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Jairon Terrero
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Jan 11, 2024
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,178 @@ | ||
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| /// Represents a reduced fractional number. | ||
| /// An invariant exists such that it is not possible to create a ``Fraction`` | ||
| /// that is not represented in its most reduced form. | ||
| public struct Fraction: Hashable, Equatable, Sendable { | ||
| public let numerator: Int | ||
| public let denominator: Int | ||
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| /// Combines the provided `numerator` and `denominator` into a reduced ``Fraction``. | ||
| /// - Warning: Attempts to create a ``Fraction`` with a zero denominator will fatally error. | ||
| public init(numerator: Int, denominator: Int) { | ||
| let gcd = Self.gcd(numerator, denominator) | ||
| self.numerator = numerator / gcd | ||
| self.denominator = denominator / gcd | ||
| } | ||
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| public var positive: Bool { | ||
| switch (numerator, denominator) { | ||
| // 0/0 is not positive in this logic | ||
| case let (n, d) where n >= 0 && d > 0: true | ||
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| // Seems like this case can't happen because | ||
| // all Fractions are reduced. | ||
| case let (n, d) where n < 0 && d < 0: true | ||
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| default: false | ||
| } | ||
| } | ||
| } | ||
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| private extension Fraction { | ||
| static func gcd(_ a: Int, _ b: Int) -> Int { | ||
| // See: https://en.wikipedia.org/wiki/Euclidean_algorithm | ||
| var latestRemainder = max(a, b) | ||
| var previousRemainder = min(a, b) | ||
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| while latestRemainder != 0 { | ||
| let tmp = latestRemainder | ||
| latestRemainder = previousRemainder % latestRemainder | ||
| previousRemainder = tmp | ||
| } | ||
| return previousRemainder | ||
| } | ||
| } | ||
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| extension Fraction { | ||
| public static func * (lhs: Self, rhs: Self) -> Self { | ||
| Self(numerator: lhs.numerator * rhs.numerator, denominator: lhs.denominator * rhs.denominator) | ||
| } | ||
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| public static func / (lhs: Self, rhs: Self) -> Self { | ||
| Self(numerator: lhs.numerator * rhs.denominator, denominator: lhs.denominator * rhs.numerator) | ||
| } | ||
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| public static func + (lhs: Self, rhs: Self) -> Self { | ||
| Self(numerator: (lhs.numerator * rhs.denominator) + (rhs.numerator * lhs.denominator), denominator: lhs.denominator * rhs.denominator) | ||
| } | ||
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| public static func - (lhs: Self, rhs: Self) -> Self { | ||
| Self(numerator: (lhs.numerator * rhs.denominator) - (rhs.numerator * lhs.denominator), denominator: lhs.denominator * rhs.denominator) | ||
| } | ||
| } | ||
| extension Fraction { | ||
| public static func * (lhs: Self, rhs: Int) -> Self { | ||
| lhs * Self(integerLiteral: rhs) | ||
| } | ||
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| public static func / (lhs: Self, rhs: Int) -> Self { | ||
| lhs / Self(integerLiteral: rhs) | ||
| } | ||
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| public static func * (lhs: Int, rhs: Self) -> Self { | ||
| Self(integerLiteral: lhs) * rhs | ||
| } | ||
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| public static func / (lhs: Int, rhs: Self) -> Self { | ||
| Self(integerLiteral: lhs) / rhs | ||
| } | ||
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| public static func + (lhs: Self, rhs: Int) -> Self { | ||
| lhs + Self(integerLiteral: rhs) | ||
| } | ||
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| public static func - (lhs: Self, rhs: Int) -> Self { | ||
| lhs - Self(integerLiteral: rhs) | ||
| } | ||
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| public static func + (lhs: Int, rhs: Self) -> Self { | ||
| Self(integerLiteral: lhs) + rhs | ||
| } | ||
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| public static func - (lhs: Int, rhs: Self) -> Self { | ||
| Self(integerLiteral: lhs) - rhs | ||
| } | ||
| } | ||
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| extension Fraction: ExpressibleByIntegerLiteral { | ||
| public typealias IntegerLiteralType = Int | ||
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| public init(integerLiteral value: Int) { | ||
| self.init(numerator: value, denominator: 1) | ||
| } | ||
| } | ||
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| extension Fraction: SignedNumeric { | ||
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| public init?<T>(exactly source: T) where T : BinaryInteger { | ||
| self.init(integerLiteral: Int(source)) | ||
| } | ||
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| public static func *= (lhs: inout Fraction, rhs: Fraction) { | ||
| lhs = lhs * rhs | ||
| } | ||
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| public var magnitude: Fraction { | ||
| Self(numerator: abs(numerator), denominator: abs(denominator)) | ||
| } | ||
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| public typealias Magnitude = Self | ||
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| } | ||
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| extension Fraction { | ||
| public var asDouble: Double { | ||
| Double(numerator) / Double(denominator) | ||
| } | ||
| } | ||
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| extension Fraction: Comparable { | ||
| public static func < (lhs: Fraction, rhs: Fraction) -> Bool { | ||
| lhs.numerator * rhs.denominator < rhs.numerator * lhs.denominator | ||
| } | ||
| } | ||
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| extension Fraction: LosslessStringConvertible { | ||
| /// The format for string conversion is: `(<integer>|<integer>)` or `<integer>` | ||
| public init?(_ description: String) { | ||
| if | ||
| description.first == "(", | ||
| description.last == ")" | ||
| { | ||
| let parts = description.dropFirst().dropLast().split(separator: "|").compactMap({ Int(String($0)) }) | ||
| guard | ||
| parts.count == 2, | ||
| let numerator = parts.first, | ||
| let denominator = parts.last | ||
| else { | ||
| return nil | ||
| } | ||
| self.init(numerator: numerator, denominator: denominator) | ||
| } else if let number = Int(description) { | ||
| self.init(integerLiteral: number) | ||
| } else { | ||
| return nil | ||
| } | ||
| } | ||
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| public var description: String { | ||
| if denominator == 1 { | ||
| "\(!positive && numerator != 0 ? "-" : "")\(abs(numerator))" | ||
| } else { | ||
| "(\(positive ? "" : "-")\(abs(numerator))|\(abs(denominator)))" | ||
| } | ||
| } | ||
| } | ||
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| extension SignedInteger { | ||
| func over<T: SignedInteger>(_ denominator: T) -> Fraction { | ||
| Fraction(numerator: Int(self), denominator: Int(denominator)) | ||
| } | ||
| } | ||
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| extension Int { | ||
| public static func |(_ lhs: Self, _ rhs: Self) -> Fraction { | ||
| Fraction(numerator: lhs, denominator: rhs) | ||
| } | ||
| } |
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