a.cpp

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <cassert>

using namespace std;

inline int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
}

struct Line {
    // a*x+b*y+c=0
    int a, b, c;

    Line(int x1, int y1, int x2, int y2) {
        // a*(x-x1)+b*(y-y1)=0
        // a*x+b*y-(a*x1+b*y1)=0
        int dx = x2-x1;
        int dy = y2-y1;
        a = -dy;
        b = dx;
        c = -(a*x1+b*y1);
        int d = gcd(abs(a), abs(b));
        assert(abs(a) % d == 0 && abs(b) % d == 0 && abs(c) % d == 0);
        a /= d; b /= d; c /= d;
        if (a < 0 || (a == 0 && b < 0)) {
            a *= -1; b *= -1; c *= -1;
        }
    }
};

inline bool operator<(const Line& left, const Line& right) {
    return left.a < right.a || (left.a == right.a && (left.b < right.b || (left.b == right.b && left.c < right.c)));
}

inline bool operator==(const Line& left, const Line& right) {
    return left.a == right.a && left.b == right.b && left.c == right.c;
}

int solve(int n) {
    vector<pair<int,int>> points;
    for (int i = 1; i <= n; ++i) for (int j = 1; j <= n; ++j) points.push_back({i,j});

    vector<Line> lines;
    for (int i = 0; i < n*n; ++i)
        for (int j = i+1; j < n*n; ++j) {
            auto& a = points[i];
            auto& b = points[j];
            lines.push_back(Line(a.first, a.second, b.first, b.second));
        }
    sort(lines.begin(), lines.end());
    lines.erase(unique(lines.begin(), lines.end()), lines.end());
    return lines.size();
}

int main() {
    for (int n = 2; n <= 100; ++n) {
        cout << "answ(" << n << ")=" << solve(n) << endl;
    }
    return 0;
}