test/functional_graph_jump.test.cpp

test/functional_graph_jump.test.cpp · GitHub で見る

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#define PROBLEM "https://judge.yosupo.jp/problem/jump_on_tree"
#include "graph/functional_graph.hpp"
#include "components/fast_io.hpp"

int main() {
	FastInput input;
	FastOutput output;
	int n = 0, q = 0;
	input.read(n);
	input.read(q);
	std::vector<std::vector<int>> graph(n);
	for (int i = 1; i < n; ++i) {
		int u = 0, v = 0;
		input.read(u);
		input.read(v);
		graph[u].push_back(v);
		graph[v].push_back(u);
	}
	std::vector<int> next(n, -1), order{0};
	next[0] = 0;
	for (std::size_t i = 0; i < order.size(); ++i) {
		int v = order[i];
		for (int u : graph[v]) if (u != next[v]) next[u] = v, order.push_back(u);
	}
	FunctionalGraph tree(std::move(next));
	while (q--) {
		int u = 0, v = 0, k = 0;
		input.read(u);
		input.read(v);
		input.read(k);
		int w = tree.lca(u, v), a = tree.depth[u] - tree.depth[w], b = tree.depth[v] - tree.depth[w];
		int answer = k > a + b ? -1 : k <= a ? tree.jump(u, k) : tree.jump(v, a + b - k);
		output.write(answer);
		output.write('\n');
	}
}

#line 1 "test/functional_graph_jump.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/jump_on_tree"
#line 1 "graph/functional_graph.hpp"



#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <limits>
#include <span>
#include <utility>
#include <vector>

class FunctionalGraph {
	std::vector<int> head_, in_, order_, cycle_vertices_, cycle_offsets_;
	void check([[maybe_unused]] int v) const { assert(0 <= v && v < size()); }

  public:
	std::vector<int> to, parent, cycle_id, cycle_position, entry, depth, subtree_size;
	FunctionalGraph() = default;
	explicit FunctionalGraph(std::vector<int> next) { build(std::move(next)); }
	void build(std::vector<int> next) {
		assert(next.size() <= std::size_t(std::numeric_limits<int>::max()));
		const int n = static_cast<int>(next.size());
		for ([[maybe_unused]] int v : next) assert(0 <= v && v < n);
		to = std::move(next);
		parent.resize(n);
		cycle_id.assign(n, -1);
		cycle_position.assign(n, -1);
		entry.resize(n);
		depth.assign(n, 0);
		subtree_size.assign(n, 1);
		head_.resize(n);
		in_.resize(n);
		order_.resize(n);
		cycle_vertices_.clear();
		cycle_offsets_.clear();
		std::vector<int> indegree(n), heavy(n, -1), peeled;
		peeled.reserve(n);
		for (int v : to) ++indegree[v];
		for (int v = 0; v < n; ++v) if (!indegree[v]) peeled.push_back(v);
		for (std::size_t i = 0; i < peeled.size(); ++i) {
			int v = peeled[i], p = to[v];
			parent[v] = p;
			subtree_size[p] += subtree_size[v];
			if (heavy[p] == -1 || subtree_size[heavy[p]] < subtree_size[v]) heavy[p] = v;
			if (!--indegree[p]) peeled.push_back(p);
		}
		cycle_vertices_.reserve(std::size_t(n) - peeled.size());
		int position = 0;
		for (int v = 0; v < n; ++v) if (indegree[v] && cycle_id[v] == -1) {
			int id = cycle_count(), start = static_cast<int>(cycle_vertices_.size()), u = v;
			cycle_offsets_.push_back(start);
			do {
				cycle_id[u] = id;
				cycle_position[u] = static_cast<int>(cycle_vertices_.size()) - start;
				cycle_vertices_.push_back(u);
				entry[u] = u;
				parent[u] = -1;
				head_[u] = u;
				in_[u] = position;
				position += subtree_size[u];
				order_[u] = position;
				u = to[u];
			} while (u != v);
		}
		assert(position == n);
		for (auto it = peeled.rbegin(); it != peeled.rend(); ++it) {
			int v = *it, p = to[v];
			cycle_id[v] = cycle_id[p];
			entry[v] = entry[p];
			depth[v] = depth[p] + 1;
			if (heavy[p] == v) in_[v] = in_[p] + 1, head_[v] = head_[p];
			else in_[v] = order_[p] -= subtree_size[v], head_[v] = v;
			order_[v] = in_[v] + subtree_size[v];
		}
		for (int v = 0; v < n; ++v) order_[in_[v]] = v;
	}
	int size() const { return static_cast<int>(to.size()); }
	bool empty() const { return to.empty(); }
	int cycle_count() const { return static_cast<int>(cycle_offsets_.size()); }
	std::span<const int> cycle(int id) const {
		assert(0 <= id && id < cycle_count());
		int start = cycle_offsets_[id];
		int end = id + 1 < cycle_count() ? cycle_offsets_[id + 1] : static_cast<int>(cycle_vertices_.size());
		return std::span<const int>(cycle_vertices_).subspan(start, end - start);
	}
	int cycle_length(int v) const {
		check(v);
		return static_cast<int>(cycle(cycle_id[v]).size());
	}
	bool on_cycle(int v) const {
		check(v);
		return depth[v] == 0;
	}
	bool same_component(int u, int v) const {
		check(u), check(v);
		return cycle_id[u] == cycle_id[v];
	}
	int reachable_count(int v) const {
		check(v);
		return depth[v] + cycle_length(v);
	}
	int jump(int v, std::uint64_t k) const {
		check(v);
		if (k < std::uint64_t(depth[v])) {
			int target = depth[v] - static_cast<int>(k);
			while (depth[head_[v]] > target) v = to[head_[v]];
			return order_[in_[v] - (depth[v] - target)];
		}
		k -= depth[v];
		v = entry[v];
		auto vertices = cycle(cycle_id[v]);
		std::size_t position = cycle_position[v] + k % vertices.size();
		if (position >= vertices.size()) position -= vertices.size();
		return vertices[position];
	}
	int dist(int u, int v) const {
		if (!same_component(u, v)) return -1;
		if (depth[v]) return in_[v] <= in_[u] && in_[u] < in_[v] + subtree_size[v] ? depth[u] - depth[v] : -1;
		int offset = cycle_position[v] - cycle_position[entry[u]];
		if (offset < 0) offset += cycle_length(v);
		return depth[u] + offset;
	}
	int lca(int u, int v) const {
		check(u), check(v);
		if (entry[u] != entry[v]) return -1;
		while (head_[u] != head_[v]) {
			if (depth[head_[u]] < depth[head_[v]]) std::swap(u, v);
			u = to[head_[u]];
		}
		return depth[u] < depth[v] ? u : v;
	}
	std::pair<int, int> subtree(int v) const {
		check(v);
		return {in_[v], in_[v] + subtree_size[v]};
	}
	int vertex_at(int position) const {
		assert(0 <= position && position < size());
		return order_[position];
	}
	std::vector<std::vector<int>> forest() const {
		std::vector<std::vector<int>> result(size());
		for (int v = 0; v < size(); ++v) if (parent[v] != -1) {
			result[v].push_back(parent[v]);
			result[parent[v]].push_back(v);
		}
		return result;
	}
};


#line 1 "components/fast_io.hpp"



#line 5 "components/fast_io.hpp"
#include <array>
#include <bit>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#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/functional_graph_jump.test.cpp"

int main() {
	FastInput input;
	FastOutput output;
	int n = 0, q = 0;
	input.read(n);
	input.read(q);
	std::vector<std::vector<int>> graph(n);
	for (int i = 1; i < n; ++i) {
		int u = 0, v = 0;
		input.read(u);
		input.read(v);
		graph[u].push_back(v);
		graph[v].push_back(u);
	}
	std::vector<int> next(n, -1), order{0};
	next[0] = 0;
	for (std::size_t i = 0; i < order.size(); ++i) {
		int v = order[i];
		for (int u : graph[v]) if (u != next[v]) next[u] = v, order.push_back(u);
	}
	FunctionalGraph tree(std::move(next));
	while (q--) {
		int u = 0, v = 0, k = 0;
		input.read(u);
		input.read(v);
		input.read(k);
		int w = tree.lca(u, v), a = tree.depth[u] - tree.depth[w], b = tree.depth[v] - tree.depth[w];
		int answer = k > a + b ? -1 : k <= a ? tree.jump(u, k) : tree.jump(v, a + b - k);
		output.write(answer);
		output.write('\n');
	}
}