#include <iostream>
#include <cstdlib>
#include <ctime>
#include <vector>
#include <cmath>

using namespace std;

class Cluster//聚類，每個聚類都包含兩個屬性，一個是簇心的屬性（維數），另一個是距離本簇心最近的樣本點
{
public:
    vector <double> centroid;//存放簇心的屬性（維數）
    vector <int> samples;//存放屬於相同簇心樣本的下標
};

double CalculateDistance(vector<double> a, vector<double> b)//計算兩個向量之間的距離
{
    int len1 = a.size();
    int len2 = b.size();
    if(len1 != len2)
        cerr<<"Dimensions of two vectors must be same!!\n";
    double temp = 0;
    for(int i = 0; i  < len1; ++i)
        temp += pow(a[i]-b[i], 2);
    return sqrt(temp);
}

//max_iteration表示最大的迭代次數，min_move_distance
vector<Cluster> KMeans(vector<vector<double> >data_set, int k, int max_iteration, double threshold)
{
    int row_number = data_set.size();//資料的個數
    int col_number = data_set[0].size();//每個向量(屬性)的維數

    //初始隨機選取k個質心
    vector<Cluster> cluster(k);//存放k個簇心。vector<T> v(n,i)形式，v包含n 個值為 i 的元素
    srand((int)time(0));
    for(int i = 0; i < k; ++i)
    {
        int c = rand()%row_number;
        cluster[i].centroid = data_set[c];//把第c個作為簇心，並把它相應的屬性賦值給centroid
    }

    //iteration
    int iter = 0;
    while(iter < max_iteration)
    {
        iter++;
        for(int i = 0; i < k; ++i)
            cluster[i].samples.clear();
        //找出每個樣本點所屬的質心
        for(int i = 0; i < row_number; ++i)
        {
            double min_distance = INT_MAX;
            int index = 0;
            //計算離樣本點i最近的質心
            for(int j = 0; j < k; ++j)
            {
                double temp_distance = CalculateDistance(data_set[i], cluster[j].centroid);
                if(min_distance > temp_distance)
                {
                    min_distance = temp_distance;
                    index = j;
                }
            }
            cluster[index].samples.push_back(i);//把第i個樣本點放入，距離其最近的質心的samples
        }

        double max_move_distance = INT_MIN;
        //更新簇心
        for(int i = 0; i < k; ++i)
        {
            vector<double> temp_value(col_number, 0.0);
            for(int num = 0; num < cluster[i].samples.size(); ++num)//計算每個樣本的屬性之和
            {
                int temp_same = cluster[i].samples[num];
                for(int j = 0; j < col_number; ++j)
                    temp_value[j] += data_set[temp_same][j];
            }
            vector<double> temp_centroid = cluster[i].centroid;
            for(int j = 0; j < col_number; ++j)
                cluster[i].centroid[j] = temp_value[j]/cluster[i].samples.size();
            //計算從上一個簇心移動到當前新的簇心的距離
            double temp_distance = CalculateDistance(temp_centroid, cluster[i].centroid);
            if(max_move_distance < temp_distance)
                max_move_distance = temp_distance;
        }
        if(max_move_distance < threshold)
            break;
    }
    return cluster;
}

int main()
{
    int threshold = 0.001;//當從上一個簇心移動到當前粗心的距離幾乎不變時，可以結束。這裡用threshold作為閾值
    vector <vector<double> >data_set(9, vector<double>(2, 0.0));
    int point_number;
    cin>>point_number;
    for(int i = 0; i < point_number; ++i)
    {
        for(int j = 0; j < 2; ++j)
            cin>>data_set[i][j];
    }

    int col = data_set[0].size();
    vector<Cluster> cluster_res = KMeans(data_set, 2, 200, threshold);
    for(int i = 0; i < cluster_res.size(); ++i)
    {
        cout<<"Cluster "<<i<<" : "<<endl;
        cout<<"\t"<<"Centroid: ";//<<endl;
        cout<<"(";
        for(int j = 0; j < cluster_res[i].centroid.size()-1; ++j)
            cout<< cluster_res[i].centroid[j]<<",";
        cout<<cluster_res[i].centroid[cluster_res[i].centroid.size()-1]<<")"<<endl;
        cout<<"\t"<<"Samples: ";
        for(int j = 0; j < cluster_res[i].samples.size(); ++j)
        {
            int c = cluster_res[i].samples[j];
            cout<<"(";
            for(int m = 0; m < col-1; ++m)
                cout<<data_set[c][m]<<",";
            cout<<data_set[c][col-1]<<")  ";
        }
        cout<<endl;
    }
    return 0;
}

/**

1 1
2 1
1 2
2 2
3 3
8 8
8 9
9 8
9 9

*/