Root of number - mock interview 30 minutes

RootOfNumber_20Minutes.cs

using System;

class Solution
{
    public static double Root(double x, int n) // x = 7, n = 3
    {
      
      if(x < 0)      // false
      {
        return -1; 
      }
      
      if(x < 1) // false 
      {
        return binarySearch(x, n, x, 1); 
      }
      else 
      {
        return binarySearch(x, n, 1, x); // 1, 7 
      }
    }
  
    private static double binarySearch(double x, int n, double start, double end)
    {
      const double range = 0.001; 
      
      while (start <= end) // 1, 7, 1 - 4.5 
      {
        var middle = start + (end - start)/ 2; // 1 + 6.0/2 = 4.5 , 1 + 3.5/2 = 2.75
        
        var middleValue = Math.Pow(middle, n); // 4.5^3        
        
        // base case
        if(Math.Abs(middleValue - x) < range)  // 7 - 4.5^3  false 
        {
          return middle; 
        }
        else if( middleValue < x)
        {
          start = middle; 
        }
        else 
        {
          end = middle; // 4.5 
        }
      }
      
      return -1; 
    }

    static void Main(string[] args)
    {
        Console.WriteLine(Root(1, 3)); 
    }
}

// guess and check
// x = 7, 0 - 7 , n = 3, 1 - 7 
// binary search 1 + (7 -1)/ 2 = 4.5 ^3 vs 7, get rid of half range -> left side 
// error range < 0.001 -> 1.913
// 0< x < 1, [x, 1)
//