直线（蓝桥杯2021C）

#include<iostream>
#include<stdio.h>
#define X_r 20
#define Y_r 21
using namespace std;
typedef struct Dot {
	int x,y;
}Dot;
typedef struct Node {
	int a,b,c;
	struct Node* next;
}Node,*Linklist;
//aX + by + c = 0;
int main() {
	int index = 0;
	Dot* dot = new Dot[X_r * Y_r];
	for (int x = 0; x < X_r;x++) {
		for (int y = 0; y < Y_r;y++) {
			dot[index].x = x;
			dot[index].y = y;
			index++;
		}
	}
	int cnt = 0;
	Linklist head = new Node;
	head->next = NULL;
	for (int i = 0; i < index-1;i++) {
		for (int j = i + 1; j < index;j++) {
			Linklist node = new Node;
			node->a = dot[i].y - dot[j].y;
			node->b = dot[j].x - dot[i].x;
			node->c = 0 - (((node->a) * dot[i].x) + ((node->b) * dot[i].y));
			if (cnt == 0) {
				node->next = head->next;
				head->next = node;
				cnt++;
			}
			else {
				Linklist p = head->next;
				int flag = 0;
				while (p != NULL) {
					if ((p->a)*(node->b) == (p->b) * (node->a) &&
						(p->a) * (node->c) == (p->c) * (node->a)&&
						(p->b) * (node->c) == (p->c) * (node->b)) {
						flag = 1;
						break;
					}
					p = p->next;
				}
				if (flag == 0) {
					node->next = head->next;
					head->next = node;
					cnt++;
				}
				else {
					delete node;
				}
			}
		}
	}
	Linklist q = head,tmp;
	while (q != NULL) {
		tmp = q->next;
		delete q;
		q = tmp;
	}
	cout << cnt;
	return 0;
}

//两点式：（x-x1）/(x2-x1) = (y-y1)/(y2-y1)
//变为一般式：（y1-y2）x+(x2-x1)y+(x1y2-x2y1) = 0
#include<iostream>
#include<set>
#include<vector>
#include<cmath>
using namespace std;
const int INF = 0x3f3f3f3f;
typedef pair<int, int> PII;
typedef pair<PII, int> PIII;
set<PIII> s;//字典
vector<PII>vec;//栈
int gcd(int a,int b) {
	a = abs(a);
	b = abs(b);
	int tmp;
	if (b > a) {
		tmp = a;
		a = b;
		b = tmp;
	}
	if (b == 0) {
		return a;
	}
	return gcd(b,a%b);
}
int main() {
	int x, y;
	cin >> x >> y;
	for (int i = 0; i < x;i++) {
		for (int j = 0; j < y;j++) {
			vec.push_back({i,j});
		}
	}
	for (int i = 0; i < vec.size()-1;i++) {
		for (int j = i + 1; j < vec.size();j++) {
			int x1 = vec[i].first, y1 = vec[i].second;
			int x2 = vec[j].first, y2 = vec[j].second;
			int A = x2 - x1, B = y1 - y2, C = x1*y2 - x2*y1;
			int gcdd = gcd(gcd(A, B), C);
			s.insert({ {B / gcdd,A / gcdd},C / gcdd });
		}
	}
	cout << s.size();
	return 0;
}