Lax Lean Archive

Encoding signed integers and missing distances

Lax489179.IntegerEncoding · concepts/Lax489179/IntegerEncoding.lean · lax-489179

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    Natural Language Statement

    Definition

    Signed integers are stored in natural-number words using 0↦00\mapsto0, −1↦1-1\mapsto1, 1↦21\mapsto2, −2↦3-2\mapsto3, and so on. For an optional integer, zero denotes absence and an integer is encoded by its signed code plus one. This separates a missing edge or infinite distance from every finite weight, including zero and negative weights.

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    1import Mathlib.Data.Int.Basic
    2
    3/-!
    4---
    5title: Encoding signed integers and missing distances
    6type: definition
    7---
    8Signed integers are stored in natural-number words using
    90↦00\mapsto0, −1↦1-1\mapsto1, 1↦21\mapsto2, −2↦3-2\mapsto3, and so on.
    10For an optional integer, zero denotes absence and an integer is encoded
    11by its signed code plus one. This separates a missing edge or infinite
    12distance from every finite weight, including zero and negative weights.
    13-/
    14
    15namespace Lax489179.IntegerEncoding
    16
    17def encodeInt : ℤ → ℕ
    18 | .ofNat n => 2 * n
    19 | .negSucc n => 2 * n + 1
    20
    21def decodeInt (n : ℕ) : ℤ :=
    22 if n % 2 = 0 then .ofNat (n / 2) else .negSucc (n / 2)
    23
    24def encodeOption : Option ℤ → ℕ
    25 | none => 0
    26 | some z => encodeInt z + 1
    27
    28def decodeOption : ℕ → Option ℤ
    29 | 0 => none
    30 | n + 1 => some (decodeInt n)
    31
    32end Lax489179.IntegerEncoding
    33
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    From Mathlib

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