day7_1

//In this challenge, we practice calculating the Pearson correlation coefficient.//

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
#include <iomanip>
using namespace std;

float covariance(vector<float> x, vector<float> y, float meanX, float meanY){
    float cov = 0.0f;
    for(long unsigned i = 0; i < x.size(); i++){
        cov += ((x[i] - meanX) * (y[i] - meanY));
    }
    return (cov / x.size());
}

float stdDev(vector<float> v, float mean){
    float denominator = 0.0f;
    for(long unsigned i = 0; i < v.size(); i++){
        denominator += pow((v[i] - mean), 2);
    }
    return (sqrt(denominator / v.size()));
}


int main() {
    /* Enter your code here. Read input from STDIN. Print output to STDOUT */
    int n = 0;
    vector<float> x;
    vector<float> y;
    float curr, meanX, meanY, sumX, sumY = 0.0f;
    cin >> n;
    for(int i = 0; i < n; i++){
        cin >> curr;
        x.push_back(curr);
        sumX += curr;
    }
    for(int i = 0; i < n; i++){
        cin >> curr;
        y.push_back(curr);
        sumY += curr;
    }
    meanX = sumX / x.size();
    meanY = sumY / y.size();
    float stdDevX = stdDev(x, meanX);
    float stdDevY = stdDev(y, meanY);
    float cov = covariance(x,y,meanX, meanY);
    float pearsonCoef = cov / (stdDevX * stdDevY);
    
    cout << fixed << setprecision(3) << pearsonCoef; 
    return 0;
}