From 7fa7c5bae06440a8544afceb5e2ee8b363906f3d Mon Sep 17 00:00:00 2001
From: Amos Paribocci <aparibocci@gmail.com>
Date: Mon, 6 Feb 2023 18:45:44 +0100
Subject: [PATCH 1/2] Adding max-heap implementation

---
 data_structures/heaps/max_heap.rb      | 87 ++++++++++++++++++++++++++
 data_structures/heaps/max_heap_test.rb | 36 +++++++++++
 2 files changed, 123 insertions(+)
 create mode 100644 data_structures/heaps/max_heap.rb
 create mode 100644 data_structures/heaps/max_heap_test.rb

diff --git a/data_structures/heaps/max_heap.rb b/data_structures/heaps/max_heap.rb
new file mode 100644
index 0000000..7996f7c
--- /dev/null
+++ b/data_structures/heaps/max_heap.rb
@@ -0,0 +1,87 @@
+##
+# This class represents an array-backed max-heap.
+
+class MaxHeap
+
+  attr_reader :arr
+  attr_accessor :heap_size
+
+  ##
+  # Creates a new max-heap using the provided collection of initial values, if provided (empty by default).
+  # Note: a clone of the input collection is created to avoid alterations to the input.
+
+  def initialize(elements = [])
+    @arr = [0] + elements.map(&:clone)
+    @heap_size = arr.size - 1
+    for i in ((arr.size / 2).floor).downto 1
+      max_heapify(i)
+    end
+  end
+
+  def to_array
+    return arr[1..heap_size].map(&:clone)
+  end
+
+  def empty?
+    return heap_size == 0
+  end
+
+  def max
+    return nil if empty?
+    return @arr[1]
+  end
+
+  def extract_max
+    return nil if empty?
+    m = max
+    @arr[1] = @arr[heap_size]
+    @heap_size -= 1
+    max_heapify(1)
+    return m
+  end
+
+  def insert(k)
+    @heap_size += 1
+    @arr[heap_size] = -Float::INFINITY
+    increase_to(heap_size, k)
+  end
+
+  private
+  def max_heapify(i)
+    l = left(i)
+    r = right(i)
+    m = i
+    if l <= heap_size && arr[l] > arr[i]
+      m = l
+    end
+    if r <= heap_size && arr[r] > arr[m]
+      m = r
+    end
+    if m != i
+      arr[i], arr[m] = arr[m], arr[i]
+      max_heapify(m)
+    end
+  end
+
+  def increase_to(i, k)
+    raise ArgumentError.new('MaxHeap#increase_to does not support lower values for the key') if arr[i] > k
+    @arr[i] = k
+    j = i
+    while parent(j) > 0 && arr[parent(j)] < arr[j]
+      arr[j], arr[parent(j)] = arr[parent(j)], arr[j]
+      j = parent(j)
+    end
+  end
+
+  def parent(i)
+    return (i / 2).floor
+  end
+
+  def left(i)
+    return 2*i
+  end
+
+  def right(i)
+    return 2*i + 1
+  end
+end
\ No newline at end of file
diff --git a/data_structures/heaps/max_heap_test.rb b/data_structures/heaps/max_heap_test.rb
new file mode 100644
index 0000000..502fe6f
--- /dev/null
+++ b/data_structures/heaps/max_heap_test.rb
@@ -0,0 +1,36 @@
+require 'minitest/autorun'
+require_relative 'max_heap'
+
+class TestMaxHeap < Minitest::Test
+  def test_to_array_returns_array_representation
+    heap = MaxHeap.new([4, 1, 3, 3, 16, 9, 10, 14, 8, 7])
+    assert heap.to_array == [16, 14, 10, 8, 7, 9, 3, 3, 4, 1]
+  end
+
+  def test_empty_returns_true_for_empty_heap
+    heap = MaxHeap.new
+    assert heap.empty?
+  end
+
+  def test_empty_returns_false_for_non_empty_heap
+    heap = MaxHeap.new([1])
+    assert !heap.empty?
+  end
+
+  def test_max_returns_maximum_heap_element
+    heap = MaxHeap.new([4, 1, 3])
+    assert heap.max == 4
+  end
+
+  def test_extract_max_returns_and_removes_maximum_heap_element
+    heap = MaxHeap.new([4, 1, 3])
+    assert heap.extract_max == 4
+    assert heap.to_array == [3, 1]
+  end
+
+  def test_insert_adds_element_to_appropriate_position
+    heap = MaxHeap.new([4, 1, 3])
+    heap.insert(2)
+    assert heap.to_array == [4, 2, 3, 1]
+  end
+end

From fb1f5dd67936be0919f25578b27fc8b246585f68 Mon Sep 17 00:00:00 2001
From: Amos Paribocci <aparibocci@gmail.com>
Date: Mon, 6 Feb 2023 18:52:42 +0100
Subject: [PATCH 2/2] Adding unit tests for element not found in max-heap

---
 data_structures/heaps/max_heap_test.rb | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/data_structures/heaps/max_heap_test.rb b/data_structures/heaps/max_heap_test.rb
index 502fe6f..ef0bbf7 100644
--- a/data_structures/heaps/max_heap_test.rb
+++ b/data_structures/heaps/max_heap_test.rb
@@ -22,12 +22,22 @@ class TestMaxHeap < Minitest::Test
     assert heap.max == 4
   end
 
+  def test_max_returns_nil_if_empty_heap
+    heap = MaxHeap.new
+    assert heap.max.nil?
+  end
+
   def test_extract_max_returns_and_removes_maximum_heap_element
     heap = MaxHeap.new([4, 1, 3])
     assert heap.extract_max == 4
     assert heap.to_array == [3, 1]
   end
 
+  def test_extract_max_returns_nil_if_empty_heap
+    heap = MaxHeap.new
+    assert heap.extract_max.nil?
+  end
+
   def test_insert_adds_element_to_appropriate_position
     heap = MaxHeap.new([4, 1, 3])
     heap.insert(2)