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Lehmer code #7

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62 changes: 62 additions & 0 deletions algos/mathematics/combinatorics/lehmer_code.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,62 @@
from collections import Counter
from functools import reduce
from typing import Final

ELEMENTS: Final = (
"A",
"B",
"C",
"D",
"E",
)
N_PERMUTATIONS: Final = reduce(lambda x, y: x * y, range(len(ELEMENTS), 0, -1))


def rank(permutation: tuple[str, ...]) -> int:
if Counter(permutation) != Counter(ELEMENTS):
raise ValueError("Invalid permutation")

rank = 0
for i, element in enumerate(permutation):
rank += ELEMENTS.index(element) * len(ELEMENTS) ** (len(permutation) - i - 1)
return rank


def unrank(rank: int) -> tuple[str, ...]:
if rank < 0 or rank >= len(ELEMENTS) ** len(ELEMENTS):
raise ValueError("Invalid rank")

permutation = []
for i in range(len(ELEMENTS)):
permutation.append(ELEMENTS[rank % len(ELEMENTS)])
rank //= len(ELEMENTS)

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Bug: Missing Return and Incorrect Validation

The unrank function implicitly returns None because it's missing a return statement for the permutation it computes. Additionally, its rank validation incorrectly uses len(ELEMENTS) ** len(ELEMENTS) as the upper bound instead of N_PERMUTATIONS (n!), which is not correct for Lehmer codes.

Fix in Cursor Fix in Web


if __name__ == "__main__":
print(N_PERMUTATIONS)
print(ELEMENTS)
print(
rank(
(
"A",
"B",
"C",
"D",
"E",
)
)
)
print(
unrank(
rank(
(
"A",
"B",
"C",
"D",
"E",
)
)
)
)
print(unrank(1))