結果
| 問題 | No.196 典型DP (1) |
| ユーザー |
 iiljj
|
| 提出日時 | 2020-03-31 22:58:08 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 60 ms / 2,000 ms |
| コード長 | 9,165 bytes |
| コンパイル時間 | 4,651 ms |
| コンパイル使用メモリ | 209,940 KB |
| 最終ジャッジ日時 | 2025-01-09 11:22:35 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 |
ソースコード
/* #region Head */
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#define DEBUG_
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " \
<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) cout << unitbuf;
}
} ATCODER_INITIALIZE;
string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";
/* #endregion */
/* #region Graph */
using Weight = ll;
using Flow = ll;
// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
struct Edge {
ll src; // エッジ始点となる頂点
ll dst; // エッジ終点となる頂点
Weight weight; // 重み
Flow cap;
Edge() : src(0), dst(0), weight(0) {}
Edge(ll src, ll dst, Weight weight) : src(src), dst(dst), weight(weight) {}
};
using Node = vc<Edge>; // 同じ頂点を始点とするエッジ集合
using Graph = vc<Node>; // graph[i] := 頂点 i を始点とするエッジ集合
using Array = vector<Weight>;
using Matrix = vector<Array>;
// 双方向のエッジを追加する
void add_edge(Graph &g, ll a, ll b, Weight w = 1) {
g[a].emplace_back(a, b, w);
g[b].emplace_back(b, a, w);
}
// 単方向のアークを追加する
void add_arc(Graph &g, ll a, ll b, Weight w = 1) { g[a].emplace_back(a, b, w); }
// Edge 標準出力
ostream &operator<<(ostream &os, Edge &edge) {
os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
return os;
}
/* #endregion */
/* #region mint */
// 自動で MOD を取る整数
struct mint {
ll x;
mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
mint &operator+=(const mint a) {
if ((x += a.x) >= MOD) x -= MOD;
return *this;
}
mint &operator-=(const mint a) {
if ((x += MOD - a.x) >= MOD) x -= MOD;
return *this;
}
mint &operator*=(const mint a) {
(x *= a.x) %= MOD;
return *this;
}
mint operator+(const mint a) const {
mint res(*this);
return res += a;
}
mint operator-(const mint a) const {
mint res(*this);
return res -= a;
}
mint operator*(const mint a) const {
mint res(*this);
return res *= a;
}
// O(log(t))
mint pow(ll t) const {
if (!t) return 1;
mint a = pow(t >> 1); // ⌊t/2⌋ 乗
a *= a; // ⌊t/2⌋*2 乗
if (t & 1) // ⌊t/2⌋*2 == t-1 のとき
a *= *this; // ⌊t/2⌋*2+1 乗 => t 乗
return a;
}
// for prime mod
mint inv() const {
return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
}
mint &operator/=(const mint a) { return (*this) *= a.inv(); }
mint operator/(const mint a) const {
mint res(*this);
return res /= a;
}
bool operator==(const mint a) const { return this->x == a.x; }
bool operator==(const ll a) const { return this->x == a; }
// mint 入力
friend istream &operator>>(istream &is, mint &x) {
is >> x.x;
return is;
}
// mint 出力
friend ostream &operator<<(ostream &os, mint x) {
os << x.x;
return os;
}
};
/* #endregion */
// Problem
void solve() {
ll n, k;
cin >> n >> k;
vll a(n - 1), b(n - 1);
REP(i, 0, n - 1) cin >> a[i] >> b[i];
Graph graph(n, Node(0));
REP(i, 0, n - 1) add_edge(graph, a[i], b[i]);
vc<vc<mint>> dp(n, vc<mint>(1, 0)); // vc<mint>(k + 1, 0);
vll sizes(n, 0); // 部分木のサイズ
auto merge = [&](vc<mint> v1, vc<mint> v2) {
ll sz1 = SIZE(v1), sz2 = SIZE(v2);
vc<mint> merged(sz1 + sz2, 0);
REP(i, 0, sz1) REP(j, 0, sz2) merged[i + j] += v1[i] * v2[j];
while (!merged.empty() && merged.back() == 0) merged.pop_back();
return merged;
};
function<void(ll, ll)> dfs = [&](ll idx, ll par) {
sizes[idx] = 1;
dp[idx][0] = 1;
for (Edge &edge : graph[idx]) {
if (edge.dst == par) continue;
dfs(edge.dst, edge.src);
dp[idx] = merge(dp[idx], dp[edge.dst]);
sizes[edge.src] += sizes[edge.dst];
}
if (SIZE(dp[idx]) <= sizes[idx]) {
// if (sizes[idx] == 1 && SIZE(dp[idx]) < 2) {
dp[idx].resize(sizes[idx] + 1);
dp[idx][sizes[idx]] = 1;
}
};
dfs(0, -1);
// dump(dp, sizes);
cout << dp[0][k] << endl;
}
// entry point
int main() {
solve();
return 0;
}