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

The provided Kotlin code defines two functions, median and fivenum to calculate the median and five-number summary of an input array of doubles, respectively. The following is a breakdown of the code:

1. median Function:

   • This function calculates the median of a given slice of a double array.
   • It takes three arguments:
     • x: The input double array
     • start: The starting index of the slice (inclusive)
     • endInclusive: The ending index of the slice (inclusive)
   • It calculates the median as follows:
     • If the slice size is odd, the median is the element at index start + size / 2.
     • If the slice size is even, the median is the average of the two elements at indices start + size / 2 - 1 and start + size / 2.

2. fivenum Function:

   • This function calculates the five-number summary of a given double array. The five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
   • It takes one argument:
     • x: The input double array
   • It calculates the five-number summary as follows:
     • It first checks that the array contains no NaN (Not-a-Number) values.
     • It sorts the array in ascending order.
     • It calculates the minimum (x[0]) and maximum (x[x.lastIndex]) values.
     • It calculates the median (Q2) using the median function on the entire array.
     • It calculates the first quartile (Q1) as the median of the lower half of the sorted array (indices 0 to x.size / 2 - 1 if the array size is even, or 0 to x.size / 2 if the array size is odd).
     • It calculates the third quartile (Q3) as the median of the upper half of the sorted array (indices x.size / 2 to x.size - 1 if the array size is even, or x.size / 2 to x.size - 1 if the array size is odd).
   • It returns a double array containing the five-number summary: [minimum, Q1, Q2, Q3, maximum].

3. main Function:

   • The main function demonstrates the usage of the fivenum function.
   • It defines a list of double arrays (xl) and iterates through it, printing the five-number summary of each array.

// version 1.2.21

fun median(x: DoubleArray, start: Int, endInclusive: Int): Double {
    val size = endInclusive - start + 1
    require (size > 0) { "Array slice cannot be empty" }
    val m = start + size / 2
    return if (size % 2 == 1) x[m] else (x[m - 1] + x[m]) / 2.0
}

fun fivenum(x: DoubleArray): DoubleArray {
    require(x.none { it.isNaN() }) { "Unable to deal with arrays containing NaN" }
    val result = DoubleArray(5)
    x.sort()
    result[0] = x[0]
    result[2] = median(x, 0, x.size - 1)
    result[4] = x[x.lastIndex]
    val m = x.size / 2
    var lowerEnd = if (x.size % 2 == 1) m else m - 1
    result[1] = median(x, 0, lowerEnd)
    result[3] = median(x, m, x.size - 1)
    return result
}

fun main(args: Array<String>) {
    var xl = listOf(
        doubleArrayOf(15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0),
        doubleArrayOf(36.0, 40.0, 7.0, 39.0, 41.0, 15.0),
        doubleArrayOf(
             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
        )
    )
    xl.forEach { println("${fivenum(it).asList()}\n") }
}