Day 5: Normal Distribution I HackerRank Solution


Day 5: Normal Distribution I HackerRank Solution
Source : https://www.hackerrank.com/challenges/s10-normal-distribution-1



Source : https://www.hackerrank.com/challenges/s10-normal-distribution-1


Solution


// github.com/RodneyShag
public class Solution {
public static void main(String[] args) {
double mean = 20;
double std = 2;
System.out.format("%.3f%n", cumulative(mean, std, 19.5));
System.out.format("%.3f%n", cumulative(mean, std, 22) - cumulative(mean, std, 20));
}
/* Calculates cumulative probability */
public static double cumulative(double mean, double std, double x) {
double parameter = (x - mean) / (std * Math.sqrt(2));
return (0.5) * (1 + erf(parameter));
}
/* Source: http://introcs.cs.princeton.edu/java/21function/ErrorFunction.java.html */
// fractional error in math formula less than 1.2 * 10 ^ -7.
// although subject to catastrophic cancellation when z in very close to 0
// from Chebyshev fitting formula for erf(z) from Numerical Recipes, 6.2
public static double erf(double z) {
double t = 1.0 / (1.0 + 0.5 * Math.abs(z));
// use Horner's method
double ans = 1 - t * Math.exp( -z*z - 1.26551223 +
t * ( 1.00002368 +
t * ( 0.37409196 +
t * ( 0.09678418 +
t * (-0.18628806 +
t * ( 0.27886807 +
t * (-1.13520398 +
t * ( 1.48851587 +
t * (-0.82215223 +
t * ( 0.17087277))))))))));
if (z >= 0) return ans;
else return -ans;
}
}

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