uvalive5713(次小生成树)

先求出最小生成树，然后n^2枚举两个点，在两个点之间连一条边，就形成了一个环，然后求出两点间人数的和除以那个环在树上的边的最大边，更新最大值．求最大权值边可以用熟练剖分．复杂度n^2logn．

#include <cstdio>#include <cstring>#include <vector>#include<cmath>#include <algorithm>using namespace std;#define Del(a,b) memset(a,b,sizeof(a))const int N = 10005;const int inf = 0x3f3f3f3f;const int maxn = 1005;int c[maxn];double x[maxn],y[maxn];double bmap[maxn][maxn];int vis[maxn];int pre[maxn];double lowc[maxn];int dep[N],siz[N],fa[N],id[N],son[N],top[N];double val[maxn];int num;vector<int> v[N];double res = -inf*1.0;struct tree{    int x,y;    double val;    void read(int a,int b,double c){        x = a;        y = b;        val = c;    }};tree e[N];inline double cla(int a,int b){    return sqrt((x[a]-x[b])*(x[a]-x[b])+(y[a]-y[b])*(y[a]-y[b]));}inline double prim(double cost[maxn][maxn],int n){    double ans = 0;    for(int i=0;i<n;i++) pre[i] = 0;    memset(vis,0,sizeof(vis));    vis[0] = true;    for(int i=1;i<n;i++) lowc[i] = cost[0][i];    for(int i=1;i<n;i++)    {        double  minc = inf*1.0;        int p = -1;        for(int j=0;j<n;j++)            if(!vis[j]&&minc>lowc[j])            {                minc = lowc[j];                p = j;            }        if(minc==inf*1.0) return -1;        ans += minc;        e[i].read(pre[p]+1,p+1,minc);        v[pre[p]+1].push_back(p+1);        v[p+1].push_back(pre[p]+1);        vis[p] = true;        for(int j=0;j<n;j++)        {            if(!vis[j]&&lowc[j]>cost[p][j]){                lowc[j] = cost[p][j];                pre[j] = p;            }        }    }    return ans;}void dfs1(int u, int f, int d) {    dep[u] = d;    siz[u] = 1;    son[u] = 0;    fa[u] = f;    for (int i = 0; i < v[u].size(); i++) {        int ff = v[u][i];        if (ff == f) continue;        dfs1(ff, u, d + 1);        siz[u] += siz[ff];        if (siz[son[u]] < siz[ff])            son[u] = ff;    }}void dfs2(int u, int tp) {    top[u] = tp;    id[u] = ++num;    if (son[u]) dfs2(son[u], tp);    for (int i = 0; i < v[u].size(); i++) {        int ff = v[u][i];        if (ff == fa[u] || ff == son[u]) continue;        dfs2(ff, ff);    }}#define lson(x) ((x<<1))#define rson(x) ((x<<1)+1)struct Tree{    int l,r;    double val;};Tree tree[4*N];void pushup(int x) {    tree[x].val = max(tree[lson(x)].val, tree[rson(x)].val);}void build(int l,int r,int v){    tree[v].l=l;    tree[v].r=r;    if(l==r)    {        tree[v].val = val[l];        return ;    }    int mid=(l+r)>>1;    build(l,mid,v*2);    build(mid+1,r,v*2+1);    pushup(v);}void update(int o,int v,int val)  //log(n){    if(tree[o].l==tree[o].r)    {        tree[o].val = val;        return ;    }    int mid = (tree[o].l+tree[o].r)/2;    if(v<=mid)        update(o*2,v,val);    else        update(o*2+1,v,val);    pushup(o);}double query(int x,int l, int r){    if (tree[x].l >= l && tree[x].r <= r) {        return tree[x].val;    }    int mid = (tree[x].l + tree[x].r) / 2;    double ans = 0;    if (l <= mid) ans = max(ans, query(lson(x),l,r));    if (r > mid) ans = max(ans, query(rson(x),l,r));    return ans;}double Yougth(int u, int v) {    int tp1 = top[u], tp2 = top[v];    double ans = 0;    while (tp1 != tp2) {        //printf("YES\n");        if (dep[tp1] < dep[tp2]) {            swap(tp1, tp2);            swap(u, v);        }        ans = max(query(1,id[tp1], id[u]), ans);        u = fa[tp1];        tp1 = top[u];    }    if (u == v) return ans;    if (dep[u] > dep[v]) swap(u, v);    ans = max(query(1,id[son[u]], id[v]), ans);    return ans;}void Clear(int n){    for(int i=1;i<=n;i++)        v[i].clear();}int main(){    int T;    scanf("%d",&T);    while(T--)    {        int n;        scanf("%d",&n);        for(int i=0;i<n;i++)        scanf("%lf%lf%d",&x[i],&y[i],&c[i]);        for(int i=0;i<n;i++)            for(int j=i+1;j<n;j++)                bmap[i][j] = bmap[j][i] = cla(i,j);        double l = prim(bmap,n); res = -inf*1.0;        num = 0;        dfs1(1,0,1);        dfs2(1,1);        for (int i = 1; i < n; i++) {            if (dep[e[i].x] < dep[e[i].y]) swap(e[i].x, e[i].y);            val[id[e[i].x]] = e[i].val;        }        build(1,num,1);        for(int i=0;i<n;i++)        {            for(int j=i+1;j<n;j++)            {                int sum = c[i]+c[j];                res = max(res,sum/(l-Yougth(i+1,j+1)));            }        }        printf("%.2f\n",res);        Clear(n);    }    return 0;}