WIP

Author: modiase

algos/mathematics/combinatorics/lehmer_code.py

@@ -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)
+
+
+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))