This plugin provides pairing functions to Polars. These functions encode a pair of natural numbers into a single natural number.
pip install polars-pairingThis plugin implements three pairing functions (Hagen1, Szudzik2, and Cantor3), along with their corresponding unpairing functions, as Polars expressions. The pairing functions take two integer columns as input and produce a single column containing the encoded pair. Conversely, the unpairing functions accept a single column as input and generate a struct column containing the values of the original pair.
>>> import polars as pl
>>> import polars_pairing as plp
>>> df = pl.DataFrame({
... "a": [1, 2, 38, 4],
... "b": [5, 6, 77, 80]
... })
>>> df.select(plp.col("a").pairing.pair(plp.col("b")).alias("pair"))
shape: (4, 1)
┌──────┐
│ pair │
│ --- │
│ u64 │
╞══════╡
│ 28 │
│ 40 │
│ 6006 │
│ 6408 │
└──────┘
# By default, the Hagen pairing function is used, but you can specify alternative functions:
>>> df.select(
... plp.col("a").pairing.pair(plp.col("b"), method="hagen").alias("hagen_pair"),
... plp.col("a").pairing.pair(plp.col("b"), method="szudzik").alias("szudzik_pair"),
... plp.col("a").pairing.pair(plp.col("b"), method="cantor").alias("cantor_pair")
... )
shape: (4, 3)
┌────────────┬──────────────┬─────────────┐
│ hagen_pair ┆ szudzik_pair ┆ cantor_pair │
│ --- ┆ --- ┆ --- │
│ u64 ┆ u64 ┆ u64 │
╞════════════╪══════════════╪═════════════╡
│ 28 ┆ 26 ┆ 26 │
│ 40 ┆ 38 ┆ 42 │
│ 6006 ┆ 5967 ┆ 6747 │
│ 6408 ┆ 6404 ┆ 3650 │
└────────────┴──────────────┴─────────────┘
# The corresponding unpairing functions are also available:
>>> df = pl.DataFrame({"p": [28, 40, 6006, 6408]})
>>> df.select(plp.col("p").pairing.unpair().alias("unpair"))
shape: (4, 1)
┌───────────┐
│ unpair │
│ --- │
│ struct[2] │
╞═══════════╡
│ {1,5} │
│ {2,6} │
│ {38,77} │
│ {4,80} │
└───────────┘
>>> df = pl.DataFrame({"p": [26, 38, 5967, 6404]})
>>> df.select(
... plp.col("p").pairing.unpair(method="szudzik").alias("unpair")
... ).unnest("unpair")
shape: (4, 2)
┌──────┬───────┐
│ Left ┆ Right │
│ --- ┆ --- │
│ u64 ┆ u64 │
╞══════╪═══════╡
│ 1 ┆ 5 │
│ 2 ┆ 6 │
│ 38 ┆ 77 │
│ 4 ┆ 80 │
└──────┴───────┘Footnotes
-
Hagen, D. R. Superior Pairing Function. https://drhagen.com/blog/superior-pairing-function/ (2018). ↩
-
Szudzik, Matthew. "An elegant pairing function." Wolfram Research (ed.) Special NKS 2006 Wolfram Science Conference. 2006. ↩
-
Cantor, G. Ein Beitrag zur Mannigfaltigkeitslehre. Journal für die reine und angewandte Mathematik 1878, 242–258 (1878). ↩