From d1d190052633f7fa7c8aaa8c8fc73df936bff74f Mon Sep 17 00:00:00 2001
From: Jocelyn Wang <wangjoc@gmail.com>
Date: Thu, 15 Oct 2020 14:00:20 -0700
Subject: [PATCH] added in heap sort and min heap

---
 lib/heap_sort.rb | 15 +++++++++-----
 lib/min_heap.rb  | 51 ++++++++++++++++++++++++++++++++++++------------
 2 files changed, 48 insertions(+), 18 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index 6b692e4..dac5c5f 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: ?
+# Time Complexity: O(log n)
+# Space Complexity: O(n)
 def heapsort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  heap = MinHeap.new
+  list.each do |element|
+    heap.add(element)
+  end 
+  list.each_with_index do |val, index|
+    list[index] = heap.remove()
+  end 
+  return list 
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..6212981 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,23 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n)
+  # Space Complexity: O(n)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    @store << HeapNode.new(key,value)
+    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(n)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    swap(0, @store.length - 1)
+    result = @store.pop()
+    heap_down(0)
+
+    return result.value
   end
 
 
@@ -44,10 +49,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(1)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return true if @store.length == 0 
   end
 
   private
@@ -55,17 +60,37 @@ 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(log n)
+  # Space complexity: O(n)
   def heap_up(index)
-    
+    return nil if @store.empty?
+
+    predecessor_index = (index - 1)/2
+  
+    if @store[index].key >= @store[predecessor_index].key || index == 0 
+      return @store
+    else  
+      swap(index, predecessor_index)
+      heap_up(predecessor_index)
+    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..."
+    min = index 
+    left, right = 2 * index + 1, 2 * index + 2 
+
+    left < @store.length && @store[left].key < @store[min].key ? min = left : nil
+
+    right < @store.length && @store[right].key < @store[min].key ? min = right : nil
+
+    if min != index 
+      swap(index, min)
+      heap_down(min)
+    end 
   end
 
   # If you want a swap method... you're welcome