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Elle #14

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@dev-elle-up dev-elle-up commented Sep 29, 2019 •
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Heaps Practice

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Comprehension Questions

Question Answer
How is a Heap different from a Binary Search Tree? They are different in structure and in the way they order themselves. Binary search trees keep nodes strictly in order by value. This can lead to lopsided, unbalanced trees (unless they are re-balanced). Heaps only require the children be < or > the parent (depending upon if they are min- or max-heaps) but do not measure the difference between siblings, and they require each level to be filled left-to-right.
Could you build a heap with linked nodes? You mean a linked list? Yes, you could. This would increase the time complexity, though.
Why is adding a node to a heap an O(log n) operation? At each level, you will only visit one branch of the tree.
Were the heap_up & heap_down methods useful? Why? These were essential to making the structure work. Without them, you would need to put code into the add and remove methods that traverse and reorganize the tree, and this probably couldn't be called recursively.

CheezItMan
CheezItMan reviewed Oct 4, 2019
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Nice work! You hit all the learning goals here. See my notes on space complexity. When you have a recursive method, you have to account for the use of the call stack.

lib/heap_sort.rb
# Time Complexity: O(nlogn),where n is the number of items in the list,
# because the add and remove methods are O(nlogn)
# Space Complexity: O(2n), where n is the number of items in the list
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So really O(n)

lib/min_heap.rb
# Time Complexity: ?
# Space Complexity: ?
# Time Complexity: O(nlogn) because heap_up is nlogn, where n is the number of nodes in the heap
# Space Complexity: O(1)
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Since heap_up is recursive, you have to account for the space complexity of the system stack.

lib/min_heap.rb
Comment on lines +103 to +116
# These helper methods find the index of the
# current item's parent node, and the indices
# of its left and right children
def find_parent_index(node_index)
return ((node_index-1)/2).floor
end

def find_left_child_index(node_index)
return node_index * 2 + 1
end

def find_right_child_index(node_index)
return node_index * 2 + 2
end
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Good set of helper methods.

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