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zc
2019-12-21 19:47:00
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二分第k大平均数w,统计平均数大于等于它的区间的个数

这样的区间满足\frac {s_r - s_{l-1}}{r-l+1} \ge w

化简一下: s_r - s_{l-1} \ge w(r-(l-1)) \\\\ s_r - wr \ge s_{l-1} - w(l-1) 那么我们只要用树状数组统计一下就可以了(当然你要用权值线段树也可以)

因为平均数可能不是整数,所以我们要离散化一下才能统计

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define rg register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i=x;i<=y;i++)
    #define Fdr(i,x,y) for(int i=x;i>=y;i--)
    #define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) (int(log2(n)))
    #define inf 0x3f3f3f3f
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const char* ln="\n";const int str=1<<20;struct IN{char buf[str],*s,*t;bool _;IN():s(buf),t(buf),_(0){}il char gc(){return s==t&&((t=(s=buf)+fread(buf,1,str,stdin))==s)?EOF:(*s++);}IN&operator>>(char&ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)_=1;else ch=c;return *this;}IN& operator>>(char* ch){clr(ch,0);if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)_=1;return *this;}IN& operator>>(string& ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)_=1;return *this;}template<typename T>IN&operator>>(T&x){if(_)return *this;char c=gc();bool ff=0;while(c!=EOF&&(c<'0'||c>'9'))ff^=(c=='-'),c=gc();if(c==EOF){_=1;return *this;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=(x<<3)+(x<<1)+c-48,c=gc();if(c==EOF)_=1;if(ff)x=-x;return *this;}}in;struct OUT{char buf[str],*s,*t;OUT():s(buf),t(buf+str){}~OUT(){fwrite(buf,1,s-buf,stdout);}void pt(char c){(s==t)?(fwrite(s=buf,1,str,stdout),*s++=c):(*s++=c);}OUT&operator<<(const char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(string s){for(int i=0;s[i];i++)pt(s[i]);return *this;}template<typename T>OUT&operator<<(T x){if(!x)return pt('0'),*this;if(x<0)pt('-'),x=-x;char a[30],t=0;while(x)a[t++]=x%10,x/=10;while(t--)pt(a[t]+'0');return *this;}}out;}using namespace IO;
#define N 100011
#define eps 1e-6
#define int unsigned
int n,k,a[N],tr[N*3],b[N];
struct node{
    db v;
    int id;
}s[N];
bool cmp(node x,node y){
    return x.v<y.v;
}
void add(int x){
    if(x<=0)return;
    while(x<=n){
        tr[x]++;
        x+=(x&-x);
    }
}
int get(int x){
    if(x<=0)return 0;
    int ans=0;
    while(x){
        ans+=tr[x];
        x-=(x&-x);
    }
    return ans;
}
bool chk(db w){
    clr(tr,0);
    s[0].v=0;s[0].id=0;
    Fur(i,1,n)s[i].v=(db)s[i-1].v+w*i,s[i].id=i;
    sort(s,s+n+1,cmp);
    int t=0;
    Fur(i,0,n){
        if(s[i].v!=s[i-1].v)t++;
        b[s[i].id]=t;
    }
    int tot=0;
    Fur(i,0,n){
        tot+=get(b[i]);
        add(b[i]);
    }
    return tot>=k;
}
signed main(){
    fin("in");
    in>>n>>k;
    db l=0,r=0,m;
    Fur(i,1,n)in>>a[i],r=MAX(r,(db)a[i]);
    while(r-l>eps){
        m=(l+r)/2.0;
        if(chk(m))l=m;
        else r=m;
    }
    printf("%.4f\n",m);
}
51nod 1711 平均数
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