羽化而登仙(Feather Ascension) 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;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n, m, q;
    if (!(cin >> n >> m >> q)) return 0;
    const long long MOD = 998244353LL;
    vector<long long> pw2(m + 1, 1);
    for (int i = 1; i <= m; ++i) {
        pw2[i] = (pw2[i - 1] * 2) % MOD;
    }
    vector<int> p(n + 1);
    iota(p.begin(), p.end(), 0);
    auto find = [&](int x) {
        while (p[x] != x) x = p[x] = p[p[x]];
        return x;
    };
    vector<vector<pair<int, long long>>> adj(n + 1);
    for (int i = 1; i <= m; ++i) {
        int u, v;
        cin >> u >> v;
        int ru = find(u), rv = find(v);
        if (ru != rv) {
            p[ru] = rv;
            adj[u].push_back({v, pw2[i]});
            adj[v].push_back({u, pw2[i]});
        }
    }
    const int LOG = 20;
    vector<vector<int>> up(LOG, vector<int>(n + 1, 0));
    vector<int> dep(n + 1, 0), comp(n + 1, 0);
    vector<long long> dist_root(n + 1, 0);
    vector<int> que;
    que.reserve(n);
    for (int i = 1; i <= n; ++i) {
        if (comp[i] != 0) continue;
        que.clear();
        que.push_back(i);
        comp[i] = i;
        dep[i] = 1;
        for (size_t head = 0; head < que.size(); ++head) {
            int u = que[head];
            for (auto& edge : adj[u]) {
                int v = edge.first;
                long long w = edge.second;
                if (comp[v] == 0) {
                    comp[v] = i;
                    dep[v] = dep[u] + 1;
                    up[0][v] = u;
                    dist_root[v] = (dist_root[u] + w) % MOD;
                    que.push_back(v);
                }
            }
        }
    }
    for (int k = 1; k < LOG; ++k) {
        for (int i = 1; i <= n; ++i) {
            up[k][i] = up[k - 1][up[k - 1][i]];
        }
    }
    auto get_lca = [&](int u, int v) {
        if (dep[u] < dep[v]) swap(u, v);
        int diff = dep[u] - dep[v];
        for (int k = 0; k < LOG; ++k) {
            if ((diff >> k) & 1) u = up[k][u];
        }
        if (u == v) return u;
        for (int k = LOG - 1; k >= 0; --k) {
            if (up[k][u] != up[k][v]) {
                u = up[k][u];
                v = up[k][v];
            }
        }
        return up[0][u];
    };
    for (int i = 0; i < q; ++i) {
        int u, v;
        cin >> u >> v;
        if (comp[u] != comp[v]) {
            cout << -1 << "\n";
        } else {
            int lca = get_lca(u, v);
            long long ans = (dist_root[u] + dist_root[v] - 2LL * dist_root[lca]) % MOD;
            if (ans < 0) ans += MOD;
            cout << ans << "\n";
        }
    }
    return 0;
}