随机树生成器(Random Tree Generator) 题解

思路分析

按题目要求使用对应数据结构与算法模拟/递推求解，注意数据范围边界与时间复杂度。

参考代码

#include <algorithm>
#include <iostream>
#include <vector>
using namespace std;

const int MOD = 1000000009;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int T;
    if (!(cin >> T)) return 0;
    vector<pair<int, int>> qs(T);
    int maxN = 2;
    for (int i = 0; i < T; ++i) {
        cin >> qs[i].first >> qs[i].second;
        maxN = max(maxN, qs[i].first);
    }
    vector<int> inv(maxN + 1, 1), fact(maxN + 1, 1), hsum(maxN + 1, 0);
    for (int i = 2; i <= maxN; ++i) {
        inv[i] = 1LL * (MOD - MOD / i) * inv[MOD % i] % MOD;
        fact[i] = 1LL * fact[i - 1] * i % MOD;
    }
    for (int i = 1; i <= maxN; ++i) {
        hsum[i] = hsum[i - 1] + inv[i];
        if (hsum[i] >= MOD) hsum[i] -= MOD;
    }
    for (const auto& [n, k] : qs) {
        if (n == 1) {
            cout << 0 << "\n";
            continue;
        }
        long long deg_exp = (k > 1 ? 1 : 0);
        int sh = hsum[n - 1] - hsum[k - 1];
        if (sh < 0) sh += MOD;
        deg_exp = (deg_exp + sh) % MOD;
        long long ans = deg_exp * fact[n - 1] % MOD;
        cout << ans << "\n";
    }
    return 0;
}