結果

問題 No.1207 グラフX
ユーザー Mister
提出日時 2020-08-30 16:20:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 239 ms / 2,000 ms
コード長 4,477 bytes
コンパイル時間 1,110 ms
コンパイル使用メモリ 88,364 KB
最終ジャッジ日時 2025-01-13 23:50:02
ジャッジサーバーID
(参考情報)
judge5 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 46
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <iostream>
#include <numeric>
#include <vector>
template <int MOD>
struct ModInt {
using lint = long long;
int val;
// constructor
ModInt(lint v = 0) : val(v % MOD) {
if (val < 0) val += MOD;
};
// unary operator
ModInt operator+() const { return ModInt(val); }
ModInt operator-() const { return ModInt(MOD - val); }
ModInt inv() const { return this->pow(MOD - 2); }
// arithmetic
ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
ModInt pow(lint n) const {
auto x = ModInt(1);
auto b = *this;
while (n > 0) {
if (n & 1) x *= b;
n >>= 1;
b *= b;
}
return x;
}
// compound assignment
ModInt& operator+=(const ModInt& x) {
if ((val += x.val) >= MOD) val -= MOD;
return *this;
}
ModInt& operator-=(const ModInt& x) {
if ((val -= x.val) < 0) val += MOD;
return *this;
}
ModInt& operator*=(const ModInt& x) {
val = lint(val) * x.val % MOD;
return *this;
}
ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }
// compare
bool operator==(const ModInt& b) const { return val == b.val; }
bool operator!=(const ModInt& b) const { return val != b.val; }
bool operator<(const ModInt& b) const { return val < b.val; }
bool operator<=(const ModInt& b) const { return val <= b.val; }
bool operator>(const ModInt& b) const { return val > b.val; }
bool operator>=(const ModInt& b) const { return val >= b.val; }
// I/O
friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept {
lint v;
is >> v;
x = v;
return is;
}
friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};
template <class Cost = int>
struct Edge {
int src, dst;
Cost cost;
Edge(int src = -1, int dst = -1, Cost cost = 1)
: src(src), dst(dst), cost(cost){};
bool operator<(const Edge<Cost>& e) const { return this->cost < e.cost; }
bool operator>(const Edge<Cost>& e) const { return this->cost > e.cost; }
};
template <class Cost = int>
struct Graph {
std::vector<std::vector<Edge<Cost>>> graph;
Graph(int n = 0) : graph(n) {}
void span(bool direct, int src, int dst, Cost cost = 1) {
graph[src].emplace_back(src, dst, cost);
if (!direct) graph[dst].emplace_back(dst, src, cost);
}
int size() const { return graph.size(); }
void clear() { graph.clear(); }
void resize(int n) { graph.resize(n); }
std::vector<Edge<Cost>>& operator[](int v) { return graph[v]; }
std::vector<Edge<Cost>> operator[](int v) const { return graph[v]; }
};
struct UnionFind {
std::vector<int> par, sz;
int gnum;
explicit UnionFind(int n)
: par(n), sz(n, 1), gnum(n) {
std::iota(par.begin(), par.end(), 0);
}
int find(int v) {
return (par[v] == v) ? v : (par[v] = find(par[v]));
}
void unite(int u, int v) {
u = find(u), v = find(v);
if (u == v) return;
if (sz[u] < sz[v]) std::swap(u, v);
sz[u] += sz[v];
par[v] = u;
--gnum;
}
bool same(int u, int v) { return find(u) == find(v); }
bool ispar(int v) { return v == find(v); }
int size(int v) { return sz[find(v)]; }
};
constexpr int MOD = 1000000007;
using mint = ModInt<MOD>;
void solve() {
int n, m;
mint x;
std::cin >> n >> m >> x;
Graph<int> graph(n);
UnionFind uf(n);
while (m--) {
int u, v, w;
std::cin >> u >> v >> w;
if (uf.same(--u, --v)) continue;
uf.unite(u, v);
graph.span(false, u, v, w);
}
mint ans = 0;
auto dfs = [&](auto f, int v, int p) -> int {
int sz = 1;
for (auto e : graph[v]) {
int u = e.dst;
if (u == p) continue;
int csz = f(f, u, v);
ans += x.pow(e.cost) * csz * (n - csz);
sz += csz;
}
return sz;
};
dfs(dfs, 0, -1);
std::cout << ans << "\n";
}
int main() {
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
solve();
return 0;
}
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