Line Segment Intersection

// ~/.vim/cpp_template.cpp
#include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <limits>

#define REP(i,a,b) for (int i = a; i < b; i++)

// Type Aliases for 1D and 2D vectors with initialization
#define vi(n, val) vector<int>(n, val) // 1D vector of ints with size n, initialized to val
#define vll(n, val) vector<long long>(n, val) // 1D vector of long longs with size n, initialized to val
#define ll long long
#define vvi(n, m, val) vector<vector<int>>(n, vector<int>(m, val)) // 2D vector of ints (n x m), initialized to val
#define vvll(n, m, val) vector<vector<long long>>(n, vector<long long>(m, val)) // 2D vector of long longs (n x m), initialized to val

#define LL_INF std::numeric_limits<long long int>::max()
#define INF std::numeric_limits<int>::max()


using namespace std;


template <typename T>
void pV(const std::vector<T>& vec, const std::string& label = "Vector") {
    std::cout << label << ": [ ";
    for (const auto& elem : vec) {
        std::cout << elem << " ";
    }
    std::cout << "]" << std::endl;
}


void dfs(int s, vector<bool> *visited, vector<int> (*adj)[]) {
    if ((*visited)[s]) return;
    (*visited)[s] = true;
    // process node s


    for (auto u: (*adj)[s]) {
        dfs(u, visited, adj);
    }
}
/*
// DEPTH-FRIRST-SEARCH
vector<int> adj[N];                                                          
vector<bool> visited(N, false);
int u, v;
for(int i = 0; i < M;i++){
    cin >> u >> v;
    u--;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
}
*/

vector<long long> dijkstra(int N, int x, vector<vector<pair<int,int>>> *adj){
    vector<bool> processed(N, false);
    vector<long long> distance(N, LL_INF);
    priority_queue<pair<long long,int>> q;
    //for (int i = 1; i <= n; i++) distance[i] = INF;
    distance[x] = 0;
    q.push({0,x});
    while (!q.empty()) {
        int a = q.top().second; q.pop();
        if (processed[a]) continue;
        processed[a] = true;
        for (auto u : (*adj)[a]) {
            int b = u.first, w = u.second;
            if (distance[a]+w < distance[b]) {
                distance[b] = distance[a]+w;
                q.push({-distance[b],b});
            }
        }
    }
    return distance;


}


/*
DIJKSTRA
//vector<vector<pair<int,int>>> adj(N, vector<pair<int, int>>(N));
*/

struct Point {
    long long x, y;
};

int oriet(Point p, Point q, Point r) {
    long long val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
    if (val == 0) return 0;
    return (val > 0) ? 1 : 2;
}

bool onS(Point p, Point q, Point r) {
    return q.x <= max(p.x, r.x) && q.x >= min(p.x, r.x) &&
           q.y <= max(p.y, r.y) && q.y >= min(p.y, r.y);
}

bool inter(Point p1, Point q1, Point p2, Point q2) {
    int o1 = oriet(p1, q1, p2);
    int o2 = oriet(p1, q1, q2);
    int o3 = oriet(p2, q2, p1);
    int o4 = oriet(p2, q2, q1);

    if (o1 != o2 && o3 != o4)
        return true;

    if (o1 == 0 && onS(p1, p2, q1)) return true;
    if (o2 == 0 && onS(p1, q2, q1)) return true;
    if (o3 == 0 && onS(p2, p1, q2)) return true;
    if (o4 == 0 && onS(p2, q1, q2)) return true;

    return false;
}


int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    // Your code starts here
    int t;
    cin >> t;
    REP(i, 0, t){
        Point p1, q1, p2, q2;
        cin >> p1.x >> p1.y >> q1.x >> q1.y >> p2.x >> p2.y >> q2.x >> q2.y;
        if(inter(p1, q1, p2, q2)){
            cout << "YES" << endl;
        }else{
            cout << "NO" << endl;
        }

    }
    


    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED