Step by Step solution about How to resolve the algorithm Fivenum step by step in the Ruby programming language

The provided Ruby code defines a method fivenum that takes an array of numbers as input and calculates the five-number summary for that array. The five-number summary includes the minimum, first quartile, median, third quartile, and maximum of the array.

Let's go through the code step by step:

1. The fivenum method starts by sorting the input array in ascending order using the sort method. The sorted array is stored in the sorted_arr variable.

2. It calculates the size of the sorted array and stores it in the variable n.

3. It calculates the index of the first quartile, Q1, using the formula:

   n4 = (((n + 3).to_f / 2.to_f) / 2.to_f).floor

   This formula ensures that n4 represents the index that divides the sorted array into four equal parts.

4. It calculates the following five indices:

   d = Array.[](1, n4, ((n.to_f + 1) / 2).to_i, n + 1 - n4, n)

   These indices represent the positions of the five values in the sorted array that will be used to calculate the five-number summary.

5. It initializes an empty array called sum_array to store the five values.

6. It enters a loop that iterates from 0 to 4. During each iteration of the loop:

   • It calculates the floor and ceiling indices for the current position in the d array using the formulas:

     index_floor = (d[e] - 1).floor
     index_ceil  = (d[e] - 1).ceil

   • It calculates the average of the values at the floor and ceil indices and stores it in the sum_array.

7. Finally, the sum_array containing the five values is returned as the five-number summary.

8. In the provided test cases, the fivenum method is called with different input arrays, and the resulting five-number summaries are printed using the p method.

def fivenum(array)
  sorted_arr = array.sort
  n = array.size
  n4 = (((n + 3).to_f / 2.to_f) / 2.to_f).floor
  d = Array.[](1, n4, ((n.to_f + 1) / 2).to_i, n + 1 - n4, n)
  sum_array = []
  (0..4).each do |e| # each loops have local scope, for loops don't
    index_floor = (d[e] - 1).floor
    index_ceil  = (d[e] - 1).ceil
    sum_array.push(0.5 * (sorted_arr[index_floor] + sorted_arr[index_ceil]))
  end
  sum_array
end

test_array = [15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43]
tukey_array = fivenum(test_array)
p tukey_array
test_array = [36, 40, 7, 39, 41, 15]
tukey_array = fivenum(test_array)
p tukey_array
test_array = [0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594,
              0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
              0.63905160,  0.61501527, -0.98983780, -1.00447874, -0.62759469,
              0.66206163,  1.04312009, -0.10305385, 0.75775634,  0.32566578]
tukey_array = fivenum(test_array)
p tukey_array