3623. Count Number of Trapezoids I

You are given a 2D integer array points, where points[i] = [xi, yi] represents the coordinates of the ith point on the Cartesian plane.

A horizontal trapezoid is a convex quadrilateral with at least one pair of horizontal sides (i.e. parallel to the x-axis). Two lines are parallel if and only if they have the same slope.

Return the number of unique horizontal\ *trapezoids* that can be formed by choosing any four distinct points from points.

Since the answer may be very large, return it modulo 109 + 7.

class Solution {
public:
    int countTrapezoids(vector<vector<int>>& points) {
        unordered_map<int,long long> freq;
        for(auto& p : points) freq[p[1]]++;
        long long res = 0, mod = 1e9 + 7, sum = 0;
        for(auto& [_, cnt] : freq) {
            long long now = cnt * (cnt - 1) / 2;
            
            res = (res + sum * now % mod) % mod;
            sum = (sum + now) % mod;
        }
        return res;
    }
};