AK: Make single pivot quick_sort guarantee a max stack depth of log(n)

- The change to quick_sort requires SimpleIterator to support
  assignment.
- Rename quick_sort to single_pivot_quick_sort to make it easier
  to choose a specific implementation (not based on signature).
- Ensure single_pivot_quick_sort does not copy the pivots
- Expand sorts_without_copy test case to cover both single and dual
  pivot implementations.

AK/Tests/TestQuickSort.cpp

@@ -46,13 +46,77 @@ TEST_CASE(sorts_without_copy)
     };
 
     Array<NoCopy, 64> array;
+
+    // Test the dual pivot quick sort.
     for (size_t i = 0; i < 64; ++i)
         array[i].value = (64 - i) % 32 + 32;
 
-    quick_sort(array, [](auto& a, auto& b) { return a.value < b.value; });
+    dual_pivot_quick_sort(array, 0, array.size() - 1, [](auto& a, auto& b) { return a.value < b.value; });
+
+    for (size_t i = 0; i < 63; ++i)
+        EXPECT(array[i].value <= array[i + 1].value);
+
+    // Test the single pivot quick sort.
+    for (size_t i = 0; i < 64; ++i)
+        array[i].value = (64 - i) % 32 + 32;
+
+    AK::single_pivot_quick_sort(&array[0], &array[64], [](auto& a, auto& b) { return a.value < b.value; });
 
     for (size_t i = 0; i < 63; ++i)
         EXPECT(array[i].value <= array[i + 1].value);
 }
 
+// This test case may fail to construct a worst-case input if the pivot choice
+// of the underlying quick_sort no longer matches the one used here.
+// So it provides no strong guarantees about the properties of quick_sort.
+TEST_CASE(maximum_stack_depth)
+{
+    const int size = 256;
+    int* data = new int[size];
+
+    for (int i = 0; i < size; i++) {
+        data[i] = i;
+    }
+
+    // Construct the data in such a way that the assumed pivot choice
+    // of (size / 2) causes the partitions to be of worst case size.
+    for (int i = 0; i < size / 2; i++) {
+        swap(data[i], data[i + (size - i) / 2]);
+    }
+
+    // Measure the depth of the call stack through the less_than argument
+    // of quick_sort as it gets copied for each recursive call.
+    struct DepthMeasurer {
+        int& max_depth;
+        int depth { 0 };
+        DepthMeasurer(int& max_depth)
+            : max_depth(max_depth)
+        {
+        }
+        DepthMeasurer(const DepthMeasurer& obj)
+            : max_depth(obj.max_depth)
+        {
+            depth = obj.depth + 1;
+            if (depth > max_depth) {
+                max_depth = depth;
+            }
+        }
+        bool operator()(int& a, int& b)
+        {
+            return a < b;
+        }
+    };
+
+    int max_depth = 0;
+    DepthMeasurer measurer(max_depth);
+    AK::single_pivot_quick_sort(data, data + size, measurer);
+
+    EXPECT(max_depth <= 64);
+
+    for (int i = 0; i < size; i++)
+        EXPECT(data[i] == i);
+
+    delete[] data;
+}
+
 TEST_MAIN(QuickSort)