传送门

三点确定一个圆的计算方法

设一个圆的圆心坐标为(x0,y)，半径为r。那么这个圆的方程可以写成

(x-x0)^2+(y-y0)^2=r^2

在这个圆上随便取三个点，设这三个点的坐标分别为(x1,y1),(x2,y2),(x3,y3)。那么有

公式(1)(2)相减，(1)(3)相减经过化简可以得到：

x0,y0有唯一解的条件是系数行列式不为0：

简单变形就是：

这样也就是三点不能共线

设：

那么结果

这样答案就出来了

 

题解 ：先判断出圆心的位置，然后进而算出半径的大小，最后跟据最后一个点与这个圆心的距离进行判断大小，还使用了个大大大的大整数类，不会JAVA，赶快学

#include<bits/stdc++.h>#define MAX_L 2005 //最大长度，可以修改using namespace std;#define max_n 100000000//因为结果可能不是整数，把小数部分去掉class bign
{
public:int len, s[MAX_L];//数的长度，记录数组
//构造函数bign();bign(const char*);bign(int);bool sign;//符号 1正数 0负数string toStr() const;//转化为字符串，主要是便于输出friend istream& operator>>(istream &,bign &);//重载输入流friend ostream& operator<<(ostream &,bign &);//重载输出流
//重载复制bign operator=(const char*);bign operator=(int);bign operator=(const string);
//重载各种比较bool operator>(const bign &) const;bool operator>=(const bign &) const;bool operator<(const bign &) const;bool operator<=(const bign &) const;bool operator==(const bign &) const;bool operator!=(const bign &) const;
//重载四则运算bign operator+(const bign &) const;bign operator++();bign operator++(int);bign operator+=(const bign&);bign operator-(const bign &) const;bign operator--();bign operator--(int);bign operator-=(const bign&);bign operator*(const bign &)const;bign operator*(const int num)const;bign operator*=(const bign&);bign operator/(const bign&)const;bign operator/=(const bign&);
//四则运算的衍生运算bign operator%(const bign&)const;//取模（余数）bign factorial()const;//阶乘bign Sqrt()const;//整数开根（向下取整）bign pow(const bign&)const;//次方
//一些乱乱的函数void clean();~bign();
};#define max(a,b) a>b ? a : b
#define min(a,b) a<b ? a : bbign::bign()
{memset(s, 0, sizeof(s));len = 1;sign = 1;
}bign::bign(const char *num)
{*this = num;
}bign::bign(int num)
{*this = num;
}string bign::toStr() const
{string res;res = "";for (int i = 0; i < len; i++)res = (char)(s[i] + '0') + res;if (res == "")res = "0";if (!sign&&res != "0")res = "-" + res;return res;
}istream &operator>>(istream &in, bign &num)
{string str;in>>str;num=str;return in;
}ostream &operator<<(ostream &out, bign &num)
{out<<num.toStr();return out;
}bign bign::operator=(const char *num)
{memset(s, 0, sizeof(s));char a[MAX_L] = "";if (num[0] != '-')strcpy(a, num);elsefor (int i = 1; i < strlen(num); i++)a[i - 1] = num[i];sign = !(num[0] == '-');len = strlen(a);for (int i = 0; i < strlen(a); i++)s[i] = a[len - i - 1] - 48;return *this;
}bign bign::operator=(int num)
{char temp[MAX_L];sprintf(temp, "%d", num);*this = temp;return *this;
}bign bign::operator=(const string num)
{const char *tmp;tmp = num.c_str();*this = tmp;return *this;
}bool bign::operator<(const bign &num) const
{if (sign^num.sign)return num.sign;if (len != num.len)return len < num.len;for (int i = len - 1; i >= 0; i--)if (s[i] != num.s[i])return sign ? (s[i] < num.s[i]) : (!(s[i] < num.s[i]));return !sign;
}bool bign::operator>(const bign&num)const
{return num < *this;
}bool bign::operator<=(const bign&num)const
{return !(*this>num);
}bool bign::operator>=(const bign&num)const
{return !(*this<num);
}bool bign::operator!=(const bign&num)const
{return *this > num || *this < num;
}bool bign::operator==(const bign&num)const
{return !(num != *this);
}bign bign::operator+(const bign &num) const
{if (sign^num.sign){bign tmp = sign ? num : *this;tmp.sign = 1;return sign ? *this - tmp : num - tmp;}bign result;result.len = 0;int temp = 0;for (int i = 0; temp || i < (max(len, num.len)); i++){int t = s[i] + num.s[i] + temp;result.s[result.len++] = t % 10;temp = t / 10;}result.sign = sign;return result;
}bign bign::operator++()
{*this = *this + 1;return *this;
}bign bign::operator++(int)
{bign old = *this;++(*this);return old;
}bign bign::operator+=(const bign &num)
{*this = *this + num;return *this;
}bign bign::operator-(const bign &num) const
{bign b=num,a=*this;if (!num.sign && !sign){b.sign=1;a.sign=1;return b-a;}if (!b.sign){b.sign=1;return a+b;}if (!a.sign){a.sign=1;b=bign(0)-(a+b);return b;}if (a<b){bign c=(b-a);c.sign=false;return c;}bign result;result.len = 0;for (int i = 0, g = 0; i < a.len; i++){int x = a.s[i] - g;if (i < b.len) x -= b.s[i];if (x >= 0) g = 0;else{g = 1;x += 10;}result.s[result.len++] = x;}result.clean();return result;
}bign bign::operator * (const bign &num)const
{bign result;result.len = len + num.len;for (int i = 0; i < len; i++)for (int j = 0; j < num.len; j++)result.s[i + j] += s[i] * num.s[j];for (int i = 0; i < result.len; i++){result.s[i + 1] += result.s[i] / 10;result.s[i] %= 10;}result.clean();result.sign = !(sign^num.sign);return result;
}bign bign::operator*(const int num)const
{bign x = num;bign z = *this;return x*z;
}
bign bign::operator*=(const bign&num)
{*this = *this * num;return *this;
}bign bign::operator /(const bign&num)const
{bign ans;ans.len = len - num.len + 1;if (ans.len < 0){ans.len = 1;return ans;}bign divisor = *this, divid = num;divisor.sign = divid.sign = 1;int k = ans.len - 1;int j = len - 1;while (k >= 0){while (divisor.s[j] == 0) j--;if (k > j) k = j;char z[MAX_L];memset(z, 0, sizeof(z));for (int i = j; i >= k; i--)z[j - i] = divisor.s[i] + '0';bign dividend = z;if (dividend < divid) { k--; continue; }int key = 0;while (divid*key <= dividend) key++;key--;ans.s[k] = key;bign temp = divid*key;for (int i = 0; i < k; i++)temp = temp * 10;divisor = divisor - temp;k--;}ans.clean();ans.sign = !(sign^num.sign);return ans;
}bign bign::operator/=(const bign&num)
{*this = *this / num;return *this;
}bign bign::operator%(const bign& num)const
{bign a = *this, b = num;a.sign = b.sign = 1;bign result, temp = a / b*b;result = a - temp;result.sign = sign;return result;
}bign bign::pow(const bign& num)const
{bign result = 1;for (bign i = 0; i < num; i++)result = result*(*this);return result;
}bign bign::factorial()const
{bign result = 1;for (bign i = 1; i <= *this; i++)result *= i;return result;
}void bign::clean()
{if (len == 0) len++;while (len > 1 && s[len - 1] == '\0')len--;
}bign bign::Sqrt()const
{if(*this<0)return -1;if(*this<=1)return *this;bign l=0,r=*this,mid;while(r-l>1){mid=(l+r)/2;if(mid*mid>*this)r=mid;elsel=mid;}return l;
}bign::~bign()
{
}
int main() {bign x,y,x1,x2,x3,y1,y2,y3,x4,y4;bign a,b,c,d,e,f;bign ling=0;int t;bign dis;bign tes;cin>>t;while(t--){cin>>x1>>y1>>x2>>y2>>x3>>y3>>x4>>y4;x1=x1*max_n;y1=y1*max_n;x2=x2*max_n;y2=y2*max_n;y3=y3*max_n;x3=x3*max_n;x4=x4*max_n;y4=y4*max_n;a=x1-x2;b=y1-y2;c=x1-x3;d=y1-y3;e=(x1*x1-x2*x2-y2*y2+y1*y1)/2;f=(x1*x1-x3*x3-y3*y3+y1*y1)/2;x= (d*e-b*f)/(b*c-a*d);y= (a*f-c*e)/(b*c-a*d);dis=(x+x1)*(x+x1)+(y+y1)*(y+y1);tes=(x+x4)*(x+x4)+(y+y4)*(y+y4);if(dis<tes)printf("Accepted\n");elseprintf("Rejected\n");}return 0;
}