Kishan_Basic_Geometry, C++ (gcc)

Kishan_Basic_Geometry

#include<bits/stdc++.h>
using namespace std;
#define ll long long int 
#define pb push_back
#define mod 1000000007
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp> 
using namespace __gnu_pbds; 
#define ordered_set tree<pair<ll,ll>, null_type,less<pair<ll,ll>>, rb_tree_tag,tree_order_statistics_node_update> 
#define Find find_by_order
#define Pos order_of_key
#define N 1000000
#define F(i,n) for(int i=1;i<=n;i++)
#define f(i,n) for(int i=0;i<n;i++)
#define pi 3.141592653589793238
struct ft {
    vector<ll> bit;
    ll n;
    ft(ll n1) {
        n = n1;
        bit.assign(n,0);
    }
    ll sum(ll r) {
        ll ret = 0;
        for(; r >= 0; r = (r&(r+1))-1)
            ret += bit[r];
        return ret;
    }
    void add(ll idx, ll d) {
        for(; idx < n; idx = idx | (idx+1))
            bit[idx] += d;
    }
    ll sum(ll l, ll r) {
        return sum(r) - sum(l-1);
    }
};
ll power(ll n,ll p)
{
    if(p==0) return 1;
    ll P=power(n,p/2);
    if(p%2==0) return ((((P%mod)*(P%mod))%mod)*(1%mod))%mod;
    if(p%2==1) return ((((P%mod)*(P%mod))%mod)*(n%mod))%mod;
}
ll prime(ll n)
{
    if(n==1) return 0;
    for(ll i=2;i<=sqrt(n);i++)
    {
        if(n%i==0) return 0;
    }
    return 1;
}
ll fact[N+1];
ll inv[N+1];
ll pre()
{
    fact[0]=1;
    inv[0]=1;
    for(int i=1;i<=N;i++)
    {
        fact[i]=(fact[i-1]*i)%mod;
        inv[i]=power(fact[i],mod-2)%mod;
    }
}
ll ncr(ll n,ll r)
{
    if(n<r) return 0;
    if(r==0 || r==n) return 1;
    return (((fact[n]*inv[r])%mod)*inv[n-r])%mod;
}
struct point2d {
    ftype x, y;
    point2d() {}
    point2d(ftype x, ftype y): x(x), y(y) {}
    point2d& operator+=(const point2d &t) {
        x += t.x;
        y += t.y;
        return *this;
    }
    point2d& operator-=(const point2d &t) {
        x -= t.x;
        y -= t.y;
        return *this;
    }
    point2d& operator*=(ftype t) {
        x *= t;
        y *= t;
        return *this;
    }
    point2d& operator/=(ftype t) {
        x /= t;
        y /= t;
        return *this;
    }
    point2d operator+(const point2d &t) const {
        return point2d(*this) += t;
    }
    point2d operator-(const point2d &t) const {
        return point2d(*this) -= t;
    }
    point2d operator*(ftype t) const {
        return point2d(*this) *= t;
    }
    point2d operator/(ftype t) const {
        return point2d(*this) /= t;
    }
};
point2d operator*(ftype a, point2d b) {
    return b * a;
}

struct point3d {
    ftype x, y, z;
    point3d() {}
    point3d(ftype x, ftype y, ftype z): x(x), y(y), z(z) {}
    point3d& operator+=(const point3d &t) {
        x += t.x;
        y += t.y;
        z += t.z;
        return *this;
    }
    point3d& operator-=(const point3d &t) {
        x -= t.x;
        y -= t.y;
        z -= t.z;
        return *this;
    }
    point3d& operator*=(ftype t) {
        x *= t;
        y *= t;
        z *= t;
        return *this;
    }
    point3d& operator/=(ftype t) {
        x /= t;
        y /= t;
        z /= t;
        return *this;
    }
    point3d operator+(const point3d &t) const {
        return point3d(*this) += t;
    }
    point3d operator-(const point3d &t) const {
        return point3d(*this) -= t;
    }
    point3d operator*(ftype t) const {
        return point3d(*this) *= t;
    }
    point3d operator/(ftype t) const {
        return point3d(*this) /= t;
    }
};
point3d operator*(ftype a, point3d b) {
    return b * a;
}

ftype dot(point2d a, point2d b) {
    return a.x * b.x + a.y * b.y;
}
ftype dot(point3d a, point3d b) {
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

ftype norm(point2d a) {
    return dot(a, a);
}
double abs(point2d a) {
    return sqrt(norm(a));
}
double proj(point2d a, point2d b) {
    return dot(a, b) / abs(b);
}
double angle(point2d a, point2d b) {
    return acos(dot(a, b) / abs(a) / abs(b));
}

point3d cross(point3d a, point3d b) {
    return point3d(a.y * b.z - a.z * b.y,
                   a.z * b.x - a.x * b.z,
                   a.x * b.y - a.y * b.x);
}
ftype triple(point3d a, point3d b, point3d c) {
    return dot(a, cross(b, c));
}
ftype cross(point2d a, point2d b) {
    return a.x * b.y - a.y * b.x;
}

point2d intersect(point2d a1, point2d d1, point2d a2, point2d d2) {
    return a1 + cross(a2 - a1, d2) / cross(d1, d2) * d1;
}

point3d intersect(point3d a1, point3d n1, point3d a2, point3d n2, point3d a3, point3d n3) {
    point3d x(n1.x, n2.x, n3.x);
    point3d y(n1.y, n2.y, n3.y);
    point3d z(n1.z, n2.z, n3.z); 
    point3d d(dot(a1, n1), dot(a2, n2), dot(a3, n3));
    return point3d(triple(d, y, z),
                   triple(x, d, z),
                   triple(x, y, d)) / triple(n1, n2, n3);
}


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