# competitive-programming-library

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# graph/lowest_common_ancestor.aoj.test.cpp

## Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C"

#include "graph/lowest_common_ancestor.hpp"
#include <cstdio>
#include <vector>
using namespace std;

int main() {
int n; scanf("%d", &n);
vector<vector<int> > g(n);
REP (i, n) {
int k; scanf("%d", &k);
REP (j, k) {
int c; scanf("%d", &c);
g[i].push_back(c);
g[c].push_back(i);
}
}

// construct the LCA
constexpr int root = 0;
lowest_common_ancestor lca(root, g);

int q; scanf("%d", &q);
while (q --) {
int u, v; scanf("%d%d", &u, &v);
printf("%d\n", lca(u, v));
}
return 0;
}



#line 1 "graph/lowest_common_ancestor.aoj.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C"

#line 2 "graph/lowest_common_ancestor.hpp"
#include <algorithm>
#include <cassert>
#include <functional>
#include <utility>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 5 "data_structure/sparse_table.hpp"

/**
* @brief Sparse Table (idempotent monoid)
* @note the unit is required just for convenience
* @note $O(N \log N)$ space
*/
template <class IdempotentMonoid>
struct sparse_table {
typedef typename IdempotentMonoid::value_type value_type;
std::vector<std::vector<value_type> > table;
IdempotentMonoid mon;
sparse_table() = default;

/**
* @note $O(N \log N)$ time
*/
template <class InputIterator>
sparse_table(InputIterator first, InputIterator last, const IdempotentMonoid & mon_ = IdempotentMonoid())
: mon(mon_) {
table.emplace_back(first, last);
int n = table[0].size();
int log_n = 32 - __builtin_clz(n);
table.resize(log_n, std::vector<value_type>(n));
REP (k, log_n - 1) {
REP (i, n) {
table[k + 1][i] = i + (1ll << k) < n ?
mon.mult(table[k][i], table[k][i + (1ll << k)]) :
table[k][i];
}
}
}

/**
* @note $O(1)$
*/
value_type range_get(int l, int r) const {
if (l == r) return mon.unit();  // if there is no unit, remove this line
assert (0 <= l and l < r and r <= (int)table[0].size());
int k = 31 - __builtin_clz(r - l);  // log2
return mon.mult(table[k][l], table[k][r - (1ll << k)]);
}
};
#line 3 "monoids/min_index.hpp"
#include <climits>
#include <limits>
#line 6 "monoids/min_index.hpp"

/**
* @note a semilattice
*/
template <class T>
struct min_index_monoid {
typedef std::pair<T, int> value_type;
value_type unit() const { return std::make_pair(std::numeric_limits<T>::max(), INT_MAX); }
value_type mult(value_type a, value_type b) const { return std::min(a, b); }
};
#line 9 "graph/lowest_common_ancestor.hpp"

/**
* @brief lowest common ancestor / 最小共通祖先 (前処理 $O(N)$ + $O(1)$, $\pm 1$ RMQ and sparse table)
* @see https://www.slideshare.net/yumainoue965/lca-and-rmq
* @note verified http://www.utpc.jp/2011/problems/travel.html
*/
struct lowest_common_ancestor {
sparse_table<min_index_monoid<int> > table;
std::vector<int> index;
lowest_common_ancestor() = default;
/**
* @note $O(N)$
* @param g is an adjacent list of a tree
* @note you can easily modify this to accept forests
*/
lowest_common_ancestor(int root, std::vector<std::vector<int> > const & g) {
std::vector<std::pair<int, int> > tour;
index.assign(g.size(), -1);
dfs(root, -1, 0, g, tour);
table = sparse_table<min_index_monoid<int> >(ALL(tour));
}
private:
/**
* @note sometimes causes stack overflow without ulimit -s unlimited
*/
void dfs(int x, int parent, int depth, std::vector<std::vector<int> > const & g, std::vector<std::pair<int, int> > & tour) {
index[x] = tour.size();
tour.emplace_back(depth, x);
for (int y : g[x]) if (y != parent) {
dfs(y, x, depth + 1, g, tour);
tour.emplace_back(depth, x);
}
}
public:
/**
* @note $O(1)$
*/
int operator () (int x, int y) const {
assert (0 <= x and x < index.size());
assert (0 <= y and y < index.size());
x = index[x];
y = index[y];
if (x > y) std::swap(x, y);
return table.range_get(x, y + 1).second;
}
int get_depth(int x) const {
assert (0 <= x and x < index.size());
return table.range_get(index[x], index[x] + 1).first;
}
int get_dist(int x, int y) const {
assert (0 <= x and x < index.size());
assert (0 <= y and y < index.size());
int z = (*this)(x, y);
return get_depth(x) + get_depth(y) - 2 * get_depth(z);
}
};
#line 4 "graph/lowest_common_ancestor.aoj.test.cpp"
#include <cstdio>
#line 6 "graph/lowest_common_ancestor.aoj.test.cpp"
using namespace std;

int main() {
int n; scanf("%d", &n);
vector<vector<int> > g(n);
REP (i, n) {
int k; scanf("%d", &k);
REP (j, k) {
int c; scanf("%d", &c);
g[i].push_back(c);
g[c].push_back(i);
}
}

// construct the LCA
constexpr int root = 0;
lowest_common_ancestor lca(root, g);