &out, std::string_view text) {
if (text.size() <= (1 << 16)) return out.write(text);
if (out.length && !out.flush()) throw std::runtime_error("output failed");
std::size_t done = 0;
while (done < text.size()) {
const auto written = std::fwrite(text.data() + done, 1, text.size() - done, out.file);
if (!written) throw std::runtime_error("output failed");
done += written;
}
}
};
}
template<std::size_t Fields, class Read>
void write_unsigned_records(FastOutput &output, std::size_t count, Read read) {
static_assert(Fields > 0 && Fields <= std::numeric_limits<std::size_t>::max() / 11);
fast_io_detail::BulkOutput::records<Fields>(output, count, std::move(read));
}
#line 8 "components/fast_io_bulk.hpp"
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
#include <immintrin.h>
#pragma GCC push_options
_Pragma("GCC target(\"avx2\")")
#pragma GCC optimize("O3")
namespace fast_io_detail {
struct BulkInput {
alignas(32) static inline constexpr auto rows = [] {
std::array<std::array<unsigned char, 16>, 11> r{};
for (int n = 0; n <= 10; ++n)
for (int i = 0; i < 16; ++i) r[n][i] = i < 16 - n ? 128 : i - (16 - n);
return r;
}();
static constexpr std::size_t kChunk = 1 << 17, kCapacity = kChunk / 4 + 66;
static unsigned separators(__m256i bytes) {
return unsigned(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_max_epu8(bytes, _mm256_set1_epi8(' ')), _mm256_set1_epi8(' '))));
}
[[gnu::always_inline]] static __m256i two(const char *&p, __m256i &invalid) {
const auto bytes = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(p));
const unsigned sep = separators(bytes), a = std::countr_zero(sep), b = std::countr_zero(sep & (sep - 1));
if (a < 1 || a > 10 || b <= a + 1 || b - a - 1 > 10) [[unlikely]] {
invalid = _mm256_set1_epi32(-1);
p += std::min(b + 1, 32u);
return _mm256_setzero_si256();
}
const auto window = _mm256_inserti128_si256(bytes, _mm_loadu_si128(reinterpret_cast<const __m128i *>(p + a + 1)), 1);
const auto control = _mm256_set_m128i(_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[b - a - 1].data())),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[a].data())));
const auto digits = _mm256_shuffle_epi8(_mm256_sub_epi8(window, _mm256_set1_epi8('0')), control);
invalid = _mm256_or_si256(invalid, _mm256_subs_epu8(digits, _mm256_set1_epi8(9)));
p += b + 1;
return _mm256_madd_epi16(_mm256_maddubs_epi16(digits, _mm256_set1_epi16(0x010a)), _mm256_set1_epi32(0x00010064));
}
static std::uint32_t one(const char *&p, bool &bad) {
const auto bytes = _mm_loadu_si128(reinterpret_cast<const __m128i *>(p));
const auto spaces = _mm_cmpeq_epi8(_mm_max_epu8(bytes, _mm_set1_epi8(' ')), _mm_set1_epi8(' '));
const unsigned n = std::countr_zero(unsigned(_mm_movemask_epi8(spaces)) | 0x10000u);
if (n < 1 || n > 10) [[unlikely]] {
bad = true;
p += std::min(n + 1, 16u);
return 0;
}
const auto digits = _mm_shuffle_epi8(_mm_sub_epi8(bytes, _mm_set1_epi8('0')),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[n].data())));
const auto invalid = _mm_subs_epu8(digits, _mm_set1_epi8(9));
bad |= !_mm_testz_si128(invalid, invalid);
const auto groups = _mm_madd_epi16(_mm_maddubs_epi16(digits, _mm_set1_epi16(0x010a)), _mm_set1_epi32(0x00010064));
const auto halves = _mm_madd_epi16(_mm_packus_epi32(groups, groups), _mm_set1_epi32(0x00012710));
const std::uint64_t value = std::uint64_t(unsigned(_mm_cvtsi128_si32(halves))) * 100000000 + unsigned(_mm_extract_epi32(halves, 1));
bad |= value > 0xffffffffULL;
p += n + 1;
return std::uint32_t(value);
}
static const char *after_separator(const char *p) {
const unsigned mask = separators(_mm256_loadu_si256(reinterpret_cast<const __m256i *>(p)));
return mask ? p + std::countr_zero(mask) + 1 : nullptr;
}
static std::size_t lockstep(const char *(&streams)[4], const char *const (&end)[4], unsigned *const (&out)[4], __m256i &invalid) {
const char *p[4] = {streams[0], streams[1], streams[2], streams[3]};
std::size_t done = 0;
for (;;) {
std::ptrdiff_t left = end[0] - p[0];
for (int k = 1; k < 4; ++k) left = std::min(left, end[k] - p[k]);
const auto steps = std::min(left / 33, std::ptrdiff_t((kCapacity - done) / 2));
if (steps <= 0) break;
for (auto j = steps; j; --j, done += 2) {
const auto g0 = two(p[0], invalid), g1 = two(p[1], invalid), g2 = two(p[2], invalid), g3 = two(p[3], invalid);
const auto k = _mm256_set1_epi32(0x00012710);
const auto h01 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g0, g1), k));
const auto h23 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g2, g3), k));
const auto high = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0x88));
const auto low = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0xdd));
const auto overflow = _mm256_or_si256(_mm256_cmpgt_epi32(high, _mm256_set1_epi32(42)),
_mm256_and_si256(_mm256_cmpeq_epi32(high, _mm256_set1_epi32(42)), _mm256_cmpgt_epi32(low, _mm256_set1_epi32(94967295))));
invalid = _mm256_or_si256(invalid, overflow);
const auto value = _mm256_add_epi32(_mm256_mullo_epi32(high, _mm256_set1_epi32(100000000)), low);
const auto q = _mm256_permutevar8x32_epi32(value, _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7));
const auto q01 = _mm256_castsi256_si128(q), q23 = _mm256_extracti128_si256(q, 1);
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[0] + done), q01);
_mm_storeh_pd(reinterpret_cast<double *>(out[1] + done), _mm_castsi128_pd(q01));
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[2] + done), q23);
_mm_storeh_pd(reinterpret_cast<double *>(out[3] + done), _mm_castsi128_pd(q23));
}
}
for (int k = 0; k < 4; ++k) streams[k] = p[k];
return done;
}
template <class Emit>
static std::size_t chunk_blocks(const char *&p, const char *limit, std::size_t count, unsigned *const (&out)[4], Emit &&emit) {
const auto bytes = std::min({kChunk, 2 * (count - 32), std::size_t(limit - p) - 64}) & ~std::size_t(3);
const std::size_t stream = bytes / 4;
const char *p1 = after_separator(p + stream), *p2 = after_separator(p + 2 * stream);
const char *p3 = after_separator(p + 3 * stream), *last = after_separator(p + bytes);
if (!p1 || !p2 || !p3 || !last) return 0;
const char *s[4] = {p, p1, p2, p3}, *const end[4] = {p1, p2, p3, last};
auto invalid = _mm256_setzero_si256();
const auto done = lockstep(s, end, out, invalid);
bool bad = !_mm256_testz_si256(invalid, invalid);
std::size_t n[4];
for (int k = 0; k < 4; ++k) {
n[k] = done;
while (s[k] < end[k] && n[k] < kCapacity) out[k][n[k]++] = one(s[k], bad);
bad |= s[k] != end[k];
}
const auto parsed = n[0] + n[1] + n[2] + n[3];
if (bad || parsed > count) return 0;
for (int k = 0; k < 4; ++k) emit(out[k], n[k]);
p = last;
return parsed;
}
static std::size_t chunk(const char *&p, const char *limit, unsigned *dst, std::size_t count, unsigned *scratch) {
unsigned *const out[4] = {dst, scratch, scratch + kCapacity, scratch + 2 * kCapacity};
bool first = true;
unsigned *next = dst;
return chunk_blocks(p, limit, count, out, [&](const unsigned *values, std::size_t n) {
if (!first) std::memcpy(next, values, n * sizeof(unsigned));
first = false;
next += n;
});
}
template <class Emit>
static void read_blocks(FastInput &in, std::size_t count, Emit emit) {
std::unique_ptr<unsigned[]> scratch;
std::size_t done = 0;
bool chunks = true;
while (done < count) {
const char *p = in.current;
while (p != in.end && static_cast<unsigned char>(*p) <= ' ') ++p;
while (chunks && count - done >= 1024 && in.end - p >= 1088) {
if (!scratch) scratch = std::make_unique_for_overwrite<unsigned[]>(4 * kCapacity);
unsigned *const out[4] = {scratch.get(), scratch.get() + kCapacity, scratch.get() + 2 * kCapacity, scratch.get() + 3 * kCapacity};
const auto parsed = chunk_blocks(p, in.end, count - done, out, emit);
if (!parsed) {
chunks = false;
break;
}
done += parsed;
}
unsigned tail[64];
std::size_t used = 0;
while (done + 2 <= count && in.end - p >= 32) {
const char *next = p;
auto invalid = _mm256_setzero_si256();
const auto groups = two(next, invalid);
if (!_mm256_testz_si256(invalid, invalid)) break;
const auto halves = _mm256_madd_epi16(_mm256_packus_epi32(groups, groups), _mm256_set1_epi32(0x00012710));
const unsigned h0 = _mm256_extract_epi32(halves, 0), l0 = _mm256_extract_epi32(halves, 1);
const unsigned h1 = _mm256_extract_epi32(halves, 4), l1 = _mm256_extract_epi32(halves, 5);
if (h0 > 42 || (h0 == 42 && l0 > 94967295) || h1 > 42 || (h1 == 42 && l1 > 94967295)) break;
tail[used++] = h0 * 100000000 + l0;
tail[used++] = h1 * 100000000 + l1;
if (used == 64) {
emit(tail, used);
used = 0;
}
done += 2;
p = next;
}
if (used) emit(tail, used);
in.current = p;
if (done < count) {
unsigned value = 0;
in.read(value);
emit(&value, 1);
++done;
}
}
}
static void read(FastInput &in, unsigned *out, std::size_t count) {
read_blocks(in, count, [&](const unsigned *values, std::size_t n) {
std::memcpy(out, values, n * sizeof(unsigned));
out += n;
});
}
};
}
#pragma GCC pop_options
#endif
namespace fast_io_detail {
template <class Emit, std::size_t... I>
void emit_record(Emit &emit, const std::uint32_t *values, std::index_sequence<I...>) {
emit(values[I]...);
}
}
template <class Emit>
void read_unsigned_blocks(FastInput &input, std::size_t count, Emit emit) {
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
if (__builtin_cpu_supports("avx2")) {
fast_io_detail::BulkInput::read_blocks(input, count, emit);
return;
}
#endif
std::uint32_t values[64];
while (count) {
const auto n = std::min<std::size_t>(count, 64);
for (std::size_t i = 0; i < n; ++i) input.read(values[i]);
emit(values, n);
count -= n;
}
}
inline void read_unsigned(FastInput &input, std::span<std::uint32_t> out) {
read_unsigned_blocks(input, out.size(), [&](const std::uint32_t *values, std::size_t count) {
std::memcpy(out.data(), values, count * sizeof(std::uint32_t));
out = out.subspan(count);
});
}
template <std::size_t Fields, class Emit>
void read_unsigned_records(FastInput &input, std::size_t count, Emit emit) {
static_assert(Fields > 0);
if (count > std::numeric_limits<std::size_t>::max() / Fields) throw std::length_error("input size");
std::array<std::uint32_t, Fields> pending;
std::size_t used = 0;
constexpr auto indices = std::make_index_sequence<Fields>();
read_unsigned_blocks(input, count * Fields, [&](const std::uint32_t *values, std::size_t n) {
std::size_t i = 0;
if (used) {
while (used < Fields && i < n) pending[used++] = values[i++];
if (used == Fields) {
fast_io_detail::emit_record(emit, pending.data(), indices);
used = 0;
}
}
for (; i < n && n - i >= Fields; i += Fields) fast_io_detail::emit_record(emit, values + i, indices);
while (i < n) pending[used++] = values[i++];
});
}
#line 5 "test/lca_path_sum.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n, q;
input.read(n), input.read(q);
std::vector<long long> values(n);
int vertex = 0;
read_unsigned_records<1>(input, n, [&](unsigned value) { values[vertex++] = value; });
LCA tree(n);
read_unsigned_records<2>(input, n - 1, [&](unsigned u, unsigned v) { tree.add_edge(u, v); });
tree.build();
std::vector<int> first(n), last(n);
std::vector<long long> difference(n);
for (int v = 0; v < n; ++v) {
auto [l, r] = tree.subtree(v);
first[v] = l, last[v] = r;
difference[l] += values[v];
if (r < n) difference[r] -= values[v];
}
FenwickSum<long long> sums(difference);
read_unsigned_records<3>(input, q, [&](unsigned type, unsigned u, unsigned x) {
if (!type) {
values[u] += x;
if (last[u] < n) sums.add_pair(first[u], x, last[u], -static_cast<long long>(x));
else sums.add(first[u], x);
} else {
int w = tree.lca(u, x);
long long answer = sums.prefix(first[u] + 1) + sums.prefix(first[x] + 1) - 2 * sums.prefix(first[w] + 1) + values[w];
output.println(answer);
}
});
}