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

Fibonacci Sequence Calculation:

The provided Kotlin code defines a function fib that calculates the n-th number in the Fibonacci sequence.

Function Signature:

fun fib(n: Int): Int

• n: The index of the Fibonacci number to calculate. Must be non-negative.

Algorithm:

The function uses a tail-recursive algorithm to calculate the Fibonacci number. Tail recursion occurs when the recursive call is the last operation in the function. This is achieved by defining a nested function fib that performs the recursion:

fun fib(k: Int, a: Int, b: Int): Int =
   if (k == 0) a else fib(k - 1, b, a + b)

• k: The current index of the Fibonacci sequence being calculated.
• a: The previous Fibonacci number.
• b: The current Fibonacci number.

The algorithm works as follows:

• If k is 0, it returns a, which is the 0th Fibonacci number (0).
• If k is greater than 0, it recursively calls itself with k - 1, b (the current Fibonacci number), and a + b (the sum of the previous and current Fibonacci numbers).

Usage:

In the main function, the fib function is called for values of n from 0 to 20, and the results are printed.

for (i in 0..20) print("${fib(i)} ")
println()

Output:

0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 

Note:

The provided algorithm is not very efficient for large values of n due to the recursive nature of the algorithm. More efficient algorithms, such as the matrix exponentiation method, can be used for such cases.

fun fib(n: Int): Int {
   require(n >= 0)
   fun fib(k: Int, a: Int, b: Int): Int =
       if (k == 0) a else fib(k - 1, b, a + b)
   return fib(n, 0, 1)
}

fun main(args: Array<String>) {
    for (i in 0..20) print("${fib(i)} ")
    println()
}