2016 Update

Task/Set/Go/set-2.go

@@ -0,0 +1,133 @@
+package main
+
+import (
+    "fmt"
+    "math/big"
+)
+
+func main() {
+    // create an empty set
+    var s0 big.Int
+
+    // create sets with elements
+    s1 := newSet(3)
+    s2 := newSet(3, 1)
+    s3 := newSet(3, 1, 4, 1, 5, 9)
+
+    // output
+    fmt.Println("s0:", format(s0))
+    fmt.Println("s1:", format(s1))
+    fmt.Println("s2:", format(s2))
+    fmt.Println("s3:", format(s3))
+
+    // element predicate
+    fmt.Printf("%v ∈ s0: %t\n", 3, hasElement(s0, 3))
+    fmt.Printf("%v ∈ s3: %t\n", 3, hasElement(s3, 3))
+    fmt.Printf("%v ∈ s3: %t\n", 2, hasElement(s3, 2))
+
+    // union
+    b := newSet(4, 2)
+    fmt.Printf("s3 ∪ %v: %v\n", format(b), format(union(s3, b)))
+
+    // intersection
+    fmt.Printf("s3 ∩ %v: %v\n", format(b), format(intersection(s3, b)))
+
+    // difference
+    fmt.Printf("s3 \\ %v: %v\n", format(b), format(difference(s3, b)))
+
+    // subset predicate
+    fmt.Printf("%v ⊆ s3: %t\n", format(b), subset(b, s3))
+    fmt.Printf("%v ⊆ s3: %t\n", format(s2), subset(s2, s3))
+    fmt.Printf("%v ⊆ s3: %t\n", format(s0), subset(s0, s3))
+
+    // equality
+    s2Same := newSet(1, 3)
+    fmt.Printf("%v = s2: %t\n", format(s2Same), equal(s2Same, s2))
+
+    // proper subset
+    fmt.Printf("%v ⊂ s2: %t\n", format(s2Same), properSubset(s2Same, s2))
+    fmt.Printf("%v ⊂ s3: %t\n", format(s2Same), properSubset(s2Same, s3))
+
+    // delete
+    remove(&s3, 3)
+    fmt.Println("s3, 3 removed:", format(s3))
+}
+
+func newSet(ms ...int) (set big.Int) {
+    for _, m := range ms {
+        set.SetBit(&set, m, 1)
+    }
+    return
+}
+
+func remove(set *big.Int, m int) {
+    set.SetBit(set, m, 0)
+}
+
+func format(set big.Int) string {
+    if len(set.Bits()) == 0 {
+        return "∅"
+    }
+    r := "{"
+    for e, l := 0, set.BitLen(); e < l; e++ {
+        if set.Bit(e) == 1 {
+            r = fmt.Sprintf("%s%v, ", r, e)
+        }
+    }
+    return r[:len(r)-2] + "}"
+}
+
+func hasElement(set big.Int, m int) bool {
+    return set.Bit(m) == 1
+}
+
+func union(a, b big.Int) (set big.Int) {
+    set.Or(&a, &b)
+    return
+}
+
+func intersection(a, b big.Int) (set big.Int) {
+    set.And(&a, &b)
+    return
+}
+
+func difference(a, b big.Int) (set big.Int) {
+    set.AndNot(&a, &b)
+    return
+}
+
+func subset(a, b big.Int) bool {
+    ab := a.Bits()
+    bb := b.Bits()
+    if len(ab) > len(bb) {
+        return false
+    }
+    for i, aw := range ab {
+        if aw&^bb[i] != 0 {
+            return false
+        }
+    }
+    return true
+}
+
+func equal(a, b big.Int) bool {
+    return a.Cmp(&b) == 0
+}
+
+func properSubset(a, b big.Int) (p bool) {
+    ab := a.Bits()
+    bb := b.Bits()
+    if len(ab) > len(bb) {
+        return false
+    }
+    for i, aw := range ab {
+        bw := bb[i]
+        if aw&^bw != 0 {
+            return false
+        }
+        if aw != bw {
+            p = true
+        }
+    }
+    return
+}