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/Iterator.h

@@ -78,6 +78,13 @@ public:
     constexpr const ValueType* operator->() const { return &m_container[m_index]; }
     constexpr ValueType* operator->() { return &m_container[m_index]; }
 
+    SimpleIterator& operator=(const SimpleIterator& other)
+    {
+        m_index = other.m_index;
+        return *this;
+    }
+    SimpleIterator(const SimpleIterator& obj) = default;
+
 private:
     static constexpr SimpleIterator begin(Container& container) { return { container, 0 }; }
     static constexpr SimpleIterator end(Container& container)

AK/QuickSort.h

@@ -86,35 +86,50 @@ void dual_pivot_quick_sort(Collection& col, int start, int end, LessThan less_th
 }
 
 template<typename Iterator, typename LessThan>
-void quick_sort(Iterator start, Iterator end, LessThan less_than)
+void single_pivot_quick_sort(Iterator start, Iterator end, LessThan less_than)
 {
-    int size = end - start;
-    if (size <= 1)
-        return;
+    for (;;) {
+        int size = end - start;
+        if (size <= 1)
+            return;
 
-    int pivot_point = size / 2;
-    auto pivot = *(start + pivot_point);
+        int pivot_point = size / 2;
+        if (pivot_point)
+            swap(*(start + pivot_point), *start);
 
-    if (pivot_point)
-        swap(*(start + pivot_point), *start);
+        auto&& pivot = *start;
 
-    int i = 1;
-    for (int j = 1; j < size; ++j) {
-        if (less_than(*(start + j), pivot)) {
-            swap(*(start + j), *(start + i));
-            ++i;
+        int i = 1;
+        for (int j = 1; j < size; ++j) {
+            if (less_than(*(start + j), pivot)) {
+                swap(*(start + j), *(start + i));
+                ++i;
+            }
+        }
+
+        swap(*start, *(start + i - 1));
+        // Recur into the shorter part of the remaining data
+        // to ensure a stack depth of at most log(n).
+        if (i > size / 2) {
+            single_pivot_quick_sort(start + i, end, less_than);
+            end = start + i - 1;
+        } else {
+            single_pivot_quick_sort(start, start + i - 1, less_than);
+            start = start + i;
         }
     }
-
-    swap(*start, *(start + i - 1));
-    quick_sort(start, start + i - 1, less_than);
-    quick_sort(start + i, end, less_than);
 }
 
 template<typename Iterator>
 void quick_sort(Iterator start, Iterator end)
 {
-    quick_sort(start, end, [](auto& a, auto& b) { return a < b; });
+    single_pivot_quick_sort(start, end, [](auto& a, auto& b) { return a < b; });
+}
+
+template<typename Iterator, typename LessThan>
+void quick_sort(Iterator start, Iterator end, LessThan less_than)
+{
+    single_pivot_quick_sort(start, end, move(less_than));
 }
 
 template<typename Collection, typename LessThan>

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)