Solve P92 - Von Koch's conjecture

Abhijit Sarkar · Abhijit Sarkar · commit 1aa41b92cefd · 2025-05-18T15:41:10.000-07:00
diff --git a/README.md b/README.md
@@ -176,7 +176,7 @@ P90 (**) Eight queens problem
 
 [P91](misc/src/P91.scala) (**) Knight’s tour.
 
-P92 (***) Von Koch’s conjecture.
+[P92](misc/src/P92.scala) (***) Von Koch’s conjecture.
 
 P93 (***) An arithmetic puzzle.
 
diff --git a/arithmetic/test/src/P31Spec.scala b/arithmetic/test/src/P31Spec.scala
@@ -2,6 +2,7 @@ package arithmetic
 
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
+import org.scalatest.Inspectors.forAll
 
 class P31Spec extends AnyFunSpec:
 
@@ -16,6 +17,6 @@ class P31Spec extends AnyFunSpec:
       (7, true),
       (11, true)
     )
-    data.foreach { (n, prime) =>
+    forAll(data) { (n, prime) =>
       P31.isPrime(n) shouldBe prime
     }
diff --git a/arithmetic/test/src/P35Spec.scala b/arithmetic/test/src/P35Spec.scala
@@ -2,6 +2,7 @@ package arithmetic
 
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
+import org.scalatest.Inspectors.forAll
 
 class P35Spec extends AnyFunSpec:
 
@@ -15,6 +16,6 @@ class P35Spec extends AnyFunSpec:
       (315, List(3, 3, 5, 7)),
       (901255, List(5, 17, 23, 461))
     )
-    data.foreach { (n, pf) =>
+    forAll(data) { (n, pf) =>
       P35.primeFactors(n) shouldBe pf
     }
diff --git a/bintree/test/src/P55Spec.scala b/bintree/test/src/P55Spec.scala
@@ -1,7 +1,8 @@
 package bintree
 
-import scala.language.implicitConversions
+import org.scalatest.Inspectors.forAll
 
+import scala.language.implicitConversions
 import org.scalatest.funspec.AnyFunSpec
 
 class P55Spec extends AnyFunSpec:
@@ -21,7 +22,7 @@ class P55Spec extends AnyFunSpec:
         )
       )
     )
-    data.foreach { (n, expected) =>
+    forAll(data) { (n, expected) =>
       val obtained = P55.cBalanced(n, 'x')
       assertSameTrees(obtained, expected)
     }
diff --git a/bintree/test/src/P56Spec.scala b/bintree/test/src/P56Spec.scala
@@ -2,7 +2,7 @@ package bintree
 
 import scala.language.implicitConversions
 import bintree.P56.isSymmetric
-
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -13,7 +13,7 @@ class P56Spec extends AnyFunSpec:
       (true, ('a', 'b', 'c'))
     )
 
-    data.foreach { (symmetric, xs) =>
+    forAll(data) { (symmetric, xs) =>
       val tree = Tree.fromArray(xs)
       tree.isSymmetric shouldBe symmetric
     }
diff --git a/bintree/test/src/P59Spec.scala b/bintree/test/src/P59Spec.scala
@@ -1,7 +1,8 @@
 package bintree
 
-import scala.language.implicitConversions
+import org.scalatest.Inspectors.forAll
 
+import scala.language.implicitConversions
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -14,6 +15,6 @@ class P59Spec extends AnyFunSpec:
       ('x', 'x', 'x', None, None, 'x', 'x'),
       ('x', 'x', 'x', None, 'x')
     )
-    expected.foreach { xs =>
+    forAll(expected) { xs =>
       obtained.contains(Tree.fromArray(xs)) shouldBe true
     }
diff --git a/bintree/test/src/P61ASpec.scala b/bintree/test/src/P61ASpec.scala
@@ -2,7 +2,7 @@ package bintree
 
 import scala.language.implicitConversions
 import P61A.leafList
-
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -12,7 +12,7 @@ class P61ASpec extends AnyFunSpec:
       (('x', 'x'), List('x')),
       (('a', 'b', 'c', None, None, 'd', 'e'), List('b', 'd', 'e'))
     )
-    data.foreach { (xs, expected) =>
+    forAll(data) { (xs, expected) =>
       val obtained = Tree.fromArray(xs).leafList
       obtained shouldBe expected
     }
diff --git a/bintree/test/src/P61Spec.scala b/bintree/test/src/P61Spec.scala
@@ -2,7 +2,7 @@ package bintree
 
 import scala.language.implicitConversions
 import P61.leafCount
-
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -13,7 +13,7 @@ class P61Spec extends AnyFunSpec:
       (('a', 'b', 'c', None, None, 'd', 'e'), 3)
     )
 
-    data.foreach { (xs, expected) =>
+    forAll(data) { (xs, expected) =>
       val obtained = Tree.fromArray(xs).leafCount
       obtained shouldBe expected
     }
diff --git a/bintree/test/src/P62BSpec.scala b/bintree/test/src/P62BSpec.scala
@@ -2,7 +2,7 @@ package bintree
 
 import scala.language.implicitConversions
 import P62B.atLevel
-
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -12,7 +12,7 @@ class P62BSpec extends AnyFunSpec:
       (('a', 'b'), 1, List('a')),
       (('a', 'b', 'c', None, None, 'd', 'e'), 2, List('b', 'c'))
     )
-    data.foreach { (xs, level, expected) =>
+    forAll(data) { (xs, level, expected) =>
       val obtained = Tree.fromArray(xs).atLevel(level)
       obtained shouldBe expected
     }
diff --git a/bintree/test/src/P62Spec.scala b/bintree/test/src/P62Spec.scala
@@ -2,7 +2,7 @@ package bintree
 
 import scala.language.implicitConversions
 import P62.internalList
-
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -12,7 +12,7 @@ class P62Spec extends AnyFunSpec:
       (('a', 'b'), List('a')),
       (('a', 'b', 'c', None, None, 'd', 'e'), List('a', 'c'))
     )
-    data.foreach { (xs, expected) =>
+    forAll(data) { (xs, expected) =>
       val obtained = Tree.fromArray(xs).internalList
       obtained shouldBe expected
     }
diff --git a/bintree/test/src/P63Spec.scala b/bintree/test/src/P63Spec.scala
@@ -1,5 +1,6 @@
 package bintree
 
+import org.scalatest.Inspectors.forAll
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -8,7 +9,7 @@ class P63Spec extends AnyFunSpec:
     val data: List[Int] = List(
       6
     )
-    data.foreach { n =>
+    forAll(data) { n =>
       val obtained = P63.completeBinaryTree(n, "x")
       obtained.levelOrder shouldBe List.fill(n)(Some("x"))
     }
diff --git a/bintree/test/src/P67Spec.scala b/bintree/test/src/P67Spec.scala
@@ -1,7 +1,8 @@
 package bintree
 
-import scala.language.implicitConversions
+import org.scalatest.Inspectors.forAll
 
+import scala.language.implicitConversions
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -22,7 +23,7 @@ class P67Spec extends AnyFunSpec:
       ('a', 'b', 'c', 'd', 'e', None, 'f', None, None, None, None, 'g')
     )
 
-    data.foreach { xs =>
+    forAll(data) { xs =>
       val tree     = Tree.fromArray(xs)
       val s        = P67.toString(tree)
       val obtained = P67.fromString(s)
diff --git a/bintree/test/src/TreeSpec.scala b/bintree/test/src/TreeSpec.scala
@@ -1,7 +1,8 @@
 package bintree
 
-import scala.language.implicitConversions
+import org.scalatest.Inspectors.forAll
 
+import scala.language.implicitConversions
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 
@@ -28,7 +29,7 @@ class TreeSpec extends AnyFunSpec:
       (10, 5, 15, 3, 7, 13, 18, 1, None, 6),
       (3, 5, 1, 6, 2, 0, 8, None, None, 7, 4)
     )
-    data.foreach { nums =>
+    forAll(data) { nums =>
       val tree     = Tree.fromArray(nums)
       val obtained = tree.levelOrder.toArray
       val result = nums
diff --git a/graph/test/src/P81Spec.scala b/graph/test/src/P81Spec.scala
@@ -3,6 +3,8 @@ package graph
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 import P81.findPaths
+import org.scalatest.Inspectors.forAll
+
 import scala.math.Ordering.Implicits.seqOrdering
 
 class P81Spec extends AnyFunSpec:
@@ -12,7 +14,7 @@ class P81Spec extends AnyFunSpec:
       ("[p>q/9, m>q/7, k, p>m/5]", "p", "k", Nil)
     )
 
-    data.foreach { (s, u, v, expected) =>
+    forAll(data) { (s, u, v, expected) =>
       val g = Graph.fromString(s)
       g.findPaths(u, v).sorted shouldBe expected
     }
diff --git a/graph/test/src/P82Spec.scala b/graph/test/src/P82Spec.scala
@@ -3,6 +3,8 @@ package graph
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.shouldBe
 import P82.findCycles
+import org.scalatest.Inspectors.forAll
+
 import scala.math.Ordering.Implicits.seqOrdering
 
 class P82Spec extends AnyFunSpec:
@@ -15,7 +17,7 @@ class P82Spec extends AnyFunSpec:
       )
     )
 
-    data.foreach { (s, u, expected) =>
+    forAll(data) { (s, u, expected) =>
       val g = Graph.fromString(s)
       g.findCycles(u).sorted shouldBe expected
     }
diff --git a/graph/test/src/P83Spec.scala b/graph/test/src/P83Spec.scala
@@ -5,6 +5,8 @@ import org.scalatest.matchers.should.Matchers.*
 import P83.spanningTrees
 import org.scalactic.Equality
 import graph.Util.given
+import org.scalatest.Inspectors.forAll
+
 import scala.language.implicitConversions
 
 class P83Spec extends AnyFunSpec:
@@ -40,11 +42,11 @@ class P83Spec extends AnyFunSpec:
             case _             => false
         else false
 
-    data.foreach { (vertices, edges) =>
+    forAll(data) { (vertices, edges) =>
       val g  = Graph.buildUG(vertices, edges)
       val st = g.spanningTrees
       val n  = g.vertices.size
-      st.foreach { t =>
+      forAll(st) { t =>
         t.size shouldBe n
         t.sliding(2).foreach(e => (edges should contain(e))(using edgeEq))
       }
diff --git a/graph/test/src/P84Spec.scala b/graph/test/src/P84Spec.scala
@@ -5,6 +5,8 @@ import org.scalatest.matchers.should.Matchers.*
 import P84.minimalSpanningTree
 import org.scalactic.Equality
 import graph.Util.given
+import org.scalatest.Inspectors.forAll
+
 import scala.language.implicitConversions
 
 class P84Spec extends AnyFunSpec:
@@ -41,9 +43,9 @@ class P84Spec extends AnyFunSpec:
             case Edge(u, v, _) => (u, v) == (a.u, a.v) || (v, u) == (a.u, a.v)
         else false
 
-    data.foreach { (vertices, edges, cost) =>
+    forAll(data) { (vertices, edges, cost) =>
       val g   = Graph.buildUG(vertices, edges)
       val mst = g.minimalSpanningTree
-      mst.foreach(e => (edges should contain(e))(using edgeEq))
+      forAll(mst)(e => (edges should contain(e))(using edgeEq))
       mst.foldLeft(0)((s, e) => s + e.data.getOrElse(0)) shouldBe cost
     }
diff --git a/graph/test/src/P86Spec.scala b/graph/test/src/P86Spec.scala
@@ -4,6 +4,8 @@ import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.*
 import P86.colorNodes
 import graph.Util.given
+import org.scalatest.Inspectors.forAll
+
 import scala.language.implicitConversions
 
 class P86Spec extends AnyFunSpec:
@@ -51,10 +53,10 @@ class P86Spec extends AnyFunSpec:
       )
     )
 
-    data.foreach { (vertices, edges) =>
+    forAll(data) { (vertices, edges) =>
       val g      = Graph.buildUG(vertices, edges)
       val clrMap = g.colorNodes.toMap
-      vertices.foreach { u =>
+      forAll(vertices) { u =>
         g.neighbors(u).map(v => clrMap(v._1)) should not contain (clrMap(u))
       }
     }
diff --git a/graph/test/src/P87Spec.scala b/graph/test/src/P87Spec.scala
@@ -3,6 +3,7 @@ package graph
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.*
 import P87.nodesByDepthFrom
+import org.scalatest.Inspectors.forAll
 
 class P87Spec extends AnyFunSpec:
   it("depth-first order graph traversal"):
@@ -19,7 +20,7 @@ class P87Spec extends AnyFunSpec:
       )
     )
 
-    data.foreach { (s, u, expected) =>
+    forAll(data) { (s, u, expected) =>
       val g = Graph.fromString(s)
       g.nodesByDepthFrom(u) shouldBe expected
     }
diff --git a/graph/test/src/P88Spec.scala b/graph/test/src/P88Spec.scala
@@ -3,6 +3,7 @@ package graph
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.*
 import P88.splitGraph
+import org.scalatest.Inspectors.forAll
 
 class P88Spec extends AnyFunSpec:
   it("connected components"):
@@ -13,7 +14,7 @@ class P88Spec extends AnyFunSpec:
       )
     )
 
-    data.foreach { (s, expected) =>
+    forAll(data) { (s, expected) =>
       val g = Graph.fromString(s)
       g.splitGraph shouldBe expected
     }
diff --git a/graph/test/src/P89Spec.scala b/graph/test/src/P89Spec.scala
@@ -3,6 +3,7 @@ package graph
 import org.scalatest.funspec.AnyFunSpec
 import org.scalatest.matchers.should.Matchers.*
 import P89.isBipartite
+import org.scalatest.Inspectors.forAll
 
 class P89Spec extends AnyFunSpec:
   it("bipartite graphs"):
@@ -13,7 +14,7 @@ class P89Spec extends AnyFunSpec:
       ("[a-b, b-c, d, e-f, f-g, g-e, h]", false)
     )
 
-    data.foreach { (s, expected) =>
+    forAll(data) { (s, expected) =>
       val g = if s.contains(">") then Graph.fromStringLabel(s) else Graph.fromString(s)
       g.isBipartite shouldBe expected
     }
diff --git a/misc/src/P91.scala b/misc/src/P91.scala
diff --git a/misc/src/P92.scala b/misc/src/P92.scala
diff --git a/misc/test/resources/92.jpg b/misc/test/resources/92.jpg
diff --git a/misc/test/src/P91Spec.scala b/misc/test/src/P91Spec.scala
diff --git a/misc/test/src/P92Spec.scala b/misc/test/src/P92Spec.scala
diff --git a/mtree/test/src/P73Spec.scala b/mtree/test/src/P73Spec.scala

Original file line number	Diff line number	Diff line change
`@@ -2,6 +2,7 @@ package arithmetic`
`2`	`2`
`3`	`3`	`import org.scalatest.funspec.AnyFunSpec`
`4`	`4`	`import org.scalatest.matchers.should.Matchers.shouldBe`
	`5`	`+import org.scalatest.Inspectors.forAll`
`5`	`6`
`6`	`7`	`class P31Spec extends AnyFunSpec:`
`7`	`8`
`@@ -16,6 +17,6 @@ class P31Spec extends AnyFunSpec:`
`16`	`17`	`(7, true),`
`17`	`18`	`(11, true)`
`18`	`19`	`)`
`19`		`- data.foreach { (n, prime) =>`
	`20`	`+ forAll(data) { (n, prime) =>`
`20`	`21`	`P31.isPrime(n) shouldBe prime`
`21`	`22`	`}`
Original file line number	Diff line number	Diff line change
`@@ -1,7 +1,8 @@`
`1`	`1`	`package bintree`
`2`	`2`
`3`		`-import scala.language.implicitConversions`
	`3`	`+import org.scalatest.Inspectors.forAll`
`4`	`4`
	`5`	`+import scala.language.implicitConversions`
`5`	`6`	`import org.scalatest.funspec.AnyFunSpec`
`6`	`7`
`7`	`8`	`class P55Spec extends AnyFunSpec:`
`@@ -21,7 +22,7 @@ class P55Spec extends AnyFunSpec:`
`21`	`22`	`)`
`22`	`23`	`)`
`23`	`24`	`)`
`24`		`- data.foreach { (n, expected) =>`
	`25`	`+ forAll(data) { (n, expected) =>`
`25`	`26`	`val obtained = P55.cBalanced(n, 'x')`
`26`	`27`	`assertSameTrees(obtained, expected)`
`27`	`28`	`}`
Original file line number	Diff line number	Diff line change
`@@ -2,7 +2,7 @@ package bintree`
`2`	`2`
`3`	`3`	`import scala.language.implicitConversions`
`4`	`4`	`import bintree.P56.isSymmetric`
`5`		`-`
	`5`	`+import org.scalatest.Inspectors.forAll`
`6`	`6`	`import org.scalatest.funspec.AnyFunSpec`
`7`	`7`	`import org.scalatest.matchers.should.Matchers.shouldBe`
`8`	`8`
`@@ -13,7 +13,7 @@ class P56Spec extends AnyFunSpec:`
`13`	`13`	`(true, ('a', 'b', 'c'))`
`14`	`14`	`)`
`15`	`15`
`16`		`- data.foreach { (symmetric, xs) =>`
	`16`	`+ forAll(data) { (symmetric, xs) =>`
`17`	`17`	`val tree = Tree.fromArray(xs)`
`18`	`18`	`tree.isSymmetric shouldBe symmetric`
`19`	`19`	`}`
Original file line number	Diff line number	Diff line change
`@@ -2,7 +2,7 @@ package bintree`
`2`	`2`
`3`	`3`	`import scala.language.implicitConversions`
`4`	`4`	`import P61.leafCount`
`5`		`-`
	`5`	`+import org.scalatest.Inspectors.forAll`
`6`	`6`	`import org.scalatest.funspec.AnyFunSpec`
`7`	`7`	`import org.scalatest.matchers.should.Matchers.shouldBe`
`8`	`8`
`@@ -13,7 +13,7 @@ class P61Spec extends AnyFunSpec:`
`13`	`13`	`(('a', 'b', 'c', None, None, 'd', 'e'), 3)`
`14`	`14`	`)`
`15`	`15`
`16`		`- data.foreach { (xs, expected) =>`
	`16`	`+ forAll(data) { (xs, expected) =>`
`17`	`17`	`val obtained = Tree.fromArray(xs).leafCount`
`18`	`18`	`obtained shouldBe expected`
`19`	`19`	`}`