tasks a-s

Task/Nth-root/Groovy/nth-root-1.groovy

@@ -0,0 +1,13 @@
+import static Constants.tolerance
+import static java.math.RoundingMode.HALF_UP
+
+def root(double base, double n) {
+    double xOld = 1
+    double xNew = 0
+    while (true) {
+        xNew = ((n - 1) * xOld + base/(xOld)**(n - 1))/n
+    if ((xNew - xOld).abs() < tolerance) { break }
+        xOld = xNew
+    }
+    (xNew as BigDecimal).setScale(7, HALF_UP)
+}

Task/Nth-root/Groovy/nth-root-2.groovy

@@ -0,0 +1,21 @@
+class Constants {
+    static final tolerance = 0.00001
+}
+
+print '''
+   Base   Power  Calc'd Root  Actual Root
+-------  ------  -----------  -----------
+'''
+def testCases = [
+    [b:32.0, n:5.0, r:2.0],
+    [b:81.0, n:4.0, r:3.0],
+    [b:Math.PI**2, n:4.0, r:Math.PI**(0.5)],
+    [b:7.0, n:0.5, r:49.0],
+]
+
+testCases.each {
+    def r = root(it.b, it.n)
+    printf('%7.4f  %6.4f  %11.4f  %11.4f\n',
+        it.b, it.n, r, it.r)
+    assert (r - it.r).abs() <= tolerance
+}