2017 ACM/ICPC Asia Regional Qingdao Online 青岛区域赛

1001Apple

Problem Description
Apple is Taotao's favourite fruit. In his backyard, there are three apple trees with coordinates (x1,y1), (x2,y2), and (x3,y3). Now Taotao is planning to plant a new one, but he is not willing to take these trees too close. He believes that the new apple tree should be outside the circle which the three apple trees that already exist is on. Taotao picked a potential position (x,y) of the new tree. Could you tell him if it is outside the circle or not?
 

Input
The first line contains an integer T, indicating that there are T(T≤30) cases.
In the first line of each case, there are eight integers x1,y1,x2,y2,x3,y3,x,y, as described above.
The absolute values of integers in input are less than or equal to 1,000,000,000,000.
It is guaranteed that, any three of the four positions do not lie on a straight line.
 

Output
For each case, output "Accepted" if the position is outside the circle, or "Rejected" if the position is on or inside the circle.
 

Sample Input
3
-2 0 0 -2 2 0 2 -2
-2 0 0 -2 2 0 0 2
-2 0 0 -2 2 0 1 1
 

Sample Output
Accepted
Rejected
Rejected
 

大意是给你三个点，绘制一个圆形区域，再输入一个点，问在不在圆内

难点：高精度

#include <cmath>
#include <map>
#include <vector>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <set>
#include <bitset>
#include <memory.h>
#include <functional>
#include <queue>
#include <fstream>
#include <ctime>
#include <deque>
#include <utility>
#include <stack>
#include <sstream>
#include <list>
#include <cctype> 
#include <numeric>
#include <iomanip>
#include <assert.h>
#define EPS 1e-8
using namespace std;
const int maxn = 550;
typedef long long LL;

#define MAX_L 2005 

class bign
{
public:
    int len, s[MAX_L];
    bign();
    bign(const char*);
    bign(int);
    bool sign;
    string toStr() const;
    friend istream& operator>>(istream &,bign &);
    friend ostream& operator<<(ostream &,bign &);
    bign operator=(const char*);
    bign operator=(int);
    bign operator=(const string);
    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;
    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&);
    bign operator%(const bign&)const;
    bign factorial()const;
    bign Sqrt()const;
    bign pow(const bign&)const;
    void clean();
    ~bign();
};
#define max(a,b) a>b ? a : b
#define min(a,b) a<b ? a : b

bign::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);
    else
        for (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] == '')
        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;
        else
            l=mid;
    }
    return l;
}
bign::~bign()
{
}
struct point{
    bign x, y;
};
bign get_distance( point &a,  point &b)
{ 
    return ((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y)); 
}
/*
point get_circle_center(const point a, const point b, const point c)
{
    point center;
    bign a1 = b.x - a.x;
    bign b1 = b.y - a.y;
    bign c1 = (a1 * a1 + b1 * b1) / 2.0;
    bign a2 = c.x - a.x;
    bign b2 = c.y - a.y;
    bign c2 = (a2 * a2 + b2 * b2) / 2.0;
    bign d = a1 * b2 - a2 * b1;
    center.x = a.x + (c1 * b2 - c2 * b1) / d;
    center.y = a.y + (a1 * c2 - a2 * c1) / d;
    return center;
}
*/
bign D;
point get_circle_center( point a,  point b,  point c)
{
    point center;
    bign a1 = b.x - a.x;
    bign b1 = b.y - a.y;
    bign c1 = (a1 * a1 + b1 * b1);
    bign a2 = c.x - a.x;
    bign b2 = c.y - a.y;
    bign c2 = (a2 * a2 + b2 * b2);
    bign d = a1 * b2 - a2 * b1;
    D = d * 2;
    center.x = a.x * 2 * d + (c1 * b2 - c2 * b1);
    center.y = a.y * 2 * d + (a1 * c2 - a2 * c1);
    return center;
}
void solve()
{
    point a, b, c, d;
    //scanf("%lf%lf%lf%lf%lf%lf%lf%lf", &a.x, &a.y, &b.x, &b.y, &c.x, &c.y, &d.x, &d.y);
    cin >> a.x >> a.y >> b.x >> b.y >> c.x >> c.y >> d.x >> d.y;
    /*
    int ax, ay, bx, by, cx, cy, dx, dy;
    cin >> ax >> ay >> bx >> by >> cx >> cy >> dx >> dy;
    a.x = ax + 1000000000;
    a.y = ay + 1000000000;
    b.x = bx + 1000000000;
    b.y = by + 1000000000;
    c.x = cx + 1000000000;
    c.y = cy + 1000000000;
    d.x = dx + 1000000000;
    d.y = dy + 1000000000;
    */
    point o = get_circle_center(a, b, c);
    a.x = a.x * D, a.y = a.y * D, d.x = d.x * D, d.y = d.y * D;
    //cout << get_distance(o, a).toStr() << " " << get_distance(o, d).toStr() << endl;
    if (get_distance(o, a) < get_distance(o, d))
        puts("Accepted");
    else
        puts("Rejected");
}
int main()
{
    int test;
    scanf("%d", &test);
    for (int i = 0; i < test; ++i)
        solve();
    return 0;
}