From 2adf0250e3f6d94322a9c9c92be2f2e11a09cefa Mon Sep 17 00:00:00 2001
From: Taylor Tompkins <taylormililani@gmail.com>
Date: Thu, 22 Jul 2021 16:37:51 -0700
Subject: [PATCH 1/2] tests passing

---
 lib/min_heap.rb | 52 ++++++++++++++++++++++++++++++++++++-------------
 1 file changed, 38 insertions(+), 14 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..02d1625 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,24 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
-  def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+  # Time Complexity: O(log n)
+  # Space Complexity: O(1)
+  def add(key, value)
+    node = HeapNode.new(key, value)
+    @store << node
+    heap_up(@store.length-1)
   end
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n)
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+    swap(0, @store.length-1)
+    removed = @store.pop 
+    heap_down(0)
+    return removed.value
   end
 
 
@@ -44,10 +50,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(n)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    @store.empty?
   end
 
   private
@@ -55,17 +61,35 @@ def empty?
   # This helper method takes an index and
   #  moves it up the heap, if it is less than it's parent node.
   #  It could be **very** helpful for the add method.
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(n)
+  # Space complexity: O(1)
   def heap_up(index)
-    
+    return if index == 0
+
+    parent = (index - 1) / 2
+
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      heap_up(parent)
+    end
   end
 
   # This helper method takes an index and 
   #  moves it up the heap if it's smaller
   #  than it's parent node.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left = index * 2 + 1
+    right = index * 2 + 2
+
+    if right < @store.length
+      min = @store[left].key < @store[right].key ? left : right
+      if @store[index].key > @store[min].key
+        swap(index, min)
+        heap_down(min)
+      end
+    elsif left < @store.length && @store[index].key > @store[left].key
+      swap(index, left)
+    end
   end
 
   # If you want a swap method... you're welcome

From a0aa3bfb11b24473251d448aab16cdc75fb20591 Mon Sep 17 00:00:00 2001
From: Taylor Tompkins <taylormililani@gmail.com>
Date: Thu, 22 Jul 2021 17:03:15 -0700
Subject: [PATCH 2/2] forgot heapsort

---
 lib/heap_sort.rb      | 24 +++++++++++++++++++++++-
 test/heapsort_test.rb |  8 ++++----
 2 files changed, 27 insertions(+), 5 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..ff2009e 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -4,5 +4,27 @@
 # Time Complexity:  ?
 # Space Complexity: ?
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  n = list.length
+  a = [nil] + list
+
+  (n/2).downto(1) do |i|
+    heapify(a, i, n)
+  end
+
+  while n > 1
+    a[1], a[n] = a[n], a[1]
+    n -= 1
+    heapify(a, 1, n)
+  end
+  a.drop(1)
+end
+
+def heapify(list, parent, limit)
+  root = list[parent]
+  while (child=2 * parent) <= limit
+    child += 1 if child < limit && list[child] < list[child+1]
+    break if root >= list[child]
+    list[parent], parent = list[child], child
+  end
+  list[parent] = root
 end
\ No newline at end of file
diff --git a/test/heapsort_test.rb b/test/heapsort_test.rb
index 34402ac..76e3fdc 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,12 +1,12 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heap_sort" do
   it "sorts an empty array" do
     # Arrange 
     list = []
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal []
@@ -17,7 +17,7 @@
     list = [5]
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal [5]
@@ -28,7 +28,7 @@
     list = [5, 27, 3, 16, -50]
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]