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Heaps Practice

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Comprehension Questions

Question Answer
How is a Heap different from a Binary Search Tree? Heap guarantees that elements on higher levels are greater (for max-heap) or smaller (for min-heap) than elements on lower levels, whereas BST guarantees order from left to right.
Could you build a heap with linked nodes? Yes, a Heap can be implemented with linked nodes, but normally heaps are built using an array as the underlying data structure.
Why is adding a node to a heap an O(log n) operation? Since a full tree has O(log n) levels, where n is the number of elements in the heap, there would be O(log n) swaps. So Adding an element is O(log n).
Were the heap_up & heap_down methods useful? Why? Yes. They made it easier to be used as a recursive call in the add and remove methods.

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@CheezItMan CheezItMan left a comment

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Nice work Haben, you hit the learning goals here. Well done.

Comment on lines +4 to 6
# Time Complexity: O(n log(n))
# Space Complexity: O(n)
def heapsort(list)

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👍

Comment on lines +28 to 31
# maintaining the heap structure
# Time Complexity: O(log(n))
# Space Complexity: O(1)
def remove()

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👍 Due to the recursion the space complexity is O(log n) due to the call stack.

Comment on lines +61 to 63
# Time complexity: O(1)
# Space complexity: O(1)
def empty?

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👍

Comment on lines +17 to 19
# Time Complexity: O(log(n))
# Space Complexity: O(1)
def add(key, value = key)

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👍 Due to the recursion the space complexity is O(log n) due to the call stack.

Comment on lines +74 to 76
# Time complexity: O(log(n))
# Space complexity: O(1)
def heap_up(index)

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👍 Due to the recursion the space complexity is O(log n) due to the call stack.

Comment on lines +97 to 99
# Time complexity: O(log(n))
# Space complexity: O(1)
def heap_down(index)

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👍 Due to the recursion the space complexity is O(log n) due to the call stack.

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2 participants