week4 - task2 - baseline

Author: proton

week4/priority-queues/task2/TASK.md

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+### Randomized priority queue
+
+Describe how to add the methods `sample()` and `delRandom()` to our binary heap implementation.
+The two methods return a key that is chosen uniformly at random among the remaining keys, with the latter method also removing that key.
+The `sample()` method should take constant time; the `delRandom()` method should take logarithmic time.
+Do not worry about resizing the underlying array.

week4/priority-queues/task2/solution.rb

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+class Heap
+  attr_reader :arr
+
+  def initialize(values = [])
+    @arr = values.dup
+
+    (arr.size / 2 - 1).downto(0).each do |i|
+      heapify!(i)
+    end
+  end
+
+  def push(value)
+    i = arr.size
+    arr << value
+    parent_i = (i - 1) / 2
+
+    while i > 0 && arr[parent_i] < arr[i]
+      swap(i, parent_i)
+      i = parent_i
+      parent_i = (i - 1) / 2
+    end
+  end
+
+  def max
+    arr.first
+  end
+
+  def pop
+    value = arr[0]
+    last  = arr.pop
+    unless arr.empty?
+      arr[0] = last
+      heapify!(0)
+    end
+    value
+  end
+
+  def length
+    arr.size
+  end
+
+  def sample
+    arr.sample
+  end
+
+  # logarithmic time
+  def delRandom
+    i = rand(arr.size)
+    x = arr[i]
+
+    swap(i, arr.size - 1)
+    arr.pop
+
+    (0...arr.size).each do |k|
+      heapify!(k)
+    end
+    (0...arr.size).each do |k|
+      heapify!(k)
+    end
+    (0...arr.size).each do |k|
+      heapify!(k)
+    end
+
+    x
+  end
+
+  def valid_heap?
+    return true if arr.empty?
+    (0..(arr.size / 2 - 1)).each do |parent_idx|
+      left_child_idx  = 2 * parent_idx + 1
+      right_child_idx = 2 * parent_idx + 2
+      return false if left_child_idx  < arr.size && arr[left_child_idx]  > arr[parent_idx]
+      return false if right_child_idx < arr.size && arr[right_child_idx] > arr[parent_idx]
+    end
+    true
+  end
+
+  private def heapify!(i)
+    loop do
+      left_child  = 2 * i + 1
+      right_child = 2 * i + 2
+      largest_child = i
+
+      largest_child = left_child  if left_child  < arr.size && arr[left_child]  > arr[largest_child]
+      largest_child = right_child if right_child < arr.size && arr[right_child] > arr[largest_child]
+
+      break if largest_child == i
+
+      swap(i, largest_child)
+      i = largest_child
+    end
+  end
+
+  private def swap(i, j)
+    arr[i], arr[j] = arr[j], arr[i]
+  end
+end
+
+n = rand(3..9)
+a = Array.new(n) { rand(1..99) }.uniq
+
+h1 = Heap.new(a)
+x  = h1.delRandom
+b  = a - [x]
+h2 = Heap.new(b)
+
+p h1.arr.sort == h2.arr.sort && h1.valid_heap? && h2.valid_heap?