Codeforces 348B

348B - Apple Tree

我们设最后答案为 x ， 我们我们就能用x表示出所有节点下面的苹果个数， 然后用叶子节点求lcm， 取最大的可行解。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long
using namespace std;

const int N = 1e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;

int n, a[N];
LL dv[N], sum[N], all;
vector<int> leaf;
vector<int> G[N];

void solve(int u, int fa) {
    if(u != 1 && SZ(G[u]) == 1) leaf.push_back(u);
    sum[u] = a[u];
    for(int v : G[u]) {
        if(v == fa) continue;
        solve(v, u);
        sum[u] += sum[v];
    }
}

void dfs(int u, int fa) {
    if(dv[u] > all) {
        printf("%lld
", all);
        exit(0);
    }
    for(int v : G[u]) {
        if(v == fa) continue;
        if(u == 1) dv[v] = dv[u] * SZ(G[u]);
        else dv[v] = dv[u] * (SZ(G[u]) - 1);
        dfs(v, u);
    }
}

bool check(LL x) {
    for(auto& id : leaf) {
        if(x / dv[id] > a[id]) return false;
    }
    return true;
}
int main() {
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) scanf("%d", &a[i]), all += a[i];
    for(int i = 1; i < n; i++) {
        int u, v; scanf("%d%d", &u, &v);
        G[u].push_back(v);
        G[v].push_back(u);
    }
    dv[1] = 1;
    solve(1, 0);
    dfs(1, 0);
    LL lcm = 1;
    for(auto& id : leaf) {
        LL gcd = __gcd(lcm, dv[id]);
        if(1.0 * lcm / gcd * dv[id] > all) {
            printf("%lld
", all);
            return 0;
        }
        lcm = lcm / gcd * dv[id];
    }
    LL low = 1, high = all / lcm, ans = 0;
    while(low <= high) {
        LL mid = low + high >> 1;
        if(check(mid * lcm)) ans = mid, low = mid + 1;
        else high = mid - 1;
    }
    printf("%lld
", all - ans * lcm);
    return 0;
}

/*
*/