From 8066ec2a000700870aae2fdcc068baaa2c35e86b Mon Sep 17 00:00:00 2001
From: Citlalli I Zarate <37793116+MiffyBruna@users.noreply.github.com>
Date: Tue, 21 Jun 2022 16:56:29 -0700
Subject: [PATCH 1/2] All tests pass

---
 heaps/heap_sort.py | 15 +++++++++---
 heaps/min_heap.py  | 59 ++++++++++++++++++++++++++++++++++++----------
 2 files changed, 58 insertions(+), 16 deletions(-)

diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..95d0eab 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,17 @@
-
-
+from heaps.min_heap import MinHeap
 def heap_sort(list):
     """ This method uses a heap to sort an array.
         Time Complexity:  ?
         Space Complexity: ?
     """
-    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
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..39bd867 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -1,3 +1,5 @@
+
+
 class HeapNode:
   
     def __init__(self, key, value):
@@ -19,18 +21,29 @@ 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(log n)
         """
-        pass
+        if value == None:
+            value = key
+        new_node =HeapNode(key, value)
+    
+        self.store.append(new_node)
+        self.heap_up(len(self.store) - 1)
+
 
     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(log n)
         """
-        pass
+        if len(self.store) ==0:
+            return None
+        self.swap(0, len(self.store) -1)
+        min = self.store.pop()
+        self.heap_down(0)
+        return min.value
 
 
     
@@ -44,10 +57,10 @@ 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)
         """
-        pass
+        return len(self.store) == 0
 
 
     def heap_up(self, index):
@@ -57,10 +70,16 @@ 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(log n)
         """
-        pass
+        if index == 0:
+            return
+
+        parent = (index -1) // 2
+        if self.store[parent].key > self.store[index].key:
+            self.swap(index, parent)
+            self.heap_up(parent)
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -68,7 +87,21 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
+        left_child = index * 2 + 1
+        right_child = index * 2 + 2
+
+        if left_child < len(self.store):
+            if right_child < len(self.store):
+                if self.store[left_child].key < self.store[right_child].key:
+                    child = left_child
+                else:
+                    child = right_child
+            else:
+                child = left_child
+
+            if self.store[child].key < self.store[index].key:
+                self.swap(child, index)
+                self.heap_down(child)
 
     
     def swap(self, index_1, index_2):

From aacfbc650408c50a68331925454fa1ecd6900b3d Mon Sep 17 00:00:00 2001
From: Citlalli I Zarate <37793116+MiffyBruna@users.noreply.github.com>
Date: Tue, 21 Jun 2022 17:02:04 -0700
Subject: [PATCH 2/2] Added complexity to heap_sort

---
 heaps/heap_sort.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 95d0eab..83f2966 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,8 @@
 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 logn)
+        Space Complexity: O(n)
     """
     heap = MinHeap()