From 9c88bfd61782d80296698ab342d6d1837fd10ecd Mon Sep 17 00:00:00 2001
From: Jasmine <jasylop@gmail.com>
Date: Wed, 28 Apr 2021 22:04:30 -0700
Subject: [PATCH] implemented min_heap & heapsort

---
 lib/heap_sort.rb      | 59 ++++++++++++++++++++++++++++++++++++++++---
 lib/min_heap.rb       | 55 ++++++++++++++++++++++++++++++----------
 test/heapsort_test.rb |  2 +-
 3 files changed, 98 insertions(+), 18 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..0c68407 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,59 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+# Time Complexity:  O(n * log(n)) where n is the number of elements. 
+# Space Complexity: O(log(n)) worsecase because of recursion inside of heapify? 
+# list = [5, 27, 3, 16, -50]
+def heapsort(list)
+  return list if list.empty? || list.length == 1
+
+  # i = the parent of the last element 
+  i = (list.size - 1) / 2
+  # initial heapify of list 
+  while i >= 0
+    heapify(list, i, list.length)
+    i -= 1
+  end
+
+  # list = [-50, 5, 3, 16, 27 ]
+  i = 0
+  j = list.length - 1
+  while j >= 0
+    swap(i, j, list)
+    j -= 1
+    heapify(list, 0, j)
+  end
+
+return list
+end
+
+def swap(index1, index2, list)
+  temp = list[index1]
+  list[index1] = list[index2]
+  list[index2] = temp
+end
+
+def heapify(list, index, size)
+    # index here will be the "root" node
+    largest = index
+    left = 2 * index + 1
+    right = 2 * index + 2
+
+    # check if left child is greater than parent
+    if left < size && list[left] > list[largest]
+      largest = left
+    end
+
+    # also check if right child is greater than parent
+    if right < size && list[right] > list[largest]
+      largest = right
+    end
+
+    # if the largest no longer equals it's original value
+    if largest != index
+      # swap the root and the found largest value
+      swap(largest, index, list)
+      # make sure the order is still maintained for the children of that new index
+      heapify(list, largest, size)
+    end
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..b25a36f 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,27 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log(n))
+  # Space Complexity: O(log(n) due to the stack call in heap_up, could be O(1) using a loop
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    node = HeapNode.new(key, value)
+    @store.push(node)
+    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)) - where n is the number of elements and log(n) reps the levels
+  # Space Complexity: O(log(n) due to the stack call in heap_down, could be O(1) using a loop
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    if @store.length == 0
+      raise "the heap is empty"
+    end
+
+    swap(0, @store.length - 1)
+    removed = @store.pop
+    heap_down(0)
+    return removed.value
   end
 
 
@@ -44,10 +53,10 @@ 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 @store.length == 0
   end
 
   private
@@ -55,17 +64,37 @@ 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)) - n for number of elements. log(n) represents the number of levels. 
+  # Space complexity: O(log(n)) - the stack for the resursive calls could be as tall as the number of levels. 
   def heap_up(index)
-    
+    return if index == 0
+    parent_idx = (index - 1) / 2
+    if @store[parent_idx].key > @store[index].key
+      swap(parent_idx, index)
+      heap_up(parent_idx)
+    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..."
+    left = 2 * index + 1
+    right = 2 * index + 2
+    if @store[left] && @store[right] # if both left and right are not nil 
+      child_idx = @store[left].key > @store[right].key ? right : left
+    elsif @store[left] # there's no case where the left would be null and the right have a value
+      child_idx = left
+    else # if they're both null stop the function and return. 
+      return 
+    end
+
+    if @store[child_idx].key < @store[index].key
+      swap(child_idx, index)
+      heap_down(child_idx)
+    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 = []