DOJ1187 ： 重建家园 （分数规划 && 二分 && kruskal）

Posted 2020-10-05 cminus

最优答案一定是一颗树

那么二分比值，不断kruskal找到最大可以满足的解就可以了

代码如下

#include <cstdio>
#include <algorithm>
using namespace std;
typedef double db;

struct Node{
    int a, b, c, d;
    db w;
    inline void init() {
        scanf("%d %d %d %d", &a, &b, &c, &d);
    }
    bool operator < (const Node &o) const{
        return w < o.w;
    }
}a[10010];
int n, m, f, fa[410];

int find(int x) {
    return (fa[x] == x) ? x : fa[x] = find(fa[x]);
}

inline bool kruskal(db x) {
    for (int i = 1; i <= n; i++)    fa[i] = i;
    for (int i = 1; i <= m; i++)
        a[i].w = (db)a[i].c + (db)a[i].d * x;
    sort(a + 1, a + m + 1);
    db ans = 0;
    int tot = 0;
    for (int i = 1; i <= m; i++) {
        int x = find(a[i].a);
        int y = find(a[i].b);
        if (x != y) {
            fa[x] = y;
            ans += a[i].w;
            tot++;
        }
        if (ans > f)    return false;
        if (tot == n - 1)    return true;
    }
}

int main() {
    scanf("%d %d %d", &n, &m, &f);
    for (int i = 1; i <= m; i++)
        a[i].init();
    db l = 0, r = (db)f / (n - 1);
    while (r - l > 0.000001) {
        db mid = (l + r) / 2;
        if (kruskal(mid))    l = mid;
        else r = mid;
    }
    printf("%.4lf", l);
    return 0;
}