最小公倍树(Lowest Common Tree) 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 <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
using namespace std;

struct Edge {
    int u, v;
    long long w;
    bool operator<(const Edge& o) const { return w < o.w; }
};

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int L, R;
    if (!(cin >> L >> R)) return 0;
    int n = R - L + 1;
    vector<Edge> edges;
    for (int i = L + 1; i <= R; ++i) {
        edges.push_back({0, i - L, 1LL * L * i / std::gcd(L, i)});
    }
    for (int d = 2; d <= R; ++d) {
        int first = ((L + d - 1) / d) * d;
        if (first > R) continue;
        for (int mult = first + d; mult <= R; mult += d) {
            edges.push_back({first - L, mult - L, 1LL * first / d * mult});
        }
    }
    sort(edges.begin(), edges.end());
    vector<int> p(n);
    iota(p.begin(), p.end(), 0);
    auto find = [&](int x) {
        while (p[x] != x) x = p[x] = p[p[x]];
        return x;
    };
    long long ans = 0;
    int cnt = 0;
    for (const auto& e : edges) {
        int ru = find(e.u), rv = find(e.v);
        if (ru != rv) {
            p[ru] = rv;
            ans += e.w;
            if (++cnt == n - 1) break;
        }
    }
    cout << ans << "\n";
    return 0;
}