September 2017 Update

Task/Stern-Brocot-sequence/Kotlin/stern-brocot-sequence.kotlin

@@ -0,0 +1,64 @@
+// version 1.1.0
+
+val sbs = mutableListOf(1, 1)
+
+fun sternBrocot(n: Int, fromStart: Boolean = true) {
+    if (n < 4 || (n % 2 != 0)) throw IllegalArgumentException("n must be >= 4 and even")
+    var consider = if (fromStart) 1 else n / 2 - 1
+    while (true) {
+        val sum = sbs[consider] + sbs[consider - 1]
+        sbs.add(sum)
+        sbs.add(sbs[consider])
+        if (sbs.size == n) break
+        consider++
+    }
+}
+
+fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
+
+fun main(args: Array<String>) {
+    var n = 16  // needs to be even to ensure 'considered' number is added
+    println("First 15 members of the Stern-Brocot sequence")
+    sternBrocot(n)
+    println(sbs.take(15))
+
+    val firstFind = IntArray(11)  // all zero by default
+    firstFind[0] = -1 // needs to be non-zero for subsequent test
+    for ((i, v) in sbs.withIndex())
+        if (v <= 10 && firstFind[v] == 0) firstFind[v] = i + 1
+    loop@ while (true) {
+        n += 2
+        sternBrocot(n, false)
+        val vv = sbs.takeLast(2)
+        var m = n - 1
+        for (v in vv) {
+            if (v <= 10 && firstFind[v] == 0) firstFind[v] = m
+            if (firstFind.all { it != 0 }) break@loop
+            m++
+        }
+    }
+    println("\nThe numbers 1 to 10 first appear at the following indices:")
+    for (i in 1..10) println("${"%2d".format(i)} -> ${firstFind[i]}")
+
+    print("\n100 first appears at index ")
+    while (true) {
+        n += 2
+        sternBrocot(n, false)
+        val vv = sbs.takeLast(2)
+        if (vv[0] == 100) {
+            println(n - 1); break
+        }
+        if (vv[1] == 100) {
+            println(n); break
+        }
+    }
+
+    print("\nThe GCDs of each pair of the series up to the 1000th member are ")
+    for (p in 0..998 step 2) {
+        if (gcd(sbs[p], sbs[p + 1]) != 1) {
+            println("not all one")
+            return
+        }
+    }
+    println("all one")
+}