Submission #5178

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
5178	2014-02-13T23:36:58 Z	cki86201	초록색 삼각형 (YDX13_green)	C++	1 / 1	420 ms	1448 KB

C

#include<stdio.h>
#include<algorithm>
#include<math.h>

typedef long long ll;

const double PI = 3.141592653589793238;

int x[2020], y[2020], ord[2020];
double an[2020];
int n;

bool comp(const int &a,const int &b){return an[a] < an[b];}

inline ll ccw(int a,int b,int c)
{
	return (ll)(x[b]-x[a]) * (y[c]-y[a]) - (ll)(x[c]-x[a]) * (y[b]-y[a]);
}

double brute(int u)
{
	int i, j, k;
	double ans = 0;
	for(i=3;i<=u;i++){
		for(j=2;j<i;j++){
			for(k=1;k<j;k++){
				ll tmp = (ll)(x[j]-x[i])*(y[k]-y[i])-(ll)(x[k]-x[i])*(y[j]-y[i]);
				if(tmp < 0)tmp = -tmp;
				ans += tmp;
			}
		}
	}
	return ans;
}

double solve(int u)
{
	if(u <= 5)return brute(u);
	double ret = 0;
	int i;
	for(i=1;i<=u;i++)ord[i] = i;
	for(i=1;i<=u;i++)an[i] = atan2(y[i] - y[u], x[i] - x[u]);
	std::sort(ord+1,ord+1+u,comp);
	int t = (ord[1] == u)?2:1;
	ll now[2] = {0,0};
	for(i=1;i<=u;i++){
		int ni = ord[i];
		if(ni == u)continue;
		now[0] -= x[ni] - x[u], now[1] -= y[ni] - y[u];
		while(ord[t] == u || t == i)now[0] += x[ord[t]] - x[u], now[1] += y[ord[t]] - y[u], t = t%u + 1;
		while(t!=i && ccw(u,ni,ord[t]) > 0){
			now[0] += x[ord[t]] - x[u];
			now[1] += y[ord[t]] - y[u];
			t = t%u + 1;
			if(ord[t] == u)t = t%u + 1;
		}
		ret += (double)now[1] * (x[ni] - x[u]) - (double)now[0] * (y[ni] - y[u]);
	}
	return ret + solve(u-1);
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d%d",x+i,y+i);
	if(n<=2)return printf("0")&0;
	printf("%.12f\n",solve(n)*3/n/(n-1)/(n-2));
	return 0;
}

Subtask #1

1.0 / 1.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	1352 KB	Output is correct
2	Correct	0 ms	1352 KB	Output is correct
3	Correct	0 ms	1352 KB	Output is correct
4	Correct	0 ms	1352 KB	Output is correct
5	Correct	0 ms	1352 KB	Output is correct
6	Correct	0 ms	1352 KB	Output is correct
7	Correct	0 ms	1352 KB	Output is correct
8	Correct	0 ms	1352 KB	Output is correct
9	Correct	0 ms	1352 KB	Output is correct
10	Correct	0 ms	1352 KB	Output is correct
11	Correct	76 ms	1352 KB	Output is correct
12	Correct	144 ms	1356 KB	Output is correct
13	Correct	92 ms	1352 KB	Output is correct
14	Correct	376 ms	1436 KB	Output is correct
15	Correct	36 ms	1352 KB	Output is correct
16	Correct	364 ms	1428 KB	Output is correct
17	Correct	20 ms	1352 KB	Output is correct
18	Correct	56 ms	1352 KB	Output is correct
19	Correct	96 ms	1352 KB	Output is correct
20	Correct	0 ms	1352 KB	Output is correct
21	Correct	416 ms	1448 KB	Output is correct
22	Correct	416 ms	1440 KB	Output is correct
23	Correct	416 ms	1448 KB	Output is correct
24	Correct	416 ms	1444 KB	Output is correct
25	Correct	416 ms	1448 KB	Output is correct
26	Correct	416 ms	1448 KB	Output is correct
27	Correct	420 ms	1448 KB	Output is correct
28	Correct	416 ms	1444 KB	Output is correct
29	Correct	416 ms	1448 KB	Output is correct
30	Correct	416 ms	1448 KB	Output is correct
31	Correct	0 ms	1352 KB	Output is correct