From 10f4abb326e518fdc1d571d7b97e9c2561ba774a Mon Sep 17 00:00:00 2001 From: Maryam Heshmati Date: Mon, 28 Sep 2020 09:31:28 -0700 Subject: [PATCH 1/2] implemented min-heap methods --- lib/min_heap.rb | 51 +++++++++++++++++++++++++++++++++++++++---------- 1 file changed, 41 insertions(+), 10 deletions(-) diff --git a/lib/min_heap.rb b/lib/min_heap.rb index 6eaa630..719ad6e 100644 --- a/lib/min_heap.rb +++ b/lib/min_heap.rb @@ -8,7 +8,6 @@ def initialize(key, value) end class MinHeap - def initialize @store = [] end @@ -17,7 +16,9 @@ def initialize # Time Complexity: ? # Space Complexity: ? 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 @@ -25,9 +26,18 @@ def add(key, value = key) # Time Complexity: ? # Space Complexity: ? def remove() - 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 @@ -39,7 +49,7 @@ def to_s end output += @store.last.value + "]" - + return output end @@ -47,7 +57,7 @@ def to_s # Time complexity: ? # Space complexity: ? def empty? - raise NotImplementedError, "Method not implemented yet..." + @store.empty? end private @@ -58,14 +68,35 @@ def empty? # Time complexity: ? # Space complexity: ? def heap_up(index) - + parent = (index - 1) / 2 + return if index == 0 + + if @store[parent].key > @store[index].key + swap(parent, index) + heap_up(parent) + else #@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) - raise NotImplementedError, "Method not implemented yet..." + right = 2 * index + 2 + left = 2 * index + 1 + return if @store[right].nil? || @store[left].nil? + + #determine which is smaller + smaller = @store[left].key > @store[right].key ? right : left + + #swap + if @store[smaller].key < @store[index].key + swap(smaller, index) + heap_down(smaller) + else + return + end end # If you want a swap method... you're welcome @@ -74,4 +105,4 @@ def swap(index_1, index_2) @store[index_1] = @store[index_2] @store[index_2] = temp end -end \ No newline at end of file +end From d9e1997920eb060cdbc74ac03ed962a59f3d227e Mon Sep 17 00:00:00 2001 From: Maryam Heshmati Date: Mon, 28 Sep 2020 19:36:45 -0700 Subject: [PATCH 2/2] added heapsort and time/space complexity --- lib/heap_sort.rb | 21 +++++++++++++++++---- lib/min_heap.rb | 30 +++++++++++++++++------------- test/heapsort_test.rb | 2 +- 3 files changed, 35 insertions(+), 18 deletions(-) diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb index 6b692e4..bfcdafe 100644 --- a/lib/heap_sort.rb +++ b/lib/heap_sort.rb @@ -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) - 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 \ No newline at end of file diff --git a/lib/min_heap.rb b/lib/min_heap.rb index 719ad6e..1b38a89 100644 --- a/lib/min_heap.rb +++ b/lib/min_heap.rb @@ -13,8 +13,8 @@ def initialize 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) @store << HeapNode.new(key, value) @@ -23,8 +23,8 @@ 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(1) + # Space Complexity: O(log n) def remove() if @store.empty? return nil @@ -54,8 +54,8 @@ 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? @store.empty? end @@ -65,8 +65,8 @@ 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(1) + # Space complexity: O(log n) def heap_up(index) parent = (index - 1) / 2 return if index == 0 @@ -74,7 +74,7 @@ def heap_up(index) if @store[parent].key > @store[index].key swap(parent, index) heap_up(parent) - else #@store[parent].key < @store[index].key + else #if @store[parent].key < @store[index].key return end end @@ -85,16 +85,20 @@ def heap_up(index) def heap_down(index) right = 2 * index + 2 left = 2 * index + 1 - return if @store[right].nil? || @store[left].nil? + 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 - smaller = @store[left].key > @store[right].key ? right : left - + 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 + else #if @store[smaller].key > @store[index].key return end end 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 = []