Mutable dynamic arrays, heaps, and simple union find data structures (#585)

For writing examples, I wanted to have some standard mutable data
structures, currently:
- dynamic/resizable arrays
- min-heap (=> priority queue)
- union-find on integers

They all still need more documentation, testing and maybe some
additional functions (I only implemented what I needed).

---------

Co-authored-by: Jiří Beneš <[email protected]>

Author: marzipankaiser

examples/stdlib/acme.effekt

@@ -11,6 +11,7 @@ import char
 import dequeue
 import effekt
 import exception
+import heap
 import io
 import io/console
 import io/error
@@ -25,6 +26,7 @@ import process
 import queue
 import ref
 import regex
+import resizable_array
 import result
 import scanner
 import seq
@@ -33,5 +35,6 @@ import stream
 import string
 import test
 import tty
+import union_find
 
 def main() = ()

examples/stdlib/heap/heap.check

@@ -0,0 +1,6 @@
+HeapTests
+✓ simple heap sort on integers
+
+ 1 pass
+ 0 fail
+ 1 tests total

examples/stdlib/heap/heap.effekt

@@ -0,0 +1,27 @@
+import heap
+import test
+
+def main() = {
+  suite("HeapTests", false) {
+    test("simple heap sort on integers") {
+      with on[OutOfBounds].default { assertTrue(false); <> };
+      val h = heap[Int](box { (x: Int, y: Int) =>
+        if (x < y) {
+          Less()
+        } else Greater()  // hacky, should sometimes be Equal()
+      })
+      h.insert(12)
+      h.insert(10)
+      h.insert(7)
+      h.insert(11)
+      h.insert(14)
+      assert(h.deleteMin(), 7)
+      assert(h.deleteMin(), 10)
+      assert(h.deleteMin(), 11)
+      assert(h.deleteMin(), 12)
+      assert(h.deleteMin(), 14)
+      assert(h.size, 0)
+    }
+  };
+  ()
+}

examples/stdlib/resizable_array/resizable_array.check

@@ -0,0 +1,6 @@
+ResizableArrayTests
+✓ usage as stack
+
+ 1 pass
+ 0 fail
+ 1 tests total

examples/stdlib/resizable_array/resizable_array.effekt

@@ -0,0 +1,32 @@
+import resizable_array
+import test
+
+def main() = {
+  suite("ResizableArrayTests", false) {
+    test("usage as stack") {
+      with on[OutOfBounds].default { assertTrue(false, "out of bounds") }
+      val a = resizableArray()
+      a.add(1)
+      a.add(1)
+      a.add(2)
+      a.add(3)
+      a.add(13)
+      a.add(21)
+      a.add(34)
+      a.add(55)
+      assert(a.popRight(), 55)
+      assert(a.popRight(), 34)
+      assert(a.popRight(), 21)
+      assert(a.popRight(), 13)
+      a.add(5)
+      a.add(8)
+      assert(a.popRight(), 8)
+      assert(a.popRight(), 5)
+      assert(a.popRight(), 3)
+      assert(a.popRight(), 2)
+      assert(a.popRight(), 1)
+      assert(a.popRight(), 1)
+    }
+  };
+  ()
+}

examples/stdlib/union_find/union_find.check

@@ -0,0 +1,6 @@
+UnionFindTests
+✓ three elements
+
+ 1 pass
+ 0 fail
+ 1 tests total

examples/stdlib/union_find/union_find.effekt

@@ -0,0 +1,21 @@
+import union_find
+import test
+
+def main() = {
+  suite("UnionFindTests", false) {
+    test("three elements") {
+      with on[MissingValue].default { assertTrue(false, "MissingValue exception") }
+      val u = unionFind()
+      val a = u.makeSet()
+      val b = u.makeSet()
+      val c = u.makeSet()
+      assert(u.find(a), a)
+      assert(u.find(b), b)
+      assert(u.find(c), c)
+      u.union(a,b)
+      assert(u.find(a), u.find(b))
+      assert(u.find(c), c)
+    }
+  };
+  ()
+}

libraries/common/heap.effekt

@@ -0,0 +1,103 @@
+module heap
+import resizable_array
+
+/// Resizable 2-ary min-heap, backed by a resizable array
+/// `cmp` defines the ordering of elements
+record Heap[T](rawContents: ResizableArray[T], cmp: (T, T) => Ordering at {})
+
+/// Make a new Heap with the given comparison operation
+def heap[T](cmp: (T,T) => Ordering at {}) = 
+  Heap[T](resizableArray(), cmp)
+
+/// Make a new Heap with the given comparison operation and initial capacity
+def heap[T](cmp: (T,T) => Ordering at {}, capacity: Int) = 
+  Heap[T](resizableArray(capacity), cmp)
+
+namespace internal {
+  def left(idx: Int) = 2 * idx + 1
+  def right(idx: Int) = 2 * idx + 2
+  def parent(idx: Int) = (idx - 1) / 2
+
+  def bubbleUp[A](heap: Heap[A], idx: Int) = {
+    val arr = heap.rawContents
+    arr.boundsCheck(idx) // idx > parent(idx), parent(parent(idx)) etc
+
+    def go(idx: Int): Unit = {
+      if (idx > 0 and (heap.cmp)(arr.unsafeGet(parent(idx)), arr.unsafeGet(idx)) is Greater()) {
+        arr.unsafeSwap(parent(idx), idx)
+        go(parent(idx))
+      }
+    }
+    go(idx)
+  }
+  def sinkDown[A](heap: Heap[A], idx: Int) = {
+    val arr = heap.rawContents
+
+    def infixLt(x: A, y: A) = {
+      if ((heap.cmp)(x,y) is Less()) { true } else { false }
+    }
+    
+    def go(idx: Int): Unit = {
+      if (right(idx) < arr.size) {
+        val v = arr.unsafeGet(idx)
+        val l = arr.unsafeGet(left(idx))
+        val r = arr.unsafeGet(right(idx))
+        if (l < v && r < v) {
+          // swap with the smaller one
+          if (l < r) {
+            arr.unsafeSwap(left(idx), idx)
+            go(left(idx))
+          } else {
+            arr.unsafeSwap(right(idx), idx)
+            go(right(idx))
+          }
+        } else if (l < v) {
+          arr.unsafeSwap(left(idx), idx)
+          go(left(idx))
+        } else if (r < v) {
+          arr.unsafeSwap(right(idx), idx)
+          go(right(idx))
+        }
+      } else if (left(idx) < arr.size) {
+        if (arr.unsafeGet(left(idx)) < arr.unsafeGet(idx)) {
+          arr.unsafeSwap(left(idx), idx)
+          go(left(idx))
+        }
+      } // else: we are at the bottom
+    }
+    go(idx)
+  }
+}
+
+/// Insert value into heap
+///
+/// O(log n) worst case if capacity suffices, O(1) average
+def insert[T](heap: Heap[T], value: T): Unit = {
+  with on[OutOfBounds].panic();
+  val idx = heap.rawContents.add(value)
+  internal::bubbleUp(heap, idx)
+}
+
+/// find and return (but not remove) the minimal element in this heap
+///
+/// O(1)
+def findMin[T](heap: Heap[T]): T / Exception[OutOfBounds] = {
+  heap.rawContents.get(0)
+}
+
+/// find and remove the minimal element in this heap
+///
+/// O(log n)
+def deleteMin[T](heap: Heap[T]): T / Exception[OutOfBounds] = {
+  val res = heap.rawContents.get(0)
+  heap.rawContents.unsafeSet(0, heap.rawContents.popRight())
+  internal::sinkDown(heap, 0)
+  res
+}
+
+/// Number of elements in the heap
+///
+/// O(1)
+def size[T](heap: Heap[T]): Int = {
+  heap.rawContents.size
+}