From f55b69af920152439ca5c629b2f4fb572b59d1db Mon Sep 17 00:00:00 2001
From: Parseluni <deliagaiaglow@gmail.com>
Date: Wed, 24 Nov 2021 21:29:06 -0800
Subject: [PATCH 1/2] Completed

---
 heaps/heap_sort.py     | 18 +++++++++++++----
 heaps/min_heap.py      | 45 ++++++++++++++++++++++++++++++++++--------
 tests/test_heapsort.py |  3 +++
 3 files changed, 54 insertions(+), 12 deletions(-)

diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..19b5cc1 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,18 @@
-
+from heaps.min_heap import MinHeap
 
 def heap_sort(list):
     """ This method uses a heap to sort an array.
-        Time Complexity:  ?
-        Space Complexity: ?
+        Time Complexity:  O(n log n)
+        Space Complexity: O(n)
     """
-    pass
\ No newline at end of file
+    heap = MinHeap()
+
+    for num in list:
+        heap.add(num)
+    
+    index = 0
+    while not heap.empty():
+        list[index] = heap.remove()
+        index += 1
+
+    return list
\ No newline at end of file
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index 0095872..4303a3b 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -11,12 +11,11 @@ def __repr__(self):
         return str(self.value)
 
 
-
 class MinHeap:
 
     def __init__(self):
         self.store = []
-
+        self.size = 0
 
     def add(self, key, value = None):
         """ This method adds a HeapNode instance to the heap
@@ -24,7 +23,12 @@ def add(self, key, value = None):
             Time Complexity: ?
             Space Complexity: ?
         """
-        pass
+        if value == None:
+            value = key
+
+        self.store.append(HeapNode(key, value))
+        self.heap_up(len(self.store) - 1)
+        self.size += 1
 
     def remove(self):
         """ This method removes and returns an element from the heap
@@ -32,10 +36,17 @@ def remove(self):
             Time Complexity: ?
             Space Complexity: ?
         """
-        pass
+        if self.empty():
+            return None
+
+        self.swap(0, len(self.store) - 1)
+        min_node = self.store.pop()
+        self.heap_down(0)
+        self.size -= 1
+
+        return min_node.value
 
 
-    
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
         """
@@ -49,7 +60,7 @@ def empty(self):
             Time complexity: ?
             Space complexity: ?
         """
-        pass
+        return self.size == 0
 
 
     def heap_up(self, index):
@@ -62,7 +73,12 @@ def heap_up(self, index):
             Time complexity: ?
             Space complexity: ?
         """
-        pass
+        parent_node_index = (index - 1) // 2
+
+        if index:
+            if self.store[index].key < self.store[parent_node_index].key:
+                self.swap(index, parent_node_index)
+                self.heap_up(parent_node_index)
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -70,7 +86,20 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
+        left_child = 2 * index + 1
+        right_child = 2 * index + 2
+
+        if left_child < len(self.store):
+            if right_child >= len(self.store):
+                min_child = left_child
+            elif self.store[left_child].key < self.store[right_child].key:
+                min_child = left_child
+            else:
+                min_child = right_child
+            
+            if self.store[index].key > self.store[min_child].key:
+                self.swap(index, min_child)
+                self.heap_down(min_child)
 
     
     def swap(self, index_1, index_2):
diff --git a/tests/test_heapsort.py b/tests/test_heapsort.py
index 51b0c2e..5519045 100644
--- a/tests/test_heapsort.py
+++ b/tests/test_heapsort.py
@@ -1,3 +1,6 @@
+"""
+O(n log n)
+"""
 from heaps.heap_sort import heap_sort
 
 def test_it_sorts_an_empty_list():

From 09c889a5005a4de3dc81d1282cabe086fa0983d4 Mon Sep 17 00:00:00 2001
From: Parseluni <deliagaiaglow@gmail.com>
Date: Wed, 24 Nov 2021 21:33:56 -0800
Subject: [PATCH 2/2] Big O added

---
 heaps/min_heap.py | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index 4303a3b..3559607 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -20,8 +20,8 @@ def __init__(self):
     def add(self, key, value = None):
         """ This method adds a HeapNode instance to the heap
             If value == None the new node's value should be set to key
-            Time Complexity: ?
-            Space Complexity: ?
+            Time Complexity: O(log n)
+            Space Complexity: O(1)
         """
         if value == None:
             value = key
@@ -33,8 +33,8 @@ def add(self, key, value = None):
     def remove(self):
         """ 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)
         """
         if self.empty():
             return None
@@ -57,8 +57,8 @@ def __str__(self):
 
     def empty(self):
         """ This method returns true if the heap is empty
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(1)
+            Space complexity: O(1)
         """
         return self.size == 0
 
@@ -70,8 +70,8 @@ def heap_up(self, index):
             property is reestablished.
             
             This could be **very** helpful for the add method.
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(log n)
+            Space complexity: O(1)
         """
         parent_node_index = (index - 1) // 2