2016 Update

Task/Set/Go/set-1.go

@@ -2,7 +2,14 @@ package main
 
 import "fmt"
 
-type set map[int]bool
+// Define set as a type to hold a set of complex numbers.  A type
+// could be defined similarly to hold other types of elements.  A common
+// variation is to make a map of interface{} to represent a set of
+// mixed types.  Also here the map value is a bool.  By always storing
+// true, the code is nicely readable.  A variation to use less memory
+// is to make the map value an empty struct.  The relative advantages
+// can be debated.
+type set map[complex128]bool
 
 func main() {
     // task: set creation
@@ -11,7 +18,7 @@ func main() {
     s2 := set{3: true, 1: true} // create set with two elements
 
     // option: another way to create a set
-    s3 := newSet([]int{3, 1, 4, 1, 5, 9})
+    s3 := newSet(3, 1, 4, 1, 5, 9)
 
     // option: output!
     fmt.Println("s0:", s0)
@@ -52,7 +59,7 @@ func main() {
     fmt.Println("s3, 3 deleted:", s3)
 }
 
-func newSet(ms []int) set {
+func newSet(ms ...complex128) set {
     s := make(set)
     for _, m := range ms {
         s[m] = true
@@ -71,7 +78,7 @@ func (s set) String() string {
     return r[:len(r)-2] + "}"
 }
 
-func (s set) hasElement(m int) bool {
+func (s set) hasElement(m complex128) bool {
     return s[m]
 }
 

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
+}

Task/Set/Go/set-3.go

@@ -0,0 +1,60 @@
+package main
+
+import (
+    "fmt"
+
+    "golang.org/x/tools/container/intsets"
+)
+
+func main() {
+    var s0, s1 intsets.Sparse // create some empty sets
+    s1.Insert(3)              // insert an element
+    s2 := newSet(3, 1)        // create sets with elements
+    s3 := newSet(3, 1, 4, 1, 5, 9)
+
+    // output
+    fmt.Println("s0:", &s0)
+    fmt.Println("s1:", &s1)
+    fmt.Println("s2:", s2)
+    fmt.Println("s3:", s3)
+
+    // element predicate
+    fmt.Printf("%v ∈ s0: %t\n", 3, s0.Has(3))
+    fmt.Printf("%v ∈ s3: %t\n", 3, s3.Has(3))
+    fmt.Printf("%v ∈ s3: %t\n", 2, s3.Has(2))
+
+    // union
+    b := newSet(4, 2)
+    var s intsets.Sparse
+    s.Union(s3, b)
+    fmt.Printf("s3 ∪ %v: %v\n", b, &s)
+
+    // intersection
+    s.Intersection(s3, b)
+    fmt.Printf("s3 ∩ %v: %v\n", b, &s)
+
+    // difference
+    s.Difference(s3, b)
+    fmt.Printf("s3 \\ %v: %v\n", b, &s)
+
+    // subset predicate
+    fmt.Printf("%v ⊆ s3: %t\n", b, b.SubsetOf(s3))
+    fmt.Printf("%v ⊆ s3: %t\n", s2, s2.SubsetOf(s3))
+    fmt.Printf("%v ⊆ s3: %t\n", &s0, s0.SubsetOf(s3))
+
+    // equality
+    s2Same := newSet(1, 3)
+    fmt.Printf("%v = s2: %t\n", s2Same, s2Same.Equals(s2))
+
+    // delete
+    s3.Remove(3)
+    fmt.Println("s3, 3 removed:", s3)
+}
+
+func newSet(ms ...int) *intsets.Sparse {
+    var set intsets.Sparse
+    for _, m := range ms {
+        set.Insert(m)
+    }
+    return &set
+}