Editing Eight queens puzzle (section)

==Sample program==
The following program is a translation of [[Niklaus Wirth]]'s solution into the [[Python (programming language)|Python]] programming language, but does without the [[Array data type|index arithmetic]] found in the original and instead uses [[List (abstract data type)|lists]] to keep the program code as simple as possible. By using a [[coroutine]] in the form of a [[Generator (computer programming)|generator function]], both versions of the original can be unified to compute either one or all of the solutions. Only 15,720 possible queen placements are examined.<ref>{{cite book|last=Wirth |first=Niklaus |author-link=Niklaus Wirth |title=Algorithms + Data Structures = Programs |series=Prentice-Hall Series in Automatic Computation |publisher=Prentice-Hall |year=1976 |isbn=978-0-13-022418-7 |title-link=Algorithms + Data Structures = Programs |bibcode=1976adsp.book.....W}} p. 145</ref><ref>{{cite book |last=Wirth |first=Niklaus |date=2012 |orig-date=orig. 2004 |title=Algorithms and Data Structures |version=Oberon version with corrections and authorized modifications |url=https://informatika-21.ru/ADen/AD2012.pdf |chapter=The Eight Queens Problem |pages=114–118}}</ref>
<syntaxhighlight lang="python">
def queens(n: int, i: int, a: list, b: list, c: list):
    if i < n:
        for j in range(n):
            if j not in a and i + j not in b and i - j not in c:
                yield from queens(n, i + 1, a + [j], b + [i + j], c + [i - j])
    else:
        yield a

for solution in queens(8, 0, [], [], []):
    print(solution)
</syntaxhighlight>The following program is an implementation of [[Donald Knuth]]'s informal description of the solution on Page 31, Section 7.2.2 ''Backtrack Programming'' from [[The Art of Computer Programming]], Volume 4B into the Python programming language.<ref>{{Cite book |last=Knuth |first=Donald Ervin |title=The art of computer programming. volume 4B part 2: Combinatorial algorithms |date=2023 |publisher=Addison-Wesley |isbn=978-0-201-03806-4 |location=Boston Munich}}</ref>
<syntaxhighlight lang="python3">
def property(perm: list):
    for k in range(0, len(perm)):
        for j in range(0, len(perm)):
            if j < k:
                if perm[k] == perm[j]:
                    return False
                elif abs(perm[k] - perm[j]) == k - j:
                    return False
    return True

def extend(perm: list, n: int):
    new_perm = []
    for p in perm:
        for i in range(0, n):
            new_perm.append(p + [i])
    return new_perm

def n_queens(n: int):
    domain = list(range(0, n))
    perm = [[]]
    for i in range(n):
        new_perm = list(filter(property, extend(perm, n)))
        perm = new_perm
    return len(perm)
</syntaxhighlight>