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Branches - Julia Bouvier #15

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Heaps Practice

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Comprehension Questions

Question Answer
How is a Heap different from a Binary Search Tree? The left leaves are not necessary lesser or greater than the right leaves and a heap is always balanced unlike a BST.
Could you build a heap with linked nodes? Yes.
Why is adding a node to a heap an O(log n) operation? Because the number of swaps is cut roughly in half due to the balanced nature of the heap.
Were the heap_up & heap_down methods useful? Why? Definitely, because they do the work for moving the nodes to the correct places when a node is added or removed.

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Well done, you hit all the learning goals here. Nice work. Do take a look at my notes regarding time/space complexity. It's important to have a good grasp on this.

Comment on lines +5 to +7
# Time Complexity: n(log(n))
# Space Complexity: O(1)
def heapsort(list)

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How do you have a space complexity of O(1)? You're building a new heap of n elements...

Otherwise this works.

Comment on lines +17 to 19
# Time Complexity: log(n)
# Space Complexity: log(n)
def add(key, value = key)

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👍

Comment on lines +26 to 28
# Time Complexity: log(n)
# Space Complexity: log(n)
def remove()

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👍

def empty?
raise NotImplementedError, "Method not implemented yet..."
return true if @store.length == 0

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Suggested change
return true if @store.length == 0
return @store.length == 0

Comment on lines +53 to 55
# Time complexity: O(n)
# Space complexity: O(1)
def empty?

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How is this O(n) time complexity? Otherwise it works.

Comment on lines +64 to 66
# Time complexity: log(n)
# Space complexity: log(n)
def heap_up(index)

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👍

lc_index = index * 2 + 1
rc_index = index * 2 + 2
return if @store[lc_index].nil? && @store[rc_index].nil?
return if index == @store.length - 1

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I think this line is unnecessary since if they are at the end of the array, they have no children.

return if index == 0 || @store[index].key >= @store[parent_index].key

swap(index, parent_index)
return heap_up(parent_index)
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)

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👍

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2 participants