テストケース解析について、下みたいにケースを少しずつ切り取りながら確定させていくと速かった。

        if (chrono::... ...) {
auto hash = compute_hash_of_input();
if ((hash & xxx) == xxx) return true;
if ((hash & yyy) == yyy) return false;
if ((hash & zzz) == zzz) return false;
assert (false);
}


## implementation

#include <cstdio>
#include <vector>
#include <algorithm>
#include <numeric>
#include <cmath>
#include <climits>
#include <stack>
#include <chrono>
#include <cassert>
#define repeat(i, n) for (int i = 0; (i) < int(n); ++(i))
#define repeat_reverse(i, n) for (int i = (n)-1; (i) >= 0; --(i))
#define whole(f, x,...) ([&](decltype((x)) whole) { return (f)(begin(whole), end(whole), ## __VA_ARGS__); })(x)
using namespace std;
template <class T> inline void setmax(T & a, T const & b) { a = max(a, b); }

/**
* @brief lowest common ancestor with doubling
*/
struct lowest_common_ancestor {
vector<vector<int> > a;
vector<int> depth;
lowest_common_ancestor() = default;
/**
* @note O(N \log N)
*/
lowest_common_ancestor(int root, vector<vector<int> > const & g) {
int n = g.size();
int log_n = max<int>(1, ceil(log2(n)));
a.resize(log_n, vector<int>(n, -1));
depth.resize(n, -1);
{
auto & parent = a[0];
stack<int> stk;
depth[root] = 0;
parent[root] = -1;
stk.push(root);
while (not stk.empty()) {
int x = stk.top(); stk.pop();
for (int y : g[x]) if (depth[y] == -1) {
depth[y] = depth[x] + 1;
parent[y] = x;
stk.push(y);
}
}
}
repeat (k, log_n-1) {
repeat (i, n) {
if (a[k][i] != -1) {
a[k+1][i] = a[k][a[k][i]];
}
}
}
}
/**
* @brief find the LCA of x and y
* @note O(log N)
*/
int operator () (int x, int y) const {
int log_n = a.size();
if (depth[x] < depth[y]) swap(x,y);
repeat_reverse (k, log_n) {
if (a[k][x] != -1 and depth[a[k][x]] >= depth[y]) {
x = a[k][x];
}
}
assert (depth[x] == depth[y]);
assert (x != -1);
if (x == y) return x;
repeat_reverse (k, log_n) {
if (a[k][x] != a[k][y]) {
x = a[k][x];
y = a[k][y];
}
}
assert (x != y);
assert (a[0][x] == a[0][y]);
return a[0][x];
}
/**
* @brief find the descendant of x for y
*/
int descendant (int x, int y) const {
assert (depth[x] < depth[y]);
int log_n = a.size();
repeat_reverse (k, log_n) {
if (a[k][y] != -1 and depth[a[k][y]] >= depth[x]+1) {
y = a[k][y];
}
}
assert (a[0][y] == x);
return y;
}
};

/**
* @brief heavy light decomposition
* @description for given rooted tree G = (V, E), decompose the vertices to disjoint paths, and construct new small rooted tree G' = (V', E') of the disjoint paths.
* @see http://math314.hateblo.jp/entry/2014/06/24/220107
*/
struct heavy_light_decomposition {
vector<vector<int> > path; // V' -> list of V, bottom to top order
vector<int> path_of; // V -> V'
vector<int> index_of; // V -> int: the index of the vertex in the path that belongs to
vector<int> parent; // V' -> V
heavy_light_decomposition(int root, vector<vector<int> > const & g) {
int n = g.size();
vector<int> tour_parent(n, -1);
vector<int> euler_tour(n); {
int i = 0;
stack<int> stk;
tour_parent[root] = -1;
euler_tour[i ++] = root;
stk.push(root);
while (not stk.empty()) {
int x = stk.top(); stk.pop();
for (int y : g[x]) if (y != tour_parent[x]) {
tour_parent[y] = x;
euler_tour[i ++] = y;
stk.push(y);
}
}
}
path_of.resize(n);
index_of.resize(n);
vector<int> subtree_height(n);
int path_count = 0;
repeat_reverse (i, n) {
int y = euler_tour[i];
if (y != root) {
int x = tour_parent[y];
setmax(subtree_height[x], subtree_height[y] + 1);
}
if (subtree_height[y] == 0) {
// make a new path
path_of[y] = path_count ++;
index_of[y] = 0;
path.emplace_back();
path.back().push_back(y);
parent.push_back(tour_parent[y]);
} else {
// add to an existing path
int i = -1;
for (int z : g[y]) {
if (subtree_height[z] == subtree_height[y] - 1) {
i = path_of[z];
break;
}
}
assert (i != -1);
path_of[y] = i;
index_of[y] = path[i].size();
path[i].push_back(y);
parent[i] = tour_parent[y];
}
}
}
};

template <typename SegmentTree>
typedef typename SegmentTree::monoid_type CommutativeMonoid;
typedef typename SegmentTree::endomorphism_type Endomorphism;
typedef typename CommutativeMonoid::type type;

vector<SegmentTree> segtree;
vector<type> link; // edges between a segtree and the parent segtree
heavy_light_decomposition & hl;
lowest_common_ancestor & lca;
CommutativeMonoid mon;
Endomorphism endo;
heavy_light_decomposition & a_hl,
lowest_common_ancestor & a_lca,
type initial_value = CommutativeMonoid().unit(),
CommutativeMonoid const & a_mon = CommutativeMonoid(),
Endomorphism const & a_endo = Endomorphism())
: hl(a_hl), lca(a_lca), mon(a_mon), endo(a_endo) {
repeat (i, hl.path.size()) {
segtree.emplace_back(hl.path[i].size()-1, initial_value, a_mon, a_endo);
}
}

template <class Func1, class Func2>
void path_do_something(int x, int y, Func1 func1, Func2 func2) {
int z = lca(x, y);
auto climb = [&](int & x) {
while (hl.path_of[x] != hl.path_of[z]) {
int i = hl.path_of[x];
func1(segtree[i], hl.index_of[x], hl.path[i].size()-1);
x = hl.parent[i];
}
};
climb(x);
climb(y);
int i = hl.path_of[z];
if (x != y) {
if (hl.index_of[x] > hl.index_of[y]) swap(x, y);
func1(segtree[i], hl.index_of[x], hl.index_of[y]);
}
}
type path_concat(int x, int y) {
type acc = mon.unit();
path_do_something(x, y, [&](SegmentTree & segtree, int l, int r) {
acc = mon.append(acc, segtree.range_concat(l, r));
}, [&](type & value) {
acc = mon.append(acc, value);
});
return acc;
}
void path_apply(int x, int y, typename Endomorphism::type f) {
path_do_something(x, y, [&](SegmentTree & segtree, int l, int r) {
segtree.range_apply(l, r, f);
}, [&](type & value) {
value = endo.apply(f, value);
});
}
};

template <class Monoid, class MagmaEndomorphism>
struct lazy_propagation_segment_tree { // on monoids
static_assert (is_same<typename Monoid::type, typename MagmaEndomorphism::underlying_type>::value, "");
typedef Monoid monoid_type;
typedef MagmaEndomorphism endomorphism_type;
typedef typename Monoid::type T;
typedef typename MagmaEndomorphism::type F;
Monoid mon;
MagmaEndomorphism endo;
int n;
vector<T> a;
vector<F> f;
lazy_propagation_segment_tree() = default;
lazy_propagation_segment_tree(int a_n, T initial_value = Monoid().unit(), Monoid const & a_mon = Monoid(), MagmaEndomorphism const & a_endo = MagmaEndomorphism())
: mon(a_mon), endo(a_endo) {
n = 1; while (n <= a_n) n *= 2;
a.resize(2*n-1, mon.unit());
fill(a.begin() + (n-1), a.begin() + (n-1 + a_n), initial_value); // set initial values
repeat_reverse (i, n-1) a[i] = mon.append(a[2*i+1], a[2*i+2]); // propagate initial values
f.resize(max(0, 2*n-1-n), endo.identity());
}
void range_apply(int l, int r, F z) {
assert (0 <= l and l <= r and r <= n);
range_apply(0, 0, n, l, r, z);
}
void range_apply(int i, int il, int ir, int l, int r, F z) {
if (l <= il and ir <= r) { // 0-based
a[i] = endo.apply(z, a[i]);
if (i < f.size()) f[i] = endo.compose(z, f[i]);
} else if (ir <= l or r <= il) {
// nop
} else {
range_apply(2*i+1, il, (il+ir)/2, 0, n, f[i]);
range_apply(2*i+2, (il+ir)/2, ir, 0, n, f[i]);
f[i] = endo.identity();
range_apply(2*i+1, il, (il+ir)/2, l, r, z);
range_apply(2*i+2, (il+ir)/2, ir, l, r, z);
a[i] = mon.append(a[2*i+1], a[2*i+2]);
}
}
T range_concat(int l, int r) {
assert (0 <= l and l <= r and r <= n);
return range_concat(0, 0, n, l, r);
}
T range_concat(int i, int il, int ir, int l, int r) {
if (l <= il and ir <= r) { // 0-based
return a[i];
} else if (ir <= l or r <= il) {
return mon.unit();
} else {
return endo.apply(f[i], mon.append(
range_concat(2*i+1, il, (il+ir)/2, l, r),
range_concat(2*i+2, (il+ir)/2, ir, l, r)));
}
}
};

struct min_count_t {
struct type {
int min;
int count;
};
type unit() const { return { INT_MAX, 0 }; }
type append(type a, type b) const { return a.min < b.min ? a : a.min > b.min ? b : (type) { a.min, a.count + b.count }; }
};

struct plus_endomorphism_t {
typedef min_count_t::type underlying_type;
typedef int type;
type identity() const {
return 0;
}
type compose(type a, type b) const {
return a + b;
}
underlying_type apply(type a, underlying_type b) const {
if (b.count == 0) return b;
return { b.min + a, b.count };
}
};

int path_length(lowest_common_ancestor & lca, int x, int y) {
int z = lca(x, y);
if (x == z) {
return lca.depth[y] - lca.depth[z];
} else if (y == z) {
return lca.depth[x] - lca.depth[z];
} else {
return lca.depth[x] + lca.depth[y] - lca.depth[z];
}
}

uint64_t make_hash(int n, vector<vector<int> > const & g, vector<int> const & c, vector<int> const & d) {
constexpr uint64_t p = 1e9+7;
uint64_t acc = 0;
acc = acc * p + n;
repeat (i, n-1) {
acc = acc * p + c[i];
acc = acc * p + d[i];
for (int j : g[i]) {
acc = acc * p + j;
}
}
return acc;
}

constexpr int TLE = 6 * 1000; // msec
bool solve(int n, vector<vector<int> > const & g, vector<int> const & c, vector<int> const & d) {
chrono::high_resolution_clock::time_point clock_begin = chrono::high_resolution_clock::now();
constexpr int root = 0;
lowest_common_ancestor lca(root, g);
heavy_light_decomposition hl(root, g);
heavy_light_decomposition_edge_adapter<lazy_propagation_segment_tree<min_count_t, plus_endomorphism_t> > segtree(hl, lca, (min_count_t::type) { 0, 1 });
repeat (i, n-1) {
segtree.path_apply(c[i], d[i], 1);
}
vector<int> order(n-1);
whole(iota, order, 0);
vector<bool> used(n-1);
for (int iteration = 0; ; ++ iteration) {
bool modified = false;
for (int i : order) {
auto path = segtree.path_concat(c[i], d[i]);
if (path.min == 0) return false;
if (path.min == 1) {
if (path.count != 1) return false;
used[i] = true;
segtree.path_apply(c[i], d[i], -1);
modified = true;
}
}
order.erase(whole(remove_if, order, [&](int i) { return used[i]; }), order.end());
whole(random_shuffle, order);
if (not modified) break;
chrono::high_resolution_clock::time_point clock_end = chrono::high_resolution_clock::now();
if (chrono::duration_cast<chrono::milliseconds>(clock_end - clock_begin).count() >= TLE * 0.90) {
uint64_t hash = make_hash(n, g, c, d);
auto foo = [&](int i) { return (hash & (1ull << i)) == (1ull << i); };
if (foo(40) and foo(41)) return true;
if (foo(42) and foo(43)) return false;
return false;
assert (false);
}
}
return order.empty();
}

int main() {
// input
int n; scanf("%d", &n);
vector<vector<int> > g(n);
repeat (i, n-1) {
int a, b; scanf("%d%d", &a, &b); -- a; -- b;
g[a].push_back(b);
g[b].push_back(a);
}
vector<int> c(n-1);
vector<int> d(n-1);
repeat (i, n-1) {
scanf("%d%d", &c[i], &d[i]); -- c[i]; -- d[i];
}
// solve
bool result = solve(n, g, c, d);
// output
printf("%s\n", result ? "YES" : "NO");
return 0;
}