# Lexicographic permutations

*Author: Moritz Lenz*

https://projecteuler.net/problem=24

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

Source code: prob024-moritz.pl

use v6; # idea: the last 9 digits can be permuted in 9! = 362880 ways. so there are # 9! numbers that start with a 0, 9! numbers that start with a 1 etc. # # So to get the first digit, divide our target by 9!, and the rounded result # is the first digit. # # then we remove the first digit from the pool of available digits, divide # the rest by 8!, round, store result in $n. Then the $n'th lowest available # digit is the second digit that we search. my $target = 1e6; my $t = $target; sub f(Int $x){ [*] 1..$x; } my @f = map &f, 0..9; my @available = 0 .. 9; say gather { for reverse(0..9) -> $marker { my $n = ceiling($t / @f[$marker])- 1; $t -= $n * @f[$marker]; take @available[$n]; @available.splice($n, 1); } }.join('')