题解 | 旅游

#include <bits/stdc++.h>
using namespace std;
#define endl "\n"
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define int long long
#define pb push_back
using vi = vector<int>;
int find(vi& root, int x) {
    if (root[x] == x)return x;
    return root[x] = find(root, root[x]);
}

struct edge {
    int x, y, c;
};

void solve() {
    int n, m, c;cin >> n >> m >> c;
    vector<edge>a(m);
    for (auto& [x, y, c] : a) {
        cin >> x >> y >> c;
    }
    sort(all(a), [](edge a1, edge a2) {
        return a1.c < a2.c;
        });
    int l = 0, r = 1e9;
    int ans = 0;
    while (l <= r) {
        int mid = l + (r - l) / 2;
        vi root(n+1);
        iota(all(root), 0);
        int sum = 0;
        vi b;
        int t = n - 1;
        int idx = 0;
        while (t) {
            auto [xx, yy, aa] = a[idx++];
            int xxx = find(root, xx);
            int yyy = find(root, yy);
            if (xxx != yyy) {
                if (aa > mid) {
                    b.pb(aa);
                }
                root[xxx] = yyy;
                t--;
            }
        }
        sort(rall(b));
        int cnt = 1;
        for (int i : b) {
            sum += cnt * i;
            cnt++;
        }
        if (sum <= c) {
            ans = mid;
            r = mid - 1;
        }
        else {
            l = mid + 1;
        }
    }
    cout << ans << endl;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);cout.tie(nullptr);
    int t = 1;
    //cin >> t;
    for (int i = 1; i <= t; i++) {
        //cout << "----Test " << i << "----" << endl;
        solve();
    }
    return 0;
}

二分最小生成树（并查集解法），小于等于mid的不计入sum，根据排序不等式，先修损坏值最大的使得sum最小