Nearest vectors CodeForces - 598C

最新推荐文章于 2021-10-26 23:20:25 发布

原创最新推荐文章于 2021-10-26 23:20:25 发布 · 305 阅读

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本文介绍了一种算法，用于解决平面上寻找两向量间最小非定向角度的问题。输入为一系列起始于原点的二维向量，通过计算各向量与正x轴之间的角度并进行排序，找到角度差最小的向量对。

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You are given the set of vectors on the plane, each of them starting at the origin. Your task is to find a pair of vectors with the minimal non-oriented angle between them.

Non-oriented angle is non-negative value, minimal between clockwise and counterclockwise direction angles. Non-oriented angle is always between 0 and π. For example, opposite directions vectors have angle equals to π.

Input

First line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of vectors.

The i-th of the following n lines contains two integers x_i and y_i (|x|, |y| ≤ 10 000, x² + y² > 0) — the coordinates of the i-th vector. Vectors are numbered from 1 to n in order of appearing in the input. It is guaranteed that no two vectors in the input share the same direction (but they still can have opposite directions).

Output

Print two integer numbers a and b (a ≠ b) — a pair of indices of vectors with the minimal non-oriented angle. You can print the numbers in any order. If there are many possible answers, print any.

Example

Input

Output

3 4

Input

Output

6 5

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector> 
#define bug(x) printf("%d****\n",x) 
typedef unsigned long long ll;
using namespace std;
const long double PI=acos(-1.0);//第一次见到long double 
vector<pair<long double,int> > vec;
int main(){
	int n;
	scanf("%d",&n);
	for(int i=0;i<n;i++){
		long double x,y;
		cin>>x>>y;
		pair<long double,int> tmp;
		tmp.first=atan2(y,x);
		tmp.second=i+1;
		vec.push_back(tmp);
	}	
	sort(vec.begin(),vec.end());
	long double ans=2*PI;
	int ans1=0,ans2=0;
	for(int i=0;i<n;i++){
		long double tmp=(vec[(i+1)%n].first-vec[i].first);
		if(tmp<0)   tmp+=2*PI;
		if(tmp<ans){
			ans=tmp;
			ans1=vec[(i+1)%n].second,ans2=vec[i].second;
		}
	}
	printf("%d %d\n",ans1,ans2);
	return 0;
}