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i1e0
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Improve math functions and binary search (#18)
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14 files changed

+323
-66
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14 files changed

+323
-66
lines changed

‎Algorithms.Tests/Math/AbsMaxTests.fs‎

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namespace Algorithms.Tests.Math
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open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
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type AbsMaxTests() =
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[<TestMethod>]
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member this.Test() =
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Assert.AreEqual(-3, AbsMax.absMax [ -1; 1; 2; -2; -3; 3 ])
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Assert.AreEqual(3, AbsMax.absMax [ 1; -1; 2; -2; 3; -3 ])
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Assert.AreEqual(-1, AbsMax.absMax [ 0; -1; 0 ])

‎Algorithms.Tests/Math/AbsMinTests.fs‎

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namespace Algorithms.Tests.Math
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open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
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type AbsMinTests() =
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[<TestMethod>]
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member this.Test() =
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Assert.AreEqual(-1, AbsMin.absMin [ -1; 1; 2; -2; -3; 3 ])
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Assert.AreEqual(1, AbsMin.absMin [ 1; -1; 2; -2; 3; -3 ])
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Assert.AreEqual(0, AbsMin.absMin [ 0; -1; 0 ])

‎Algorithms.Tests/Math/AbsTests.fs‎

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namespace Algorithms.Tests.Math
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open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
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type AbsTests() =
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[<TestMethod>]
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[<DataRow(-10, 10)>]
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[<DataRow(-1, 1)>]
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[<DataRow(0, 0)>]
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[<DataRow(1, 1)>]
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[<DataRow(10, 10)>]
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member this.Test(input: int, expected: int) =
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let actual = Abs.absVal input
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Assert.AreEqual(expected, actual)

‎Algorithms.Tests/Math/FactorialTests.fs‎

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@@ -4,15 +4,56 @@ open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
7-
type FactorialTests () =
8-
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type FactorialTests() =
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99
[<TestMethod>]
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[<DataRow(0, 1)>]
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[<DataRow(1, 1)>]
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[<DataRow(2, 2)>]
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[<DataRow(3, 6)>]
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[<DataRow(5, 120)>]
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[<DataRow(8, 40320)>]
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[<DataRow(10, 3628800)>]
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member this.FactorialOf (num: int, expected: int) =
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let actual = Factorial.CalculateFactorial num
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Assert.AreEqual(expected, actual)
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[<DataRow(12, 479001600)>]
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member this.ValidInt(num: int, expected: int) =
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seq {
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Factorial.byFoldFunction
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Factorial.byReduceFunction
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Factorial.byRecursion
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Factorial.byTailRecursion
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Factorial.byTailRecursionGeneric
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}
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|> Seq.iter (fun func ->
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let actual = func num
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Assert.AreEqual(expected, actual))
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[<TestMethod>]
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[<DataRow(-1)>]
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member this.InvalidInt(num: int) =
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seq {
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Factorial.byFoldFunction
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Factorial.byReduceFunction
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Factorial.byRecursion
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Factorial.byTailRecursion
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Factorial.byTailRecursionGeneric
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}
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|> Seq.iter (fun func ->
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let action =
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new System.Action(fun () -> func num |> ignore)
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Assert.ThrowsException(action) |> ignore)
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[<TestMethod>]
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member this.Generic() =
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Assert.AreEqual(479001600, Factorial.byTailRecursionGeneric 12)
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Assert.AreEqual(479001600u, Factorial.byTailRecursionGeneric 12u)
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Assert.AreEqual(479001600.f, Factorial.byTailRecursionGeneric 12.f)
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Assert.AreEqual(2432902008176640000L, Factorial.byTailRecursionGeneric 20L)
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Assert.AreEqual(2432902008176640000UL, Factorial.byTailRecursionGeneric 20UL)
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Assert.AreEqual(2432902008176640000., Factorial.byTailRecursionGeneric 20.)
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Assert.AreEqual(10888869450418352160768000000M, Factorial.byTailRecursionGeneric 27M)
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Assert.AreEqual(
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30414093201713378043612608166064768844377641568960512000000000000I,
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Factorial.byTailRecursionGeneric 50I
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)

‎Algorithms.Tests/Math/PerfectNumbersTests.fs‎

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@@ -4,8 +4,8 @@ open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
7-
type PerfectNumbersTests () =
8-
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type PerfectNumbersTests() =
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99
[<TestMethod>]
1010
[<DataRow(-1, false)>]
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[<DataRow(0, false)>]
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[<DataRow(8128, true)>]
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[<DataRow(33550336, true)>]
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[<DataRow(33550337, false)>]
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member this.IsPerfect (n: int, expected: bool) =
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let actual = Perfect_Numbers.IsPerfect n
27-
Assert.AreEqual(expected, actual)
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member this.Test(n: int, expected: bool) =
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let actual = PerfectNumbers.isPerfect n
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Assert.AreEqual(expected, actual)

‎Algorithms.Tests/Math/PowerTests.fs‎

Lines changed: 50 additions & 5 deletions
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@@ -4,9 +4,10 @@ open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
7-
type PowerTests () =
8-
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type PowerTests() =
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99
[<TestMethod>]
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[<DataRow(0, 100, 0)>]
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[<DataRow(2, 2, 4)>]
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[<DataRow(2, 3, 8)>]
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[<DataRow(2, 4, 16)>]
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[<DataRow(10, 4, 10000)>]
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[<DataRow(1, 2, 1)>]
1920
[<DataRow(1, 50, 1)>]
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member this.PowerOf (num: int, pow: int, expected: int) =
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let actual = Power.Pow num pow
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Assert.AreEqual(expected, actual)
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member this.FoldFunction_Valid(num: int, pow: int, expected: int) =
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let actual = Power.byFoldFunction num pow
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Assert.AreEqual(expected, actual)
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[<TestMethod>]
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[<DataRow(-2, -2, 0)>]
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[<DataRow(-2, -1, 0)>]
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[<DataRow(-2, 0, 1)>]
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[<DataRow(-2, 1, -2)>]
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[<DataRow(-2, 2, 4)>]
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[<DataRow(-2, 3, -8)>]
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[<DataRow(-1, -3, -1)>]
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[<DataRow(-1, -2, 1)>]
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[<DataRow(-1, -1, -1)>]
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[<DataRow(-1, 0, 1)>]
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[<DataRow(-1, 1, -1)>]
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[<DataRow(-1, 2, 1)>]
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[<DataRow(-1, 3, -1)>]
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[<DataRow(0, 0, 1)>]
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[<DataRow(0, 1, 0)>]
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[<DataRow(0, 2, 0)>]
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[<DataRow(1, -2, 1)>]
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[<DataRow(1, -1, 1)>]
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[<DataRow(1, 0, 1)>]
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[<DataRow(1, 1, 1)>]
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[<DataRow(1, 2, 1)>]
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[<DataRow(2, 2, 4)>]
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[<DataRow(2, 3, 8)>]
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[<DataRow(2, 4, 16)>]
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[<DataRow(2, 8, 256)>]
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[<DataRow(2, 16, 65536)>]
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[<DataRow(3, 5, 243)>]
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[<DataRow(5, 3, 125)>]
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[<DataRow(10, 4, 10000)>]
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member this.ByRecursion_Valid(num: int, pow: int, expected: int) =
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let actual = Power.byRecursion num pow
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Assert.AreEqual(expected, actual)
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[<TestMethod>]
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[<DataRow(0, -1)>]
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[<DataRow(0, -2)>]
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member this.ByRecursion_Invalid(num: int, pow: int) =
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let action =
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new System.Action(fun () -> Power.byRecursion num pow |> ignore)
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Assert.ThrowsException<System.DivideByZeroException>(action)
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|> ignore

‎Algorithms.Tests/Math/PrimeTests.fs‎

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namespace Algorithms.Tests.Math
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open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Math
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[<TestClass>]
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type PrimeTests() =
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[<TestMethod>]
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[<DataRow(-3, false)>]
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[<DataRow(-2, false)>]
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[<DataRow(-1, false)>]
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[<DataRow(0, false)>]
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[<DataRow(1, false)>]
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[<DataRow(2, true)>]
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[<DataRow(49, false)>]
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[<DataRow(50, false)>]
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[<DataRow(998244353, true)>]
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[<DataRow(1000000007, true)>]
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member this.IsPrime(input: int, expected: bool) =
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let actual = Prime.isPrime input
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Assert.AreEqual(expected, actual)

‎Algorithms.Tests/Search/BinarySearchTests.fs‎

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namespace Algorithms.Tests.Search
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open Microsoft.VisualStudio.TestTools.UnitTesting
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open Algorithms.Search
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[<TestClass>]
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type BinarySearchTests() =
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let data0 =
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[| -2147483468
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-10
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-2
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-1
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0
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1
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2
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10
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20
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20
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2147483467 |]
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[<TestMethod>]
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[<DataRow(-2147483468, 0)>]
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[<DataRow(-10, 1)>]
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[<DataRow(-2, 2)>]
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[<DataRow(-1, 3)>]
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[<DataRow(0, 4)>]
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[<DataRow(1, 5)>]
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[<DataRow(2, 6)>]
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[<DataRow(10, 7)>]
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[<DataRow(2147483467, 10)>]
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member this.Data0_Exists(num: int, expected: int) =
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let actual = BinarySearch.findIndex num data0
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Assert.AreEqual(expected, actual)
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35+
[<TestMethod>]
36+
[<DataRow(20)>]
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member this.Data0_Duplicates(num: int) =
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let actual = BinarySearch.findIndex num data0
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Assert.IsTrue(actual = 8 || actual = 9)
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41+
[<TestMethod>]
42+
[<DataRow(5, -1)>]
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member this.Data0_None(num: int, expected: int) =
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let actual = BinarySearch.findIndex num data0
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Assert.AreEqual(expected, actual)

‎Algorithms/Math/Factorial.fs‎

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namespace Algorithms.Math
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module Factorial =
4-
let CalculateFactorial num =
5-
if (num < 0)
6-
then failwith "No Factorial for negative numbers"
7-
else [1..num] |> Seq.fold (fun acc n -> acc * n) 1
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/// Calculates factorial. Time complexity: O(n)
5+
let byFoldFunction n =
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if n < 0 then
7+
failwith "No factorial for negative numbers"
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else
9+
{ 1 .. n } |> Seq.fold (fun acc n -> acc * n) 1
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11+
/// Calculates factorial. Time complexity: O(n)
12+
let byReduceFunction n =
13+
match n with
14+
| n when n < 0 -> failwith "No factorial for negative numbers"
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| 0 -> 1
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| n -> { 1 .. n } |> Seq.reduce (*)
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18+
/// Calculates factorial. Time complexity: O(n)
19+
let rec byRecursion n =
20+
match sign n with
21+
| -1 -> failwith "No factorial for negative numbers"
22+
| 0 -> 1
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| _ -> n * byRecursion (n - 1)
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/// Calculates factorial. Time complexity: O(n)
26+
let byTailRecursion n =
27+
let rec inner n prod =
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match n with
29+
| 0 -> prod
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| _ -> inner (n - 1) (prod * n)
31+
32+
match n with
33+
| n when n < 0 -> failwith "No factorial for negative numbers"
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| _ -> inner n 1
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/// Calculates factorial. Time complexity: O(n)
37+
let inline byTailRecursionGeneric n =
38+
let gen0 = LanguagePrimitives.GenericZero
39+
let gen1 = LanguagePrimitives.GenericOne
40+
41+
let rec inner n prod =
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match n with
43+
| n when n = gen0 -> prod
44+
| _ -> inner (n - gen1) (prod * n)
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46+
match n with
47+
| n when n < gen0 -> failwith "No factorial for negative numbers"
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| _ -> inner n gen1

‎Algorithms/Math/PerfectNumbers.fs‎

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namespace Algorithms.Math
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module PerfectNumbers =
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/// Check if a number is perfect. Time complexity: O(√n)
5+
let isPerfect n =
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match n with
7+
| n when n <= 0 -> false
8+
| n ->
9+
{ 1 .. n - 1 }
10+
|> Seq.takeWhile (fun i -> i * i <= n)
11+
|> Seq.filter ((%) n >> (=) 0)
12+
|> Seq.fold (fun acc i -> acc + i + n / i) 0
13+
|> (=) (2 * n)

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