How to resolve the algorithm Permutations by swapping step by step in the Arturo programming language

Published on 12 May 2024 09:40 PM
#Arturo

How to resolve the algorithm Permutations by swapping step by step in the Arturo programming language

Table of Contents

Problem Statement

Generate permutations of n items in which successive permutations differ from each other by the swapping of any two items. Also generate the sign of the permutation which is +1 when the permutation is generated from an even number of swaps from the initial state, and -1 for odd. Show the permutations and signs of three items, in order of generation here. Such data are of use in generating the determinant of a square matrix and any functions created should bear this in mind. Note: The Steinhaus–Johnson–Trotter algorithm generates successive permutations where adjacent items are swapped, but from this discussion adjacency is not a requirement.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Permutations by swapping step by step in the Arturo programming language

Source code in the arturo programming language

permutations: function [arr][
    d: 1
    c: array.of: size arr 0
    xs: new arr
    sign: 1

    ret: new @[@[xs, sign]]

    while [true][
        while [d > 1][
            d: d-1
            c\[d]: 0
        ]

        while [c\[d] >= d][
            d: d+1
            if d >= size arr -> return ret
        ]

        i: (1 = and d 1)? -> c\[d] -> 0
        tmp: xs\[i]
        xs\[i]: xs\[d]
        xs\[d]: tmp

        sign: neg sign
        'ret ++ @[new @[xs, sign]]
        c\[d]: c\[d] + 1
    ]

    return ret
]

loop permutations 0..2 'row ->
    print [row\0 "-> sign:" row\1]

print ""

loop permutations 0..3 'row ->
    print [row\0 "-> sign:" row\1]

You may also check:How to resolve the algorithm Matrix-exponentiation operator step by step in the Common Lisp programming language
You may also check:How to resolve the algorithm Detect division by zero step by step in the Standard ML programming language
You may also check:How to resolve the algorithm Box the compass step by step in the LLVM programming language
You may also check:How to resolve the algorithm Achilles numbers step by step in the Julia programming language
You may also check:How to resolve the algorithm Quickselect algorithm step by step in the Scheme programming language