From ce2097ba5eb3c72592216a91947c19c87aa5f369 Mon Sep 17 00:00:00 2001
From: Jessica <jessica.homet@gmail.com>
Date: Thu, 19 Sep 2019 15:43:13 -0700
Subject: [PATCH 1/3] implement min_heap

---
 lib/min_heap.rb | 35 ++++++++++++++++++++++++++++++++---
 1 file changed, 32 insertions(+), 3 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..903165c 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -17,7 +17,9 @@ def initialize
   # Time Complexity: ?
   # Space Complexity: ?
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    heap_node = HeapNode.new(key, value)
+    @store << heap_node
+    heap_up(@store.length - 1)
   end
 
   # This method removes and returns an element from the heap
@@ -25,7 +27,10 @@ def add(key, value = key)
   # Time Complexity: ?
   # Space Complexity: ?
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    swap(0, @store.length - 1)
+    removed = @store.pop
+    heap_down(0)
+    return removed.value
   end
 
 
@@ -58,14 +63,38 @@ def empty?
   # Time complexity: ?
   # Space complexity: ?
   def heap_up(index)
+    return if index == 0
+    current_index = index
+    parent_index = (index - 1) / 2
     
+    return if @store[current_index].key > @store[parent_index].key
+      
+    swap(current_index, parent_index)
+    heap_up(parent_index)
   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..."
+    current_index = index
+    left_child_index = index * 2 + 1
+    right_child_index = index * 2 + 2
+
+    return unless @store[left_child_index] # we're at the bottom of the tree (could also use length)
+
+    if @store[right_child_index]
+      if @store[left_child_index].key < @store[right_child_index].key
+        swap(current_index, left_child_index)
+        heap_down(left_child_index)
+      else
+        swap(current_index, right_child_index)
+        heap_down(right_child_index)
+      end
+    else
+      swap(current_index, left_child_index)
+      return
+    end
   end
 
   # If you want a swap method... you're welcome

From fc093be29be368897c7187710117dc4354fe2742 Mon Sep 17 00:00:00 2001
From: Jessica <jessica.homet@gmail.com>
Date: Thu, 19 Sep 2019 15:52:13 -0700
Subject: [PATCH 2/3] add time and space complexity

---
 lib/min_heap.rb | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 903165c..19fe97f 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,8 +14,8 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(n(log(n))) where n is the number of nodes in the heap
+  # Space Complexity: O(1)
   def add(key, value = key)
     heap_node = HeapNode.new(key, value)
     @store << heap_node
@@ -24,8 +24,8 @@ def add(key, value = key)
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(nlogn) where n is the number of elements in the heap
+  # Space Complexity: O(1)
   def remove()
     swap(0, @store.length - 1)
     removed = @store.pop
@@ -60,8 +60,8 @@ 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(nlogn) where n is the number of nodes in the tree
+  # Space complexity: O(1)
   def heap_up(index)
     return if index == 0
     current_index = index

From 362abf27fc87d6466d5302000a7a9869b5c509c6 Mon Sep 17 00:00:00 2001
From: Jessica <jessica.homet@gmail.com>
Date: Thu, 19 Sep 2019 15:53:22 -0700
Subject: [PATCH 3/3] adjust time complexities

---
 lib/min_heap.rb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 19fe97f..e91a056 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -24,7 +24,7 @@ def add(key, value = key)
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: O(nlogn) where n is the number of elements in the heap
+  # Time Complexity: O(logn) where n is the number of elements in the heap
   # Space Complexity: O(1)
   def remove()
     swap(0, @store.length - 1)
@@ -60,7 +60,7 @@ 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: O(nlogn) where n is the number of nodes in the tree
+  # Time complexity: O(logn) where n is the number of nodes in the tree
   # Space complexity: O(1)
   def heap_up(index)
     return if index == 0