[CF1210C] Kamil and Making a Stream

[CF1210C] Kamil and Making a Stream - map

Description

给定一棵n个点带点权的树，i号点的点定义f(i,j)为i到j路径上所有点的gcd，其中i是j的一个祖先，求所有f(i,j)之和

Solution

对于每个点，用一个 map 维护它到所有祖先的链上的 GCD 的每种可能值及个数，暴力递推即可

#include <bits/stdc++.h>
using namespace std;

#define int long long

const int N = 1e6 + 5;
const int mod = 1e9 + 7;

int n, a[N];
vector<int> g[N];
map<int, int> f[N];

void dfs(int p, int from = 0)
{
    f[p][a[p]]++;
    for (int q : g[p])
    {
        if (q == from)
            continue;
        for (auto [x, y] : f[p])
        {
            int z = __gcd(x, a[q]);
            f[q][z] += y;
        }
        dfs(q, p);
    }
}

signed main()
{
    ios::sync_with_stdio(false);

    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> a[i];

    for (int i = 1; i < n; i++)
    {
        int p, q;
        cin >> p >> q;
        g[p].push_back(q);
        g[q].push_back(p);
    }

    dfs(1);

    int ans = 0;
    for (int i = 1; i <= n; i++)
        for (auto [x, y] : f[i])
            ans += x * y, ans %= mod;
    cout << ans << endl;
}