From f5252f7ac3cf642c0cc8dc78905f07439c1c368a Mon Sep 17 00:00:00 2001
From: Yinjing Lin <lyingjin@amazon.com>
Date: Wed, 5 May 2021 23:34:26 -0700
Subject: [PATCH 1/3] heap_sort not complete

---
 lib/heap_sort.rb      | 13 +++++++----
 lib/min_heap.rb       | 51 ++++++++++++++++++++++++++++++++-----------
 test/heapsort_test.rb |  2 +-
 3 files changed, 48 insertions(+), 18 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..fcdc122 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,13 @@
 
-
 # This method uses a heap to sort an array.
 # Time Complexity:  ?
 # Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
-end
\ No newline at end of file
+def heapsort(list)
+  return list if list.empty?
+  heap = MinHeap.new
+
+  list.each do |n|
+    heap.add(n)
+  end
+  return heap.store.map {|node| node.key}
+end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..972a5ec 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -8,24 +8,39 @@ def initialize(key, value)
 end
 
 class MinHeap
+  attr_reader :store
 
   def initialize
     @store = []
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn)
+  # Space Complexity: O(1)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    if @store.empty?
+      @store << HeapNode.new(key, value)
+    else
+      new_i = @store.length
+      @store[new_i] = HeapNode.new(key, value)
+      heap_up(new_i)
+    end
+    return key
   end
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn)
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    min = @store.min_by {|node| node.key}
+    index = @store.find_index {|node| node.key == min.key}
+    value = @store[index].value
+
+    swap(index, -1)
+    @store.delete_at(-1)
+    heap_down(index)
+    return value
   end
 
 
@@ -44,10 +59,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(0)
+  # Space complexity: O(0)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
@@ -55,17 +70,27 @@ 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(logn)
+  # Space complexity: O(0)
   def heap_up(index)
-    
+    while @store[index].key < @store[(index - 1)/2].key
+      swap(index, (index - 1)/2)
+      index = (index - 1)/2
+      return if index == 0
+    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..."
+    if @store[index * 2 + 1] != nil
+      while @store[index].key > @store[index * 2 + 1].key
+        swap(index, index * 2 + 1)
+        index = index * 2 + 1
+        return if @store[index * 2 + 1].nil?
+      end
+    end
   end
 
   # If you want a swap method... you're welcome
diff --git a/test/heapsort_test.rb b/test/heapsort_test.rb
index 34402ac..7ce79b7 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
     # Arrange 
     list = []

From 6611cd713bdfec744514e621a50c66fe1fa665e1 Mon Sep 17 00:00:00 2001
From: Yinjing Lin <lyingjin@amazon.com>
Date: Thu, 6 May 2021 12:04:18 -0700
Subject: [PATCH 2/3] fix some bugs

---
 lib/min_heap.rb | 22 +++++++++-------------
 1 file changed, 9 insertions(+), 13 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 972a5ec..d07703d 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -18,13 +18,9 @@ def initialize
   # Time Complexity: O(logn)
   # Space Complexity: O(1)
   def add(key, value = key)
-    if @store.empty?
-      @store << HeapNode.new(key, value)
-    else
-      new_i = @store.length
-      @store[new_i] = HeapNode.new(key, value)
-      heap_up(new_i)
-    end
+    new_i = @store.length
+    @store[new_i] = HeapNode.new(key, value)
+    heap_up(new_i)
     return key
   end
 
@@ -33,13 +29,11 @@ def add(key, value = key)
   # Time Complexity: O(logn)
   # Space Complexity: O(1)
   def remove()
-    min = @store.min_by {|node| node.key}
-    index = @store.find_index {|node| node.key == min.key}
-    value = @store[index].value
+    value = @store[0].value
 
-    swap(index, -1)
+    swap(0, -1)
     @store.delete_at(-1)
-    heap_down(index)
+    heap_down(0)
     return value
   end
 
@@ -73,7 +67,7 @@ def empty?
   # Time complexity: O(logn)
   # Space complexity: O(0)
   def heap_up(index)
-    while @store[index].key < @store[(index - 1)/2].key
+    while index > 0 && @store[index].key < @store[(index - 1)/2].key
       swap(index, (index - 1)/2)
       index = (index - 1)/2
       return if index == 0
@@ -87,6 +81,8 @@ def heap_down(index)
     if @store[index * 2 + 1] != nil
       while @store[index].key > @store[index * 2 + 1].key
         swap(index, index * 2 + 1)
+        swap(index, index * 2 + 2) if @store[index * 2 + 2] != nil && @store[index].key > @store[index * 2 + 2].key
+        swap(index * 2 + 1, index * 2 + 2) if @store[index * 2 + 2] != nil && @store[index * 2 + 1].key > @store[index * 2 + 2].key
         index = index * 2 + 1
         return if @store[index * 2 + 1].nil?
       end

From ca22fffc311b1351d9b79fa39bf756392c655d1b Mon Sep 17 00:00:00 2001
From: Yinjing Lin <lyingjin@amazon.com>
Date: Thu, 6 May 2021 14:36:08 -0700
Subject: [PATCH 3/3] pass all tests

---
 lib/heap_sort.rb | 11 ++++++++---
 lib/min_heap.rb  |  1 -
 2 files changed, 8 insertions(+), 4 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index fcdc122..75732a0 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,7 +1,7 @@
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  O(nlogn)
+# Space Complexity: O(n)
 def heapsort(list)
   return list if list.empty?
   heap = MinHeap.new
@@ -9,5 +9,10 @@ def heapsort(list)
   list.each do |n|
     heap.add(n)
   end
-  return heap.store.map {|node| node.key}
+
+  list.length.times do |i|
+    list[i] = heap.remove
+  end
+
+  return list
 end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index d07703d..4151604 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -82,7 +82,6 @@ def heap_down(index)
       while @store[index].key > @store[index * 2 + 1].key
         swap(index, index * 2 + 1)
         swap(index, index * 2 + 2) if @store[index * 2 + 2] != nil && @store[index].key > @store[index * 2 + 2].key
-        swap(index * 2 + 1, index * 2 + 2) if @store[index * 2 + 2] != nil && @store[index * 2 + 1].key > @store[index * 2 + 2].key
         index = index * 2 + 1
         return if @store[index * 2 + 1].nil?
       end