[training Day6] triangle [mathematics] [violence]

Ideas ：

We consider the properties of right triangle
Turn at a right angle 90° The slope of is equal to the slope of the other right angle side
Then we can enumerate right angle vertices , Turn each side 90° Slope of map Save up , Just make the final statistics

$code$

#include<iostream>
#include<cstdio>
#include<map>

using namespace std;

const int MAXN = 1510;

int n, sum;

map<pair<int, double>, int> q;

struct node {
    
	int x, y;
}a[MAXN];

int main() {
    
	scanf("%d", &n);
	for(int i = 1; i <= n; i ++) scanf("%d%d", &a[i].x, &a[i].y);
	for(int i = 1; i <= n; i ++) {
    
		int x = 0, y = 0;
		for(int j = 1; j <= n; j ++) 
			if(i != j) a[j].x -= a[i].x, a[j].y -= a[i].y;
		for(int j = 1; j <= n; j ++) {
    
			if(i != j) {
    
				int x1 = -a[j].y, y1 = a[j].x, g;
				double k = (y1 - y) * 1.0 / (x1 * 1.0 - x * 1.0);
				if(k < -1000000000 || k > 1000000000)
					k = 10000000000.0;
				if(x1 > 0 && y1 >= 0) g = 1;
				if(x1 <= 0 && y1 > 0) g = 2;
				if(x1 < 0 && y1 <= 0) g = 3;
				if(x1 >= 0 && y1 < 0) g = 4;
				q[make_pair(g, k)] ++;
// cout<<g<<' '<<k<<endl;
			}
		}
// cout<<"-----------"<<endl;
		for(int j = 1; j <= n; j ++) {
    
			if(i != j) {
    
				int x1 = a[j].x, y1 = a[j].y, g;
				double k = (y - y1) * 1.0 / (x * 1.0 - x1 * 1.0);
				if(k < -1000000000 || k > 1000000000)
					k = 10000000000.0;
				if(x1 > 0 && y1 >= 0) g = 1;
				if(x1 <= 0 && y1 > 0) g = 2;
				if(x1 < 0 && y1 <= 0) g = 3;
				if(x1 >= 0 && y1 < 0) g = 4;
				sum += q[make_pair(g, k)];
// cout<<g<<' '<<k<<endl;
			}
		}
// cout<<endl<<sum<<endl;
		q.clear();
// cout<<endl<<"----------"<<endl<<"__________"<<endl;
		for(int j = 1; j <= n; j ++) 
			if(i != j) a[j].x += a[i].x, a[j].y += a[i].y;
	}
	printf("%d", sum);
	return 0;
}