H. Degenerate Matrix
Time Limit: 20 Sec
Memory Limit: 256 MB
题目连接
http://codeforces.com/contest/549/problem/H
Description
A matrix is called degenerate if its determinant is equal to zero.
The norm ||A|| of a matrix A is defined as a maximum of absolute values of its elements.
You are given a matrix . Consider any degenerate matrix B such that norm ||A - B|| is minimum possible. Determine ||A - B||.
Input
The second line contains two integers c and d (|c|, |d| ≤ 109) the elements of the second row of matrix A.
Output
Output a single real number, the minimum possible value of ||A - B||. Your answer is considered to be correct if its absolute or relative error does not exceed 10 - 9.
Sample Input
1 2
3 4
Sample Output
0.2000000000
HINT
题意
给你一个矩阵，然后要求俩矩阵中元素相剪的最大值最小，求第二个矩阵
第二个矩阵满足ad-bc=0
题解：
2种方法可以解决这个问题
1.推公式
2.二分答案
代码：
//qscqesze
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define test freopen("test.txt","r",stdin)
#define maxn 2000001
#define mod 10007
#define eps 1e-9
int Num;
char CH[];
const int inf=0x3f3f3f3f;
const ll infll = 0x3f3f3f3f3f3f3f3fLL;
inline ll read()
{
ll x=,f=;char ch=getchar();
while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
return x*f;
}
inline void P(int x)
{
Num=;if(!x){putchar('');puts("");return;}
while(x>)CH[++Num]=x%,x/=;
while(Num)putchar(CH[Num--]+);
puts("");
}
//************************************************************************************** int main()
{
ll a,b,c,d;
//double a1,b1,c1,d1;
cin>>a>>b>>c>>d;
ll tmp=abs(a+b+c+d);
tmp=max(tmp,abs(d+c-a-b));
tmp=max(abs(d+b-a-c),tmp);
tmp=max(abs(b+c-d-a),tmp);
if(tmp==)
cout<<""<<endl;
else
{
printf("%.12lf",(.*abs(a*d-b*c)/(.*tmp)));
}
}