算法

(浮点数二分) $O(\log n)$

直接二分即可，实际上最后会搞出公式$\frac{1}{a}+\frac{1}{b}=\frac{1}{c}$，即$c=\frac{ab}{a+b}\text{。（积在和上飞）。}$

如果小了就$l=mid$，大了就$r=mid$。

C++ 代码

#include<bits/stdc++.h>
#define ns "-1"
#define fs(i,x,y,z) for(ll i=x;i<=y;i+=z)
#define ft(i,x,y,z) for(ll i=x;i>=y;i+=z)
#define ll long long
#define ull unsigned long long
#define db double
#define ms(a,b) memset(a,b,sizeof(a))
#define sz(a) sizeof(a)
using namespace std;
const int rw[]={-1,0,1,0,-1,1,-1,1},cl[]={0,1,0,-1,-1,1,1,-1};
const int N=100001,inf=0x7f7f7f7f;
const int daynum[]={114514,31,28,31,30,31,30,31,31,30,31,30,31};
const db E=2.718281828459,pi=acos(-1.0),eps=0.0000000001;
inline bool xr(bool x,bool y){
    return x==y?0:1;
}
inline int read(){
    int date=0,w=1;char c=0;
    while(c<'0'||c>'9'){if(c=='-')w=-1;c=getchar();}
    while(c>='0'&&c<='9'){date=date*10+c-'0';c=getchar();}
    return date*w;
}
ull ksm(ull a,ull b){
    ull ans=1,base=a;
    while(b){
        if(b&1){
            ans*=base;
        }
        base*=base;
        b>>=1;
    }
    return ans;
}
ll gcd(ll a,ll b){
    if(b) return gcd(b,a%b);
    return a;
}
bool prm(int k){
    if(k<2) return 0;
    if(k==2||k==3) return 1;
    if(k%6!=1&&k%6!=5) return 0;
    for(int i=5;i<=sqrt(k);i+=6)
        if(k%i==0||k%(i+2)==0) return 0;
    return 1;
}
db x,y,c;
db chk(db s){
    db p=sqrt(x*x-s*s),q=sqrt(y*y-s*s);
    return p*q/(q+p);
}
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cin>>x>>y>>c;
    db l=0,r=min(x,y);
    while(r-l>1e-5){
        db mid=(l+r)/2;
        if(chk(mid)>c) l=mid;
        else r=mid;
    }
    cout<<fixed<<setprecision(3)<<l;
    return 0;
}