diff options
| -rw-r--r-- | Scala/funsets/src/main/scala/funsets/FunSets.scala | 22 | ||||
| -rw-r--r-- | Scala/funsets/src/test/scala/funsets/FunSetSuite.scala | 60 |
2 files changed, 62 insertions, 20 deletions
diff --git a/Scala/funsets/src/main/scala/funsets/FunSets.scala b/Scala/funsets/src/main/scala/funsets/FunSets.scala index 15a6bfc..99b0748 100644 --- a/Scala/funsets/src/main/scala/funsets/FunSets.scala +++ b/Scala/funsets/src/main/scala/funsets/FunSets.scala @@ -20,25 +20,25 @@ object FunSets { /** * Returns the set of the one given element. */ - def singletonSet(elem: Int): Set = (x => x == elem) + def singletonSet(elem: Int): Set = x => x == elem /** * Returns the union of the two given sets, * the sets of all elements that are in either `s` or `t`. */ - def union(s: Set, t: Set): Set = (x => s(x) | t(x)) + def union(s: Set, t: Set): Set = x => s(x) | t(x) /** * Returns the intersection of the two given sets, * the set of all elements that are both in `s` and `t`. */ - def intersect(s: Set, t: Set): Set = (x => s(x) & t(x)) + def intersect(s: Set, t: Set): Set = x => s(x) & t(x) /** * Returns the difference of the two given sets, * the set of all elements of `s` that are not in `t`. */ - def diff(s: Set, t: Set): Set = (x => s(x) & !t(x)) + def diff(s: Set, t: Set): Set = x => s(x) & !t(x) /** * Returns the subset of `s` for which `p` holds. @@ -56,23 +56,25 @@ object FunSets { */ def forall(s: Set, p: Int => Boolean): Boolean = { def iter(a: Int): Boolean = { - if (???) ??? - else if (???) ??? - else iter(???) + if (a > bound) true + else if (contains(s, a) && !p(a)) false + else iter(a + 1) } - iter(???) + iter(-bound) } /** * Returns whether there exists a bounded integer within `s` * that satisfies `p`. */ - def exists(s: Set, p: Int => Boolean): Boolean = ??? + // elements of s do NOT all NOT satisfy p + def exists(s: Set, p: Int => Boolean): Boolean = !forall(s, x => !p(x)) /** * Returns a set transformed by applying `f` to each element of `s`. */ - def map(s: Set, f: Int => Int): Set = ??? + // x is in S' if exists y in S so that f(y) = x + def map(s: Set, f: Int => Int): Set = x => exists(s, y => f(y) == x) /** * Displays the contents of a set diff --git a/Scala/funsets/src/test/scala/funsets/FunSetSuite.scala b/Scala/funsets/src/test/scala/funsets/FunSetSuite.scala index 7c3fd53..4ca61a5 100644 --- a/Scala/funsets/src/test/scala/funsets/FunSetSuite.scala +++ b/Scala/funsets/src/test/scala/funsets/FunSetSuite.scala @@ -77,6 +77,8 @@ class FunSetSuite extends FunSuite { val s1 = singletonSet(1) val s2 = singletonSet(2) val s3 = singletonSet(3) + def boundedSet(m: Int, n: Int): Set = x => x >= m && x <= n + val v13 = boundedSet(1,3) } /** @@ -165,16 +167,54 @@ class FunSetSuite extends FunSuite { test("filter") { new TestSets { - val s = filter(s1, (x => x == 1)) - assert(!contains(s, 0), "Filter none") - assert(contains(s, 1), "Filter 1") - assert(!contains(s, 2), "Filter none") - assert(!contains(s, 3), "Filter none") - val v = filter(s1, (x => x == 0)) - assert(!contains(v, 0), "Filter none") - assert(!contains(v, 1), "Filter none") - assert(!contains(v, 2), "Filter none") - assert(!contains(v, 3), "Filter none") + val s = filter(s1, x => x == 1) + assert(!contains(s, 0), "Filter not s 0") + assert(contains(s, 1), "Filter s 1") + assert(!contains(s, 2), "Filter not s 2") + assert(!contains(s, 3), "Filter not s3") + val v = filter(s1, x => x == 0) + assert(!contains(v, 0), "Filter not v 0") + assert(!contains(v, 1), "Filter not v 1") + assert(!contains(v, 2), "Filter not v 2") + assert(!contains(v, 3), "Filter not v 3") + } + } + + test("forall") { + new TestSets { + assert(forall(s1, x => x == 1), "forall 1") + assert(forall(s2, x => x == 2), "forall 2") + assert(forall(s3, x => x == 3), "forall 3") + assert(!forall(s1, x => x == 0), "forall not s1 0") + assert(!forall(s2, x => x == 0), "forall not s2 0") + assert(!forall(s3, x => x == 0), "forall not s3 0") + assert(forall(s1, v13), "s1 v13") + assert(forall(s2, v13), "s2 v13") + assert(forall(s3, v13), "s3 v13") + } + } + + test("exists") { + new TestSets { + assert(exists(v13, x => x == 1), "exists 1") + assert(exists(v13, x => x == 2), "exists 1") + assert(exists(v13, x => x == 3), "exists 1") + assert(!exists(v13, x => x == 0), "exists not 0") + assert(!exists(v13, x => x == 4), "exists not 4") + } + } + + test("map") { + new TestSets { + val x = map(v13, x => x * 3) + assert(contains(x, 3), "map 1") + assert(!contains(x, 4), "map 2") + assert(!contains(x, 5), "map 3") + assert(contains(x, 6), "map 4") + assert(!contains(x, 7), "map 5") + assert(!contains(x, 8), "map 6") + assert(contains(x, 9), "map 7") + assert(!contains(x, 10), "map 8") } } } |