Intersectie Segmente + Punct pe Segment

#include <bits/stdc++.h>
#define pi pair<int,int>
#define x first
#define y second

using namespace std;

ifstream fin("intersectiesegmente.in");
ofstream fout("intersectiesegmente.out");

int det(const pi &A, const pi &B, const pi &C) {
    return (B.x - A.x) * (C.y - A.y) - (C.x - A.x) * (B.y - A.y);
}

bool check(const pi &A, const pi &B, const pi &C) {
    vector<pi> a{A, B, C};
    int X = a[2].x, Y = a[2].y;
    sort(a.begin(), a.end());
    if(!(X == a[1].x && Y == a[1].y))
        return false;
    if(det(a[0], a[1], a[2]) == 0)
        return true;
    return false;
}

int main() {
    vector<pi> p(4);
    for(pi &x : p)
        fin >> x.x >> x.y;
    if(check(p[0], p[1], p[2])) {
        fout << "DA";
        return 0;
    }
    if(check(p[0], p[1], p[3])) {
        fout << "DA";
        return 0;
    }
    if(check(p[2], p[3], p[0])) {
        fout << "DA";
        return 0;
    }
    if(check(p[2], p[3], p[1])) {
        fout << "DA";
        return 0;
    }
    int d1 = det(p[0], p[1], p[2]),
        d2 = det(p[0], p[1], p[3]),
        d3 = det(p[2], p[3], p[0]),
        d4 = det(p[2], p[3], p[1]);
    if(d1 * d2 < 0 && d3 * d4 < 0)
        fout << "DA";
    else
        fout << "NU";
}