题目链接

Save your cats Aizu - 2224

思路

$$ 有环图减小边成树的代价 <=> 总边权-最大生成树 $$

时间复杂度

$$ O((M)log(M)) $$

代码

#include <cstdio>
#include <algorithm>
#include <vector>
#include <cmath>

using namespace std;

class DSU {
public:
    vector<int> p, r;

    void init(int n) {
        p.resize(n + 10);
        r.resize(n + 10);
        for (int i = 0; i <= n; i++) {
            p[i] = i;
            r[i] = 0;
        }
    }

    int find(int x) {
        if (x == p[x]) {
            return x;
        } else {
            return p[x] = find(p[x]);
        }
    }

    bool unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) {
            return false;
        }

        if (r[x] < r[y]) {
            p[x] = y;
        } else {
            p[y] = x;
            if (r[x] == r[y]) {
                r[x]++;
            }
        }
        return true;
    }

    bool same(int x, int y) {
        return find(x) == find(y);
    }
};

DSU dsu;

const int MAXN = 1e5 + 10;

int a[MAXN], b[MAXN], id[MAXN];
double x[MAXN], y[MAXN];
double c[MAXN];

double dist(int u, int v) {
    return sqrt((x[u] - x[v]) * (x[u] - x[v])
              + (y[u] - y[v]) * (y[u] - y[v]));
}

bool cmp(int u, int v) {
    return c[u] > c[v];
}

int main() {
    int n, m;
    scanf("%d%d", &n, &m);// don't forget &
    dsu.init(n);
    for (int i = 1; i <= n; i++) {
        scanf("%lf%lf", &x[i], &y[i]);
    }
    double ans = 0;
    for (int i = 1; i <= m; i++) {
        id[i] = i;
        scanf("%d%d", &a[i], &b[i]);
        c[i] = dist(a[i], b[i]);
        ans += c[i];
    }
    sort(id + 1, id + 1 + m, cmp);
    for (int i = 1; i <= m; i++) {
        int u = id[i];

        if (!dsu.same(a[u], b[u])) {
            dsu.unite(a[u], b[u]);
            ans -= c[u];
        }
    }
    printf("%f", ans);
    return 0;
}