CF76A.Gift

题意：noi2014魔法森林弱化版QwQ，最小化\(max(g_i)*G + max(s_i)*S\)的最小生成树

考虑按g升序加边，用已在生成树中的边和新加入的边求当前最小生成树。

复杂度\(O(nm)\)

vector真好用

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
using namespace std;
typedef long long ll;
const int N = 205, M = 50005;
const ll inf = 2e18+5;inline int read() {int x = 0, f = 1; char c = getchar();while(c<'0' || c>'9') {if(c=='-') f=-1; c=getchar();}while(c>='0' && c<='9') {x=x*10+c-'0'; c=getchar();}return x*f;
}int n, m, G, S;
struct edge {int x, y, g, s;bool operator <(const edge &r) const {return g < r.g;}
} e[M];
bool cmp_s(const edge &a, const edge &b) {return a.s < b.s;
}
int fa[N];
int find(int x) {return x == fa[x] ? x : fa[x] = find(fa[x]);}vector<edge> v;
vector<edge>::iterator it;
ll ans = inf;
ll kruskal(int m) { //printf("kruskal %d\n", m);int mg = 0, ms = 0;for(int i=1; i<=n; i++) fa[i] = i;int cnt = 0;for(it = v.begin(); it != v.end(); ) {int x = find(it->x), y = find(it->y);//printf("%d %d    %d %d\n", e[i].x, e[i].y, x, y); cout << endl;if(x == y) {it = v.erase(it);continue; }fa[y] = x;mg = max(mg, it->g);ms = max(ms, it->s);if(++cnt == n-1) break;it++;}if(cnt == n-1) return (ll) mg * G + (ll) ms * S;else return inf;
}void solve() {sort(e+1, e+1+m);for(int i=1; i<=n-2; i++) v.push_back(e[i]);sort(v.begin(), v.end(), cmp_s);for(int p=n-1; p<=m; p++) { //printf("ppp %d\n", p);edge now = e[p];int flag = 0;for(it = v.begin(); it != v.end(); it++) {if(it->s > now.s) {v.insert(it, now);flag = 1;break;}}if(!flag) v.insert(it, now);ans = min(ans, kruskal(p));}if(ans == inf) ans = -1;cout << ans;
}int main() {//freopen("in", "r", stdin);cin >> n >> m >> G >> S;;for(int i=1; i<=m; i++) {e[i].x = read();e[i].y = read();e[i].g = read();e[i].s = read();}solve();
}