Data commit

Task/Farey-sequence/Go/farey-sequence.go

@@ -0,0 +1,61 @@
+package main
+
+import "fmt"
+
+type frac struct{ num, den int }
+
+func (f frac) String() string {
+    return fmt.Sprintf("%d/%d", f.num, f.den)
+}
+
+func f(l, r frac, n int) {
+    m := frac{l.num + r.num, l.den + r.den}
+    if m.den <= n {
+        f(l, m, n)
+        fmt.Print(m, " ")
+        f(m, r, n)
+    }
+}
+
+func main() {
+    // task 1.  solution by recursive generation of mediants
+    for n := 1; n <= 11; n++ {
+        l := frac{0, 1}
+        r := frac{1, 1}
+        fmt.Printf("F(%d): %s ", n, l)
+        f(l, r, n)
+        fmt.Println(r)
+    }
+    // task 2.  direct solution by summing totient function
+    // 2.1 generate primes to 1000
+    var composite [1001]bool
+    for _, p := range []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31} {
+        for n := p * 2; n <= 1000; n += p {
+            composite[n] = true
+        }
+    }
+    // 2.2 generate totients to 1000
+    var tot [1001]int
+    for i := range tot {
+        tot[i] = 1
+    }
+    for n := 2; n <= 1000; n++ {
+        if !composite[n] {
+            tot[n] = n - 1
+            for a := n * 2; a <= 1000; a += n {
+                f := n - 1
+                for r := a / n; r%n == 0; r /= n {
+                    f *= n
+                }
+                tot[a] *= f
+            }
+        }
+    }
+    // 2.3 sum totients
+    for n, sum := 1, 1; n <= 1000; n++ {
+        sum += tot[n]
+        if n%100 == 0 {
+            fmt.Printf("|F(%d)|: %d\n", n, sum)
+        }
+    }
+}