HDU

原题链接

题意：

给定一个边长为$n$的正方形，求阴影部分面积

思路：

现将图形顺时针旋转 $45°$ 然后建立坐标系，写出阴影部分方程，用$Simpson$积分算一下就行了，注意精度，$1e^{-10}$ $WA$ 了 ，$1e^{-20}$ $A$了

#include<bits/stdc++.h>

using namespace std;

#define X first
#define Y second
#define eps  1e-20
#define gcd __gcd
#define pb push_back
#define PI acos(-1.0)
#define lowbit(x) (x)&(-x)
#define bug printf("!!!!!
");
#define mem(x,y) memset(x,y,sizeof(x))

typedef long long LL;
typedef long double LD;
typedef pair<int,int> pii;
typedef unsigned long long uLL;

const int maxn = 1e5+2;
const int INF  = 1<<30;
const int mod  = 1e9+7;

double f(double x){
    return  sqrt(1-x*x) - sqrt(4 - x*x) + sqrt(2);
}
double simpson(double L ,double R){
    return (R-L)*(f(L)+4.0*f((L+R)/2.0)+f(R))/6.0;
}
double asr(double L,double R){
    double mid = (L+R)/2.0;
    double res = simpson(L,R);
    double left = simpson(L,mid),right = simpson(mid,R);
    if(fabs(left+right-res)<eps)return left + right;
    else return asr(L,mid)+asr(mid,R);
}
double C;
void solve(){
    int n;
    scanf("%d",&n);
    printf("%.2f
",n*n*1.0*C);
    return;
}

int main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
//    ios::sync_with_stdio(false);
    int t = 1;
    scanf("%d",&t);
    C = asr(0,sqrt(7.0/8.0));       // 离线计算单位系数
    while(t--){
    //    printf("Case %d: ",cas++);
        solve();
    }
    return 0;
}