Redblackset

QuadTree.Tests/QuadTree.Tests.fsproj

@@ -14,6 +14,7 @@
     <Compile Include="Tests.TriangleCount.fs" />
     <Compile Include="Tests.SSSP.fs" />
     <Compile Include="Tests.Boruvka.fs" />
+    <Compile Include="Tests.RedBlackSet.fs" />
   </ItemGroup>
 
   <ItemGroup>

QuadTree.Tests/Tests.RedBlackSet.fs

@@ -0,0 +1,196 @@
+module RedBlackSet.Tests
+
+open System
+open RedBlackSet
+open Xunit
+
+let rec blHeightInv tree =
+    match tree with
+    | Empty -> 0
+    | Node(color, l, _, r) ->
+        let lH = blHeightInv l
+        let rH = blHeightInv r
+
+        if lH = -1 || rH = -1 || lH <> rH then -1
+        else if color = Red then lH
+        else lH + 1
+
+let rec heightInv tree =
+    match tree with
+    | Empty -> 0
+    | Node(_, l, _, r) ->
+        let lH = heightInv l
+        let rH = heightInv r
+
+        if lH > rH then
+            if lH = -1 || rH = -1 || (float (lH + 1) / float (rH + 1) > 2) then
+                -1
+            else
+                lH
+        else if lH = -1 || rH = -1 || (float (rH + 1) / float (lH + 1) > 2) then
+            -1
+        else
+            rH
+
+let rec blackSonsOfRed tree =
+    match tree with
+    | Empty -> true
+    | Node(Red, Node(Red, _, _, _), _, _) -> false
+    | Node(Red, _, _, Node(Red, _, _, _)) -> false
+    | Node(_, l, _, r) -> blackSonsOfRed l && blackSonsOfRed r
+
+let rec numOfElements tree num =
+    match tree with
+    | Empty -> 0
+    | Node(_, l, _, r) ->
+        let lN = numOfElements l num
+        let rN = numOfElements r num
+        lN + rN + 1
+
+[<Fact>]
+let oneElement () =
+    let t1 = emptySet
+    let t2 = insert t1 4
+    let t3 = insert t2 4
+    Assert.True(contains t3 4)
+    Assert.Equal(1, blHeightInv t3)
+    Assert.NotEqual(-1, heightInv t3)
+    Assert.True(blackSonsOfRed t3)
+    Assert.Equal(1, numOfElements t3 0)
+
+[<Fact>]
+let insertSomeElem () =
+    let t1 = emptySet
+    let t2 = insert t1 5
+    let t3 = insert t2 9
+    let t4 = insert t3 -7
+    let t5 = insert t4 89
+    let t6 = insert t5 -27
+    let t7 = insert t6 13
+    Assert.True(contains t7 -7)
+    Assert.Equal(2, blHeightInv t7)
+    Assert.NotEqual(-1, heightInv t7)
+    Assert.True(blackSonsOfRed t7)
+    Assert.Equal(6, numOfElements t7 0)
+
+[<Fact>]
+let deleteSomeElem () =
+    let t1 = emptySet
+    let t2 = insert t1 5
+    let t3 = insert t2 9
+    let t4 = insert t3 -7
+    let t5 = insert t4 89
+    let t6 = insert t5 -27
+    let t7 = insert t6 13
+    let t8 = delete t7 99
+    let t9 = delete t8 13
+    Assert.False(contains t9 13)
+    Assert.Equal(2, blHeightInv t9)
+    Assert.NotEqual(-1, heightInv t9)
+    Assert.True(blackSonsOfRed t9)
+    Assert.Equal(5, numOfElements t9 0)
+
+[<Fact>]
+let unionSets () =
+    let t1 = emptySet
+    let t2 = insert t1 5
+    let t3 = insert t2 9
+    let t4 = insert t3 -7
+    let t5 = insert t4 89
+    let t6 = insert t5 -27
+    let t7 = insert t6 13
+
+    let t1' = emptySet
+    let t2' = insert t1' 2
+    let t3' = insert t2' 7
+    let t4' = insert t3' 21
+    let t5' = insert t4' 9
+    let t6' = insert t5' 5
+
+    let tU = union t7 t6'
+    Assert.NotEqual(-1, heightInv tU)
+    Assert.True(blackSonsOfRed tU)
+    Assert.Equal(9, numOfElements tU 0)
+
+[<Fact>]
+let intersectionSets () =
+    let t1 = emptySet
+    let t2 = insert t1 5
+    let t3 = insert t2 9
+    let t4 = insert t3 -7
+    let t5 = insert t4 89
+    let t6 = insert t5 -27
+    let t7 = insert t6 13
+
+    let t1' = emptySet
+    let t2' = insert t1' 2
+    let t3' = insert t2' 7
+    let t4' = insert t3' 21
+    let t5' = insert t4' 9
+    let t6' = insert t5' 5
+
+    let tI = intersection t7 t6'
+    Assert.NotEqual(-1, heightInv tI)
+    Assert.True(blackSonsOfRed tI)
+    Assert.Equal(2, numOfElements tI 0)
+
+[<Fact>]
+let differenceSets () =
+    let t1 = emptySet
+    let t2 = insert t1 5
+    let t3 = insert t2 9
+    let t4 = insert t3 -7
+    let t5 = insert t4 89
+    let t6 = insert t5 -27
+    let t7 = insert t6 13
+
+    let t1' = emptySet
+    let t2' = insert t1' 2
+    let t3' = insert t2' 7
+    let t4' = insert t3' 21
+    let t5' = insert t4' 9
+    let t6' = insert t5' 5
+
+    let tD = difference t7 t6'
+    Assert.NotEqual(-1, heightInv tD)
+    Assert.True(blackSonsOfRed tD)
+    Assert.Equal(4, numOfElements tD 0)
+
+[<Fact>]
+let emptySetProperties () =
+    let t = emptySet
+    Assert.False(contains t 0)
+    Assert.Equal(0, numOfElements t 0)
+    Assert.Equal(0, blHeightInv t)
+    Assert.True(blackSonsOfRed t)
+
+[<Fact>]
+let largeSetInsertion () =
+    let randomValues = [ for i in 1..1000 -> Random().Next(-10000, 10000) ]
+    let tree = Seq.fold (fun acc x -> insert acc x) emptySet randomValues
+
+    Assert.NotEqual(-1, blHeightInv tree)
+    Assert.True(blackSonsOfRed tree)
+
+    for x in randomValues do
+        Assert.True(contains tree x)
+
+[<Fact>]
+let deleteRoot () =
+    let t1 = insert emptySet 5
+    let t2 = insert t1 3
+    let t3 = insert t2 7
+    let t4 = delete t3 5
+
+    Assert.False(contains t4 5)
+    Assert.True(contains t4 3)
+    Assert.True(contains t4 7)
+    Assert.NotEqual(-1, blHeightInv t4)
+
+[<Fact>]
+let complexRedBlackViolations () =
+    let values = [ 1..20 ]
+    let tree = Seq.fold (fun acc x -> insert acc x) emptySet values
+
+    Assert.NotEqual(-1, blHeightInv tree)
+    Assert.True(blackSonsOfRed tree)

QuadTree/QuadTree.fsproj

@@ -14,6 +14,7 @@
         <Compile Include="TriangleCount.fs"/>
         <Compile Include="SSSP.fs"/>
         <Compile Include="Boruvka.fs"/>
+        <Compile Include="RedBlackSet.fs"/>
     </ItemGroup>
 
 </Project>