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Time - Mair H #17

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10f4abb
implemented min-heap methods
mheshmati-tech Sep 28, 2020
d9e1997
added heapsort and time/space complexity
mheshmati-tech Sep 29, 2020
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21 changes: 17 additions & 4 deletions lib/heap_sort.rb
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Original file line number Diff line number Diff line change
@@ -1,8 +1,21 @@

require_relative "./min_heap"

# This method uses a heap to sort an array.
# Time Complexity: ?
# Space Complexity: ?
# Time Complexity: O n(log n)
# Space Complexity: O(n) returning_array + internal heap array = O(2n) = O(n)?
def heapsort(list)
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@CheezItMan CheezItMan Sep 29, 2020

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👍

raise NotImplementedError, "Method not implemented yet..."
heap = MinHeap.new

#make the minheap tree
list.each do |item|
#add method will sort as adding item to heap
heap.add(item)
end

returning_list = []
(list.length).times do |i|
#remove method will pop/return the root aka smallest value
returning_list << heap.remove
end
return returning_list
end
71 changes: 53 additions & 18 deletions lib/min_heap.rb
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Expand Up @@ -8,26 +8,36 @@ def initialize(key, value)
end

class MinHeap

def initialize
@store = []
end

# This method adds a HeapNode instance to the heap
# Time Complexity: ?
# Space Complexity: ?
# Time Complexity: O(1)
# Space Complexity: O(log n)
def add(key, value = key)
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@CheezItMan CheezItMan Sep 29, 2020

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The time complexity is O(log n) because of the recursion.

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(1)
# Space Complexity: O(log n)
def remove()
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@CheezItMan CheezItMan Sep 29, 2020

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👍 Ditto on time complexity from add

raise NotImplementedError, "Method not implemented yet..."
end
if @store.empty?
return nil
end

#removing the root element
swap(0, @store.length - 1)
result = @store.pop

#re-arranging heap
heap_down(0) unless @store.empty?
return result.value
end

# Used for Testing
def to_s
Expand All @@ -39,33 +49,58 @@ def to_s
end

output += @store.last.value + "]"

return output
end

# This method returns true if the heap is empty
# Time complexity: ?
# Space complexity: ?
# Time complexity: O(1)
# Space complexity: O(1)
def empty?
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@CheezItMan CheezItMan Sep 29, 2020

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👍

raise NotImplementedError, "Method not implemented yet..."
@store.empty?
end

private

# 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(1)
# Space complexity: O(log n)
def heap_up(index)
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@CheezItMan CheezItMan Sep 29, 2020

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Since you're doing recursion to move up the tree, this is O(log n)


parent = (index - 1) / 2
return if index == 0

if @store[parent].key > @store[index].key
swap(parent, index)
heap_up(parent)
else #if @store[parent].key < @store[index].key
return
end
end

# This helper method takes an index and
# 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)
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@CheezItMan CheezItMan Sep 29, 2020

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👍 Nicely done, very compact and readable.

raise NotImplementedError, "Method not implemented yet..."
right = 2 * index + 2
left = 2 * index + 1
return if left >= @store.length #return if no child exists

#initilize smaller in case right index doesn't exist
smaller = left
#determine which is smaller
if @store[right]
smaller = @store[left].key > @store[right].key ? right : left
end

#swap
if @store[smaller].key < @store[index].key
swap(smaller, index)
heap_down(smaller)
else #if @store[smaller].key > @store[index].key
return
end
end

# If you want a swap method... you're welcome
Expand All @@ -74,4 +109,4 @@ def swap(index_1, index_2)
@store[index_1] = @store[index_2]
@store[index_2] = temp
end
end
end
2 changes: 1 addition & 1 deletion test/heapsort_test.rb
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
require_relative "test_helper"

xdescribe "heapsort" do
describe "heapsort" do
it "sorts an empty array" do
# Arrange
list = []
Expand Down