Intersection Points.cpp

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxN = 1e5+1;
const int maxX = 1e6+5;
const int SIZE = 2*maxX;

struct Operation {
    int type, y, a, b;
};

int N, ds[SIZE];
vector<Operation> ops;

void update(int idx, int val){
    for(int i = idx; i < SIZE; i += -i&i)
        ds[i] += val;
}

int query(int idx){
    int sum = 0;
    for(int i = idx; i > 0; i -= -i&i)
        sum += ds[i];
    return sum;
}

int main(){
    scanf("%d", &N);
    for(int i = 0, a, b, c, d; i < N; i++){
        scanf("%d %d %d %d", &a, &b, &c, &d);
        if(a == c){
            // Vertical
            ops.push_back({2, b, a+maxX, -1});
            ops.push_back({3, d, a+maxX, -1});
        } else {
            // Horizontal
            ops.push_back({1, b, a+maxX, c+maxX});
        }
    }
    sort(ops.begin(), ops.end(), [](Operation A, Operation B){
        return A.y < B.y;
    });

    ll ans = 0;
    for(Operation O : ops){
        if(O.type == 1)         ans += query(O.b) - query(O.a-1);
        else if(O.type == 2)    update(O.a, 1);
        else if(O.type == 3)    update(O.a, -1);
    }
    printf("%lld\n", ans);
}