Intersecting Lines（两线是否相交） · znzryb
## 思路讲解
详细解释了一下这个式子是怎么来的。
```cpp
// p+tv=q+sw
// (p-q) x w+tv x w = 0
// t=-(p-q)x w/(vxw)
// 传入的是方向式
Point getintersect(Point p,Point v,Point q,Point w){
Point u=p-q;
ld t=cross(w,u)/cross(v,w);
return p+v*t;
}
inline void __(){
Point a,b,c,d;
cin>>a>>b>>c>>d;
Point ab=b-a,cd=d-c;
if(!sgn(cross(ab,cd))){
Point bc=c-b,ad=d-a;
if(!sgn(cross(bc, ad))){
cout<<"LINE\n";
return;
}
cout<<"NONE\n";
return;
}
Point res=getintersect(a, ab, c, cd);
cout<<"POINT "<<fsp(2)<<res.real()<<" "<<res.imag()<<"\n";
}
```
## AC代码
[https://vjudge.net/solution/63256517](https://vjudge.net/solution/63256517)
::: 源代码
```cpp
// by Gospel_rock
#include <bits/stdc++.h>
#include <cstdio>
#define all(vec) vec.begin(),vec.end()
#define PB push_back
#define EB emplace_back
#define EM emplace
#define FI first
#define SE second
#define pct __builtin_popcountll
#define ctz __builtin_ctzll
#define SZ(a) ((long long) a.size())
#define FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define ROF(i, a, b) for (int i = (a); i >= (b); --i)
#define debug(var) cerr << #var <<":"<<var<<"\n";
#define cend cerr<<"\n-----------\n"
#define fsp(x) fixed<<setprecision(x)
#define minn(vec) *min_element(vec.begin(),vec.end())
#define maxx(vec) *max_element(vec.begin(),vec.end())
using namespace std;
#ifdef LOCAL
template<typename T> void _print(T x) { cerr << x; }
// 可以打印多层数组，但是格式不是很好
template<typename T> void _print(vector<T> v) { cerr << "[ "; for (T i : v) _print(i), cerr << " "; cerr << "]"; }
template<typename T> void _print(set<T> s) { cerr << "{ "; for (T i : s) _print(i), cerr << " "; cerr << "}"; }
template<typename T, typename U> void _print(pair<T, U> p) { cerr << "{"; _print(p.first); cerr << ", "; _print(p.second); cerr << "}"; }
template<typename T, typename U> void _print(map<T, U> m) { cerr << "{ "; for (auto &p : m) _print(p), cerr << " "; cerr << "}"; }
// 打印两层数组，格式好一些
template<typename T> void _print(vector<vector<T>> v){cerr<<"{\n";for (auto i : v) _print(i), cerr << "\n";cerr<<" }";}
#endif
using ll = long long;using ull = unsigned long long;
using ld=double;using LD=long double;
using i128 = __int128;
using pdd = pair<ld,ld>;using plb = pair<ll,bool>;
using pll = pair<ll,ll>;using vll=vector<ll>;using vb=vector<bool>;
using tll = tuple<ll,ll,ll>;using vii=vector<int>;
using vpll = vector<pll>;using vtll = vector<tll>;
using vdb = vector<ld>;using vc=vector<char>;
using arr3 = array<ll,3> ;using arr2 = array<ll,2>;
using CD=complex<double>;
static constexpr ll MAXN=(ll)1e6+10,INF=(ll)1e17+3; // 1e17+3是素数 1e18+9是素数
static constexpr ll mod=(ll)1e9+7; // 998244353;
static constexpr double eps=1e-8;const double pi=acos(-1.0);
ll N,M,Q,X,K,T,lT;
inline void __();
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
cin>>lT;
cout<<"INTERSECTING LINES OUTPUT\n";
while(lT--)
__();
cout<<"END OF OUTPUT\n";
return 0;
}
/*
*/
using Real = ld;
using Point = complex<Real>;
Real cross(const Point &a, const Point &b) {
return (conj(a) * b).imag();
}
Real dot(const Point &a, const Point &b) {
return (conj(a) * b).real();
}
int sgn(Real x) {
if (-eps < x && x < eps) return 0;
return x < 0 ? -1 : 1;
}
istream& operator>>(istream& in, Point& c) {
double r, i;
in >> r >> i;
c = Point(r, i);
return in;
}
// p+tv=q+sw
// (p-q) x w+tv x w = 0
// t=-(p-q)x w/(vxw)
// 传入的是方向式
Point getintersect(Point p,Point v,Point q,Point w){
Point u=p-q;
ld t=cross(w,u)/cross(v,w);
return p+v*t;
}
inline void __(){
Point a,b,c,d;
cin>>a>>b>>c>>d;
Point ab=b-a,cd=d-c;
if(!sgn(cross(ab,cd))){
Point bc=c-b,ad=d-a;
if(!sgn(cross(bc, ad))){
cout<<"LINE\n";
return;
}
cout<<"NONE\n";
return;
}
Point res=getintersect(a, ab, c, cd);
cout<<"POINT "<<fsp(2)<<res.real()<<" "<<res.imag()<<"\n";
}
/*
*/
```
:::
## 心路历程（WA，TLE，MLE……）