CF76A.Gift [最小生成樹]

CF76A.Gift

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

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考慮按g升序加邊，用已在生成樹中的邊和新加入的邊求當前最小生成樹。

複雜度\(O(nm)\)

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();
}