Create gray

gray

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+// P49 (**) Gray code.
+//     An n-bit Gray code is a sequence of n-bit strings constructed according
+//     to certain rules. For example,
+//     n = 1: C(1) = ("0", "1").
+//     n = 2: C(2) = ("00", "01", "11", "10").
+//     n = 3: C(3) = ("000", "001", "011", "010", "110", "111", "101", "100").
+//    
+//     Find out the construction rules and write a function to generate Gray
+//     codes.
+//
+//     scala> gray(3)
+//     res0 List[String] = List(000, 001, 011, 010, 110, 111, 101, 100)
+//
+//     See if you can use memoization to make the function more
+//     efficient.
+
+object P49 {
+  def gray(n: Int): List[String] =
+    if (n == 0) List("")
+    else {
+      val lower = gray(n - 1)
+      (lower map { "0" + _ }) ::: (lower.reverse map { "1" + _ })
+    }
+
+  import scala.collection.mutable
+  private val strings = mutable.Map(0 -> List(""))
+  def grayMemoized(n: Int): List[String] = {
+    if (!strings.contains(n)) {
+      strings + (n -> ((grayMemoized(n - 1) map { "0" + _ }) :::
+                       (grayMemoized(n - 1).reverse map { "1" + _ })))
+    }
+    strings(n)
+  }
+}