How to resolve the algorithm Index finite lists of positive integers step by step in the Sidef programming language

Published on 12 May 2024 09:40 PM
#Sidef

How to resolve the algorithm Index finite lists of positive integers step by step in the Sidef programming language

Table of Contents

Problem Statement

It is known that the set of finite lists of positive integers is   countable.
This means that there exists a subset of natural integers which can be mapped to the set of finite lists of positive integers.

Implement such a mapping:

Demonstrate your solution by:

There are many ways to do this.   Feel free to choose any one you like.

Make the   rank   function as a   bijection   and show   unrank(n)   for   n   varying from   0   to   10.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Index finite lists of positive integers step by step in the Sidef programming language

Source code in the sidef programming language

func rank(Array arr) {
    Number(arr.join('a'), 11)
}

func unrank(Number n) {
    n.base(11).split('a').map { Num(_) }
}

var l = [1, 2, 3, 10, 100, 987654321]
say l
var n = rank(l)
say n
var l = unrank(n)
say l


func unrank(Number n) {
    n == 1 ? [0]
           : n.base(2).substr(1).split('0', -1).map{.len}
}

func rank(Array x) {
    x.is_empty ? 0
               : Number('1' + x.map { '1' * _ }.join('0'), 2)
}

for x in (0..10) {
    printf("%3d : %-18s: %d\n", x, unrank(x), rank(unrank(x)))
}

say ''
var x = [1, 2, 3, 5, 8]
say "#{x} => #{rank(x)} => #{unrank(rank(x))}"

You may also check:How to resolve the algorithm Dice game probabilities step by step in the M2000 Interpreter programming language
You may also check:How to resolve the algorithm Fibonacci sequence step by step in the ECL programming language
You may also check:How to resolve the algorithm String interpolation (included) step by step in the Ursala programming language
You may also check:How to resolve the algorithm Roots of unity step by step in the RPL programming language
You may also check:How to resolve the algorithm Flow-control structures step by step in the Forth programming language