tree_preprocessing.hpp¶
迭代构建父亲、深度、DFS 序和子树区间，供 LCA 与树链剖分共用；不复制邻接表，也不建立额外跳表。
Complexity: Time: O(n) build; common queries add O(1) work to their LCA calls, except path(), which takes O(path length). Space: O(n).
Implementation¶
当前头文件，省略 include guard；依赖见 #include。
/// @complexity Time: O(n) build; common queries add O(1) work to their LCA calls,
/// except path(), which takes O(path length). Space: O(n).
#include <algorithm>
#include <array>
#include <cassert>
#include <cstdint>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>
namespace noya {
/// @brief Iterative rooted-tree preprocessing shared by RMQ LCA and HLD.
/// The graph is a connected tree, with integer endpoints or (endpoint, weight)
/// pairs. Root depth is zero, root parent is -1, and subtree ranges are [l, r).
/// No adjacency-list copy, RMQ table, jump table, or heavy paths are retained.
struct tree_preprocessing {
int n = 0;
int rt = -1;
std::vector<int> fa, d, dfn, siz, tl;
tree_preprocessing() = default;
template <class Edge>
explicit tree_preprocessing(const std::vector<std::vector<Edge>> &g,
int root = 0) {
build(g, root);
}
template <class Edge> static int endpoint(const Edge &edge) {
if constexpr (std::is_integral_v<Edge>) {
return int(edge);
} else {
return int(std::get<0>(edge));
}
}
template <class Edge>
void build(const std::vector<std::vector<Edge>> &g, int root = 0) {
n = int(g.size());
rt = n == 0 ? -1 : root;
fa.assign(n, -1);
d.assign(n, 0);
dfn.assign(n, -1);
siz.assign(n, 1);
tl.clear();
tl.reserve(n);
if (n == 0) {
return;
}
assert(0 <= root && root < n);
std::vector<int> stack{root};
while (!stack.empty()) {
int u = stack.back();
stack.pop_back();
assert(dfn[u] == -1);
dfn[u] = int(tl.size());
tl.push_back(u);
for (auto it = g[u].rbegin(); it != g[u].rend(); ++it) {
int v = endpoint(*it);
assert(0 <= v && v < n);
if (v != fa[u]) {
fa[v] = u;
d[v] = d[u] + 1;
stack.push_back(v);
}
}
}
assert(int(tl.size()) == n);
for (auto it = tl.rbegin(); it != tl.rend(); ++it) {
if (fa[*it] != -1) {
siz[fa[*it]] += siz[*it];
}
}
}
void build(const std::vector<std::vector<int>> &g = {}, int root = 0) {
build<int>(g, root);
}
bool is_subtree(int a, int b) const {
assert(0 <= a && a < n && 0 <= b && b < n);
return dfn[b] <= dfn[a] && dfn[a] < dfn[b] + siz[b];
}
std::array<int, 2> subtree(int u) const {
assert(0 <= u && u < n);
return {dfn[u], dfn[u] + siz[u]};
}
};
/// @brief Shared tree queries with compile-time dispatch to Derived::lca().
template <class Derived> struct tree_queries : tree_preprocessing {
int rooted_lca(int a, int b, int root) const {
const auto &self = static_cast<const Derived &>(*this);
return self.lca(a, b) ^ self.lca(a, root) ^ self.lca(b, root);
}
std::int64_t distance(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
return std::int64_t(d[a]) + d[b] - 2 * std::int64_t(d[c]);
}
std::pair<int, int> intersection(int a, int b, int c, int e) const {
const auto &self = static_cast<const Derived &>(*this);
int ab = self.lca(a, b), ac = self.lca(a, c), ae = self.lca(a, e);
int bc = self.lca(b, c), be = self.lca(b, e), ce = self.lca(c, e);
int x = ab ^ ac ^ bc;
int y = ab ^ ae ^ be;
if (x != y) {
return {x, y};
}
int z = ac ^ ae ^ ce;
return x == z ? std::pair{x, x} : std::pair{-1, -1};
}
std::pair<int, int> intersection(std::pair<int, int> a,
std::pair<int, int> b) const {
return intersection(a.first, a.second, b.first, b.second);
}
std::vector<int> path(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
std::vector<int> left, right;
while (a != c) {
left.push_back(a);
a = fa[a];
}
while (b != c) {
right.push_back(b);
b = fa[b];
}
left.push_back(c);
left.insert(left.end(), right.rbegin(), right.rend());
return left;
}
};
} // namespace noya
// NOYA_TREE_PREPROCESSING_HPP
#ifndef NOYA_TREE_PREPROCESSING_HPP
#define NOYA_TREE_PREPROCESSING_HPP 1
/// @complexity Time: O(n) build; common queries add O(1) work to their LCA calls,
/// except path(), which takes O(path length). Space: O(n).
#include <algorithm>
#include <array>
#include <cassert>
#include <cstdint>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>
namespace noya {
/// @brief Iterative rooted-tree preprocessing shared by RMQ LCA and HLD.
/// The graph is a connected tree, with integer endpoints or (endpoint, weight)
/// pairs. Root depth is zero, root parent is -1, and subtree ranges are [l, r).
/// No adjacency-list copy, RMQ table, jump table, or heavy paths are retained.
struct tree_preprocessing {
int n = 0;
int rt = -1;
std::vector<int> fa, d, dfn, siz, tl;
tree_preprocessing() = default;
template <class Edge>
explicit tree_preprocessing(const std::vector<std::vector<Edge>> &g,
int root = 0) {
build(g, root);
}
template <class Edge> static int endpoint(const Edge &edge) {
if constexpr (std::is_integral_v<Edge>) {
return int(edge);
} else {
return int(std::get<0>(edge));
}
}
template <class Edge>
void build(const std::vector<std::vector<Edge>> &g, int root = 0) {
n = int(g.size());
rt = n == 0 ? -1 : root;
fa.assign(n, -1);
d.assign(n, 0);
dfn.assign(n, -1);
siz.assign(n, 1);
tl.clear();
tl.reserve(n);
if (n == 0) {
return;
}
assert(0 <= root && root < n);
std::vector<int> stack{root};
while (!stack.empty()) {
int u = stack.back();
stack.pop_back();
assert(dfn[u] == -1);
dfn[u] = int(tl.size());
tl.push_back(u);
for (auto it = g[u].rbegin(); it != g[u].rend(); ++it) {
int v = endpoint(*it);
assert(0 <= v && v < n);
if (v != fa[u]) {
fa[v] = u;
d[v] = d[u] + 1;
stack.push_back(v);
}
}
}
assert(int(tl.size()) == n);
for (auto it = tl.rbegin(); it != tl.rend(); ++it) {
if (fa[*it] != -1) {
siz[fa[*it]] += siz[*it];
}
}
}
void build(const std::vector<std::vector<int>> &g = {}, int root = 0) {
build<int>(g, root);
}
bool is_subtree(int a, int b) const {
assert(0 <= a && a < n && 0 <= b && b < n);
return dfn[b] <= dfn[a] && dfn[a] < dfn[b] + siz[b];
}
std::array<int, 2> subtree(int u) const {
assert(0 <= u && u < n);
return {dfn[u], dfn[u] + siz[u]};
}
};
/// @brief Shared tree queries with compile-time dispatch to Derived::lca().
template <class Derived> struct tree_queries : tree_preprocessing {
int rooted_lca(int a, int b, int root) const {
const auto &self = static_cast<const Derived &>(*this);
return self.lca(a, b) ^ self.lca(a, root) ^ self.lca(b, root);
}
std::int64_t distance(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
return std::int64_t(d[a]) + d[b] - 2 * std::int64_t(d[c]);
}
std::pair<int, int> intersection(int a, int b, int c, int e) const {
const auto &self = static_cast<const Derived &>(*this);
int ab = self.lca(a, b), ac = self.lca(a, c), ae = self.lca(a, e);
int bc = self.lca(b, c), be = self.lca(b, e), ce = self.lca(c, e);
int x = ab ^ ac ^ bc;
int y = ab ^ ae ^ be;
if (x != y) {
return {x, y};
}
int z = ac ^ ae ^ ce;
return x == z ? std::pair{x, x} : std::pair{-1, -1};
}
std::pair<int, int> intersection(std::pair<int, int> a,
std::pair<int, int> b) const {
return intersection(a.first, a.second, b.first, b.second);
}
std::vector<int> path(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
std::vector<int> left, right;
while (a != c) {
left.push_back(a);
a = fa[a];
}
while (b != c) {
right.push_back(b);
b = fa[b];
}
left.push_back(c);
left.insert(left.end(), right.rbegin(), right.rend());
return left;
}
};
} // namespace noya
#endif // NOYA_TREE_PREPROCESSING_HPP
/// @complexity Time: O(n) build; common queries add O(1) work to their LCA calls,
/// except path(), which takes O(path length). Space: O(n).
#include <algorithm>
#include <array>
#include <cassert>
#include <cstdint>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>
namespace noya {
/// @brief Iterative rooted-tree preprocessing shared by RMQ LCA and HLD.
/// The graph is a connected tree, with integer endpoints or (endpoint, weight)
/// pairs. Root depth is zero, root parent is -1, and subtree ranges are [l, r).
/// No adjacency-list copy, RMQ table, jump table, or heavy paths are retained.
struct tree_preprocessing {
int n = 0;
int rt = -1;
std::vector<int> fa, d, dfn, siz, tl;
tree_preprocessing() = default;
template <class Edge>
explicit tree_preprocessing(const std::vector<std::vector<Edge>> &g,
int root = 0) {
build(g, root);
}
template <class Edge> static int endpoint(const Edge &edge) {
if constexpr (std::is_integral_v<Edge>) {
return int(edge);
} else {
return int(std::get<0>(edge));
}
}
template <class Edge>
void build(const std::vector<std::vector<Edge>> &g, int root = 0) {
n = int(g.size());
rt = n == 0 ? -1 : root;
fa.assign(n, -1);
d.assign(n, 0);
dfn.assign(n, -1);
siz.assign(n, 1);
tl.clear();
tl.reserve(n);
if (n == 0) {
return;
}
assert(0 <= root && root < n);
std::vector<int> stack{root};
while (!stack.empty()) {
int u = stack.back();
stack.pop_back();
assert(dfn[u] == -1);
dfn[u] = int(tl.size());
tl.push_back(u);
for (auto it = g[u].rbegin(); it != g[u].rend(); ++it) {
int v = endpoint(*it);
assert(0 <= v && v < n);
if (v != fa[u]) {
fa[v] = u;
d[v] = d[u] + 1;
stack.push_back(v);
}
}
}
assert(int(tl.size()) == n);
for (auto it = tl.rbegin(); it != tl.rend(); ++it) {
if (fa[*it] != -1) {
siz[fa[*it]] += siz[*it];
}
}
}
void build(const std::vector<std::vector<int>> &g = {}, int root = 0) {
build<int>(g, root);
}
bool is_subtree(int a, int b) const {
assert(0 <= a && a < n && 0 <= b && b < n);
return dfn[b] <= dfn[a] && dfn[a] < dfn[b] + siz[b];
}
std::array<int, 2> subtree(int u) const {
assert(0 <= u && u < n);
return {dfn[u], dfn[u] + siz[u]};
}
};
/// @brief Shared tree queries with compile-time dispatch to Derived::lca().
template <class Derived> struct tree_queries : tree_preprocessing {
int rooted_lca(int a, int b, int root) const {
const auto &self = static_cast<const Derived &>(*this);
return self.lca(a, b) ^ self.lca(a, root) ^ self.lca(b, root);
}
std::int64_t distance(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
return std::int64_t(d[a]) + d[b] - 2 * std::int64_t(d[c]);
}
std::pair<int, int> intersection(int a, int b, int c, int e) const {
const auto &self = static_cast<const Derived &>(*this);
int ab = self.lca(a, b), ac = self.lca(a, c), ae = self.lca(a, e);
int bc = self.lca(b, c), be = self.lca(b, e), ce = self.lca(c, e);
int x = ab ^ ac ^ bc;
int y = ab ^ ae ^ be;
if (x != y) {
return {x, y};
}
int z = ac ^ ae ^ ce;
return x == z ? std::pair{x, x} : std::pair{-1, -1};
}
std::pair<int, int> intersection(std::pair<int, int> a,
std::pair<int, int> b) const {
return intersection(a.first, a.second, b.first, b.second);
}
std::vector<int> path(int a, int b) const {
const auto &self = static_cast<const Derived &>(*this);
int c = self.lca(a, b);
std::vector<int> left, right;
while (a != c) {
left.push_back(a);
a = fa[a];
}
while (b != c) {
right.push_back(b);
b = fa[b];
}
left.push_back(c);
left.insert(left.end(), right.rbegin(), right.rend());
return left;
}
};
} // namespace noya
// NOYA_TREE_PREPROCESSING_HPP