Created
September 28, 2013 21:55
-
-
Save wmwong/6747122 to your computer and use it in GitHub Desktop.
Fun with heaps
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
module Heap | |
def parent_index(i) | |
# +1 because the math works with indices starting from 1. | |
# -1 because we need to convert back to 0-index. | |
(i + 1) / 2 - 1 | |
end | |
def left_child_index(i) | |
# +1 because the math works with indices starting from 1. | |
# -1 because we need to convert back to 0-index. | |
# (i + 1) * 2 - 1 | |
# Use the simplified form. | |
i * 2 + 1 | |
end | |
def right_child_index(i) | |
left_child_index(i) + 1 | |
end | |
# Sort the array according to the order. | |
# order can either be :inc or :dec. | |
def sort(array, order = :inc) | |
order == :inc ? sort_increasing(array) : sort_decreasing(array) | |
end | |
# Sort the array in increasing order. | |
def sort_increasing(array) | |
create_max_heap(array) | |
(array.length - 1).downto(1).each do |i| | |
temp = array[i] | |
array[i] = array[0] | |
array[0] = temp | |
max_heapify(array, 0, i) | |
end | |
end | |
# Create a max-heap from the given array. | |
def create_max_heap(array) | |
return unless array.length > 1 | |
# -1 because 0-index. | |
((array.length / 2) - 1).downto(0).each do |i| | |
max_heapify(array, i, array.length) | |
end | |
end | |
# The left and right subtrees of the node at the given index must already be | |
# max-heaps. | |
def max_heapify(array, index, heap_length) | |
return if array.empty? | |
# Find the larger of parent, left child, and right child. | |
left_index = left_child_index(index) | |
right_index = right_child_index(index) | |
largest_index = index | |
largest_value = array[index] | |
if left_index < heap_length && array[left_index] > array[index] | |
largest_index = left_index | |
largest_value = array[left_index] | |
end | |
if right_index < heap_length && array[right_index] > largest_value | |
largest_index = right_index | |
end | |
# If the largest is a child, swap the parent with the child. | |
unless largest_index == index | |
temp = array[largest_index] | |
array[largest_index] = array[index] | |
array[index] = temp | |
max_heapify(array, largest_index, heap_length) | |
end | |
end | |
# Sort the array in decreasing order. | |
def sort_decreasing(array) | |
create_min_heap(array) | |
(array.length - 1).downto(1).each do |i| | |
temp = array[i] | |
array[i] = array[0] | |
array[0] = temp | |
min_heapify(array, 0, i) | |
end | |
end | |
# Create a min-heap from the given array. | |
def create_min_heap(array) | |
return unless array.length > 1 | |
((array.length / 2) - 1).downto(0).each do |i| | |
min_heapify(array, i, array.length) | |
end | |
end | |
# The left and right subtrees of the node at the given index must already be | |
# min-heaps. | |
def min_heapify(array, index, heap_length) | |
return if array.empty? | |
# Find the smallest of parent, left child, and right child. | |
left_index = left_child_index(index) | |
right_index = right_child_index(index) | |
smallest_index = index | |
smallest_value = array[index] | |
if left_index < heap_length && array[left_index] < array[index] | |
smallest_index = left_index | |
smallest_value = array[left_index] | |
end | |
if right_index < heap_length && array[right_index] < smallest_value | |
smallest_index = right_index | |
end | |
# If the smallest is a child, swap the parent with the child. | |
unless smallest_index == index | |
temp = array[smallest_index] | |
array[smallest_index] = array[index] | |
array[index] = temp | |
min_heapify(array, smallest_index, heap_length) | |
end | |
end | |
end |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
require './heap' | |
require 'test/unit' | |
class HeapTest < Test::Unit::TestCase | |
include Heap | |
def test_parent_index | |
assert_equal(2, parent_index(6)) | |
assert_equal(2, parent_index(5)) | |
assert_equal(1, parent_index(4)) | |
assert_equal(1, parent_index(3)) | |
assert_equal(0, parent_index(2)) | |
assert_equal(0, parent_index(1)) | |
end | |
def test_left_child_index | |
assert_equal(1, left_child_index(0)) | |
assert_equal(3, left_child_index(1)) | |
assert_equal(5, left_child_index(2)) | |
end | |
def test_right_child_index | |
assert_equal(2, right_child_index(0)) | |
assert_equal(4, right_child_index(1)) | |
assert_equal(6, right_child_index(2)) | |
end | |
def test_max_heapify | |
# Empty array. | |
array = [] | |
max_heapify(array, 0, 0) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
max_heapify(array, 0, 1) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [1, 2] | |
max_heapify(array, 0, 2) | |
assert_equal(2, array[0]) | |
assert_equal(1, array[1]) | |
# Two levels, full. | |
array = [1, 2, 3] | |
max_heapify(array, 0, 3) | |
assert_equal(3, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(1, array[2]) | |
# Three levels. | |
array = [1, 4, 3, 2] | |
max_heapify(array, 0, 4) | |
assert_equal(4, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(1, array[3]) | |
# Respects heap length. | |
array = [1, 4, 3, 2, 5, 6, 7] | |
max_heapify(array, 0, 4) | |
assert_equal(4, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(1, array[3]) | |
assert_equal(5, array[4]) | |
assert_equal(6, array[5]) | |
assert_equal(7, array[6]) | |
end | |
def test_create_max_heap | |
# Empty array. | |
array = [] | |
create_max_heap(array) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
create_max_heap(array) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [1, 2] | |
create_max_heap(array) | |
assert_equal(2, array[0]) | |
assert_equal(1, array[1]) | |
# Two levels, full. | |
array = [1, 2, 3] | |
create_max_heap(array) | |
assert_equal(3, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(1, array[2]) | |
# Three levels. | |
array = [1, 2, 3, 4] | |
create_max_heap(array) | |
assert_equal(4, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(1, array[3]) | |
end | |
def test_sort_increasing | |
# Empty array. | |
array = [] | |
sort_increasing(array) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
sort_increasing(array) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [2, 1] | |
sort_increasing(array) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
# Two levels, full. | |
array = [3, 2, 1] | |
sort_increasing(array) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
# Three levels. | |
array = [4, 3, 2, 1] | |
sort_increasing(array) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(4, array[3]) | |
end | |
def test_min_heapify | |
# Empty array. | |
array = [] | |
min_heapify(array, 0, 0) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
min_heapify(array, 0, 1) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [2, 1] | |
min_heapify(array, 0, 2) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
# Two levels, full. | |
array = [3, 2, 1] | |
min_heapify(array, 0, 3) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
# Three levels. | |
array = [4, 1, 3, 2] | |
min_heapify(array, 0, 4) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(4, array[3]) | |
# Respects heap length. | |
array = [4, 1, 3, 2, 5, 6, 7] | |
min_heapify(array, 0, 4) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
assert_equal(4, array[3]) | |
assert_equal(5, array[4]) | |
assert_equal(6, array[5]) | |
assert_equal(7, array[6]) | |
end | |
def test_create_min_heap | |
# Empty array. | |
array = [] | |
create_min_heap(array) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
create_min_heap(array) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [2, 1] | |
create_min_heap(array) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
# Two levels, full. | |
array = [3, 2, 1] | |
create_min_heap(array) | |
assert_equal(1, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(3, array[2]) | |
# Three levels. | |
array = [4, 3, 2, 1] | |
create_min_heap(array) | |
assert_equal(1, array[0]) | |
assert_equal(3, array[1]) | |
assert_equal(2, array[2]) | |
assert_equal(4, array[3]) | |
end | |
def test_sort_decreasing | |
# Empty array. | |
array = [] | |
sort_decreasing(array) | |
assert(array.empty?) | |
# Single element. | |
array = [1] | |
sort_decreasing(array) | |
assert_equal(1, array[0]) | |
# Two levels. | |
array = [1, 2] | |
sort_decreasing(array) | |
assert_equal(2, array[0]) | |
assert_equal(1, array[1]) | |
# Two levels, full. | |
array = [1, 2, 3] | |
sort_decreasing(array) | |
assert_equal(3, array[0]) | |
assert_equal(2, array[1]) | |
assert_equal(1, array[2]) | |
# Three levels. | |
array = [1, 2, 3, 4] | |
sort_decreasing(array) | |
assert_equal(4, array[0]) | |
assert_equal(3, array[1]) | |
assert_equal(2, array[2]) | |
assert_equal(1, array[3]) | |
end | |
end |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
require './heap' | |
module PriorityQueue | |
class Max | |
include Heap | |
# For testing purposes. | |
attr_reader :array | |
def initialize(array) | |
@array = array | |
create_max_heap(@array) | |
end | |
def get_max | |
@array[0] | |
end | |
def extract_max | |
return nil if @array.empty? | |
max = get_max | |
temp = @array.pop | |
unless @array.empty? | |
@array[0] = temp | |
max_heapify(@array, 0, @array.length) | |
end | |
max | |
end | |
def increase(index, obj) | |
raise "#{obj} is less than #{@array[index]} and is not an increase." if obj < @array[index] | |
@array[index] = obj | |
while index > 0 && @array[parent_index(index)] < obj | |
temp = @array[index] | |
@array[index] = @array[parent_index(index)] | |
@array[parent_index(index)] = temp | |
index = parent_index(index) | |
end | |
end | |
def insert(obj) | |
@array.push(obj) | |
increase(@array.length - 1, obj) | |
end | |
end | |
class Min | |
include Heap | |
# For testing purposes. | |
attr_reader :array | |
def initialize(array) | |
@array = array | |
create_min_heap(@array) | |
end | |
def get_min | |
@array[0] | |
end | |
def extract_min | |
return nil if @array.empty? | |
min = get_min | |
temp = @array.pop | |
unless @array.empty? | |
@array[0] = temp | |
min_heapify(@array, 0, @array.length) | |
end | |
min | |
end | |
def decrease(index, obj) | |
raise "#{obj} is greater than #{@array[index]} and is not a decrease." if obj > @array[index] | |
@array[index] = obj | |
while index > 0 && @array[parent_index(index)] > obj | |
temp = @array[index] | |
@array[index] = @array[parent_index(index)] | |
@array[parent_index(index)] = temp | |
index = parent_index(index) | |
end | |
end | |
def insert(obj) | |
@array.push(obj) | |
decrease(@array.length - 1, obj) | |
end | |
end | |
end |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
require './priority_queue' | |
require 'test/unit' | |
class TestMaxPriorityQueue < Test::Unit::TestCase | |
def test_get_max | |
queue = PriorityQueue::Max.new([1, 2, 3, 4, 5, 6]) | |
assert_equal(6, queue.get_max) | |
end | |
def test_extract_max | |
queue = PriorityQueue::Max.new([1, 2, 3, 4, 5, 6]) | |
assert_equal(6, queue.extract_max) | |
assert_equal(5, queue.extract_max) | |
assert_equal(4, queue.extract_max) | |
assert_equal(3, queue.extract_max) | |
assert_equal(2, queue.extract_max) | |
assert_equal(1, queue.extract_max) | |
assert_equal(nil, queue.extract_max) | |
end | |
def test_increase | |
queue = PriorityQueue::Max.new([1, 2, 3, 4, 5, 6]) | |
assert_raise RuntimeError do | |
queue.increase(0, 0) | |
end | |
queue.increase(5, 7) | |
assert_equal(7, queue.array[0]) | |
assert_equal(5, queue.array[1]) | |
assert_equal(6, queue.array[2]) | |
assert_equal(4, queue.array[3]) | |
assert_equal(2, queue.array[4]) | |
assert_equal(3, queue.array[5]) | |
end | |
def test_insert | |
queue = PriorityQueue::Max.new([1, 2, 3, 4, 5, 6]) | |
queue.insert(7) | |
assert_equal(7, queue.array[0]) | |
assert_equal(5, queue.array[1]) | |
assert_equal(6, queue.array[2]) | |
assert_equal(4, queue.array[3]) | |
assert_equal(2, queue.array[4]) | |
assert_equal(1, queue.array[5]) | |
assert_equal(3, queue.array[6]) | |
end | |
end | |
class TestMinPriorityQueue < Test::Unit::TestCase | |
def test_get_min | |
queue = PriorityQueue::Min.new([6, 5, 4, 3, 2, 1]) | |
assert_equal(1, queue.get_min) | |
end | |
def test_extract_min | |
queue = PriorityQueue::Min.new([6, 5, 4, 3, 2, 1]) | |
assert_equal(1, queue.extract_min) | |
assert_equal(2, queue.extract_min) | |
assert_equal(3, queue.extract_min) | |
assert_equal(4, queue.extract_min) | |
assert_equal(5, queue.extract_min) | |
assert_equal(6, queue.extract_min) | |
assert_equal(nil, queue.extract_min) | |
end | |
def test_increase | |
queue = PriorityQueue::Min.new([6, 5, 4, 3, 2, 1]) | |
assert_raise RuntimeError do | |
queue.decrease(0, 7) | |
end | |
queue.decrease(5, 0) | |
assert_equal(0, queue.array[0]) | |
assert_equal(2, queue.array[1]) | |
assert_equal(1, queue.array[2]) | |
assert_equal(3, queue.array[3]) | |
assert_equal(5, queue.array[4]) | |
assert_equal(4, queue.array[5]) | |
end | |
def test_insert | |
queue = PriorityQueue::Min.new([6, 5, 4, 3, 2, 1]) | |
queue.insert(0) | |
assert_equal(0, queue.array[0]) | |
assert_equal(2, queue.array[1]) | |
assert_equal(1, queue.array[2]) | |
assert_equal(3, queue.array[3]) | |
assert_equal(5, queue.array[4]) | |
assert_equal(6, queue.array[5]) | |
assert_equal(4, queue.array[6]) | |
end | |
end |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment