# [BZOJ3080]Minimum Variance Spanning Tree/[BZOJ3754]Tree之最小方差树

## 题目大意：

3080数据范围：$n\le50,m\le1000,w_i\le50$
3754数据范围：$n\le100,m\le1000,w_i\le100$

## 源代码（3080）：

#include<cstdio>
#include<cctype>
#include<algorithm>
inline int getint() {
register char ch;
while(!isdigit(ch=getchar()));
register int x=ch^'0';
while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0');
return x;
}
const int N=51,M=1001;
double d;
inline double sqr(const double &x) {
return x*x;
}
struct Edge {
int u,v,w;
bool operator < (const Edge &rhs) const {
return sqr(w-d)<sqr(rhs.w-d);
}
};
Edge edge[M];
class DisjointSet {
private:
int anc[N];
int find(const int &x) {
return x==anc[x]?x:anc[x]=find(anc[x]);
}
public:
void reset(const int &n) {
for(register int i=1;i<=n;i++) anc[i]=i;
}
void merge(const int &x,const int &y) {
anc[find(x)]=find(y);
}
bool same(const int &x,const int &y) {
return find(x)==find(y);
}
};
DisjointSet djs;
int main() {
for(register int i=1;;i++) {
const int n=getint(),m=getint();
if(n==0&&m==0) return 0;
for(register int i=1;i<=m;i++) {
edge[i].u=getint();
edge[i].v=getint();
edge[i].w=getint();
}
d=0;
std::sort(&edge[1],&edge[m]+1);
int l=0,r=0;
for(register int i=1;i<n;i++) l+=edge[i].w;
for(register int i=m;i>m-n+1;i--) r+=edge[i].w;
double ans=1e18;
for(register int i=l;i<=r;i++) {
d=1.*i/(n-1);
std::sort(&edge[1],&edge[m]+1);
djs.reset(n);
int sum1=0;
double sum2=0;
for(register int i=1;i<=m;i++) {
const int &u=edge[i].u,&v=edge[i].v;
if(djs.same(u,v)) continue;
djs.merge(u,v);
sum1+=edge[i].w;
sum2+=sqr(edge[i].w-d);
}
if(sum1==i) {
ans=std::min(ans,sum2/(n-1));
}
}
printf("Case %d: %.2f\n",i,ans);
}
}


## 源代码（3754）：

#include<cmath>
#include<cstdio>
#include<cctype>
#include<algorithm>
inline int getint() {
register char ch;
while(!isdigit(ch=getchar()));
register int x=ch^'0';
while(isdigit(ch=getchar())) x=(((x<<2)+x)<<1)+(ch^'0');
return x;
}
const int N=101,M=2001;
double d;
inline double sqr(const double &x) {
return x*x;
}
struct Edge {
int u,v,w;
bool operator < (const Edge &rhs) const {
return sqr(w-d)<sqr(rhs.w-d);
}
};
Edge edge[M];
class DisjointSet {
private:
int anc[N];
int find(const int &x) {
return x==anc[x]?x:anc[x]=find(anc[x]);
}
public:
void reset(const int &n) {
for(register int i=1;i<=n;i++) anc[i]=i;
}
void merge(const int &x,const int &y) {
anc[find(x)]=find(y);
}
bool same(const int &x,const int &y) {
return find(x)==find(y);
}
};
DisjointSet djs;
int main() {
const int n=getint(),m=getint();
for(register int i=1;i<=m;i++) {
edge[i].u=getint();
edge[i].v=getint();
edge[i].w=getint();
}
std::sort(&edge[1],&edge[m]+1);
int l=0,r=0;
for(register int i=1;i<n;i++) l+=edge[i].w;
for(register int i=m;i>m-n+1;i--) r+=edge[i].w;
double ans=1e18;
for(register int i=l;i<=r;i++) {
d=1.*i/(n-1);
std::sort(&edge[1],&edge[m]+1);
djs.reset(n);
int sum1=0;
double sum2=0;
for(register int i=1;i<=m;i++) {
const int &u=edge[i].u,&v=edge[i].v;
if(djs.same(u,v)) continue;
djs.merge(u,v);
sum1+=edge[i].w;
sum2+=sqr(edge[i].w-d);
}
if(sum1==i) {
ans=std::min(ans,sum2/(n-1));
}
}
printf("%.4f\n",sqrt(ans));
}

posted @ 2018-09-30 14:12  skylee03  阅读(226)  评论(0编辑  收藏  举报