CF1230E Kamil and Making a Stream

题目大意是求

\(\sum_{v,fa,lca(v,fa)=fa}gcd(v \to fa)\)
容易发现 \(\gcd\) 只会变小，所以根据这玩意是从上到下的，每次暴力一下就可以了，\(\gcd\)数量不会超过\(\log\)，所以复杂度大概是 \(n \log n\)
// powered by c++11

// by Isaunoya

#include <bits/stdc++.h>

#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)

#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

using namespace std;

using db = double;

using ll = long long;

using uint = unsigned int;

#define int long long

using pii = pair<int, int>;

#define ve vector

#define Tp template

#define all(v) v.begin(), v.end()

#define sz(v) ((int)v.size())

#define pb emplace_back

#define fir first

#define sec second

// the cmin && cmax

Tp<class T> void cmax(T& x, const T& y) {

  if (x < y) x = y;

}

Tp<class T> void cmin(T& x, const T& y) {

  if (x > y) x = y;

}

// sort , unique , reverse

Tp<class T> void sort(ve<T>& v) { sort(all(v)); }

Tp<class T> void unique(ve<T>& v) {

  sort(all(v));

  v.erase(unique(all(v)), v.end());

}

Tp<class T> void reverse(ve<T>& v) { reverse(all(v)); }

const int SZ = 0x191981;

struct FILEIN {

  ~FILEIN() {}

  char qwq[SZ], *S = qwq, *T = qwq, ch;

  char GETC() { return (S == T) && (T = (S = qwq) + fread(qwq, 1, SZ, stdin), S == T) ? EOF : *S++; }

  FILEIN& operator>>(char& c) {

    while (isspace(c = GETC()))

      ;

    return *this;

  }

  FILEIN& operator>>(string& s) {

    while (isspace(ch = GETC()))

      ;

    s = ch;

    while (!isspace(ch = GETC())) s += ch;

    return *this;

  }

  Tp<class T> void read(T& x) {

    bool sign = 1;

    while ((ch = GETC()) < 0x30)

      if (ch == 0x2d) sign = 0;

    x = (ch ^ 0x30);

    while ((ch = GETC()) > 0x2f) x = x * 0xa + (ch ^ 0x30);

    x = sign ? x : -x;

  }

  FILEIN& operator>>(int& x) { return read(x), *this; }

  FILEIN& operator>>(signed& x) { return read(x), *this; }

  FILEIN& operator>>(unsigned& x) { return read(x), *this; }

} in;

struct FILEOUT {

  const static int LIMIT = 0x114514;

  char quq[SZ], ST[0x114];

  signed sz, O;

  ~FILEOUT() { flush(); }

  void flush() {

    fwrite(quq, 1, O, stdout);

    fflush(stdout);

    O = 0;

  }

  FILEOUT& operator<<(char c) { return quq[O++] = c, *this; }

  FILEOUT& operator<<(string str) {

    if (O > LIMIT) flush();

    for (char c : str) quq[O++] = c;

    return *this;

  }

  Tp<class T> void write(T x) {

    if (O > LIMIT) flush();

    if (x < 0) {

      quq[O++] = 0x2d;

      x = -x;

    }

    do {

      ST[++sz] = x % 0xa ^ 0x30;

      x /= 0xa;

    } while (x);

    while (sz) quq[O++] = ST[sz--];

    return;

  }

  FILEOUT& operator<<(int x) { return write(x), *this; }

  FILEOUT& operator<<(signed x) { return write(x), *this; }

  FILEOUT& operator<<(unsigned x) { return write(x), *this; }

} out;

int n, ans;

const int maxn = 1e5 + 10;

vector<int> g[maxn];

int val[maxn];

int gcd(int x, int y) { return y ? gcd(y, x % y) : x; }

const int mod = 1e9 + 7;

void dfs(vector<pii> vc, int u, int p) {

  vector<pii> nvc;

  nvc.pb(val[u], 1ll);

  ans = (ans + val[u]) % mod;

  for (pii x : vc) {

    int y = x.first;

    int c = x.second;

    int ny = gcd(y, val[u]);

    ans = (ans + ny * c) % mod;

    if (ny == nvc.back().first)

      nvc.back().second += c;

    else

      nvc.pb(ny, c);

  }

  nvc.swap(vc);

  for (int v : g[u])

    if (v != p) dfs(vc, v, u);

}

signed main() {

#ifdef _WIN64

  freopen("testdata.in", "r", stdin);

#else

  ios_base ::sync_with_stdio(false);

  cin.tie(nullptr), cout.tie(nullptr);

#endif

  // code begin.

  in >> n;

  for (int i = 0; i < n; i++) {

    in >> val[i];

  }

  for (int i = 1; i < n; i++) {

    int u, v;

    in >> u >> v;

    --v, --u;

    g[u].pb(v);

    g[v].pb(u);

  }

  dfs({}, 0, -1);

  out << ans << '\n';

  return 0;

  // code end.

}
巴特西

CF1230E Kamil and Making a Stream

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