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Vera - Time #14

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veralizeth
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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 is better to find Min and find Max O(1) while Binary Seach Tree is good at all finds (O(logN)) - Heaps are priority-related.
Could you build a heap with linked nodes? Yes we could but since we need to find the left and Right child it does not make sense looking for k using a linked list, it is more efficiently find the kth element in an array.
Why is adding a node to a heap an O(log n) operation? Because of its height is O(log N), where N is the number of nodes. Therefore, the Overall Complexity of adding or deleting operation is O(log N).
Were the heap_up & heap_down methods useful? Why? They are the helpers' methods, heap_ud to add a new element to the heap and Heap_down to check if the heap property is met, reorganizing the heap and remove the root node.

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@CheezItMan CheezItMan left a comment

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Well done Vera, you hit the learning goals here. Take a look at my comments regarding space/time complexity for Heapsort.

Comment on lines +4 to 6
# Time Complexity: O(n)
# Space Complexity: O(1)
def heap_sort(list)

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👍 Since you are building a heap, the space complexity is O(n), and each add to the heap is O(log n) and you're doing it n times. Then you have the same complexity for removing elements, so the time complexity is O(n log n)

Comment on lines +16 to 18
# Time Complexity: O(log n)
# Space Complexity: o(log n)
def add(key, value = key)

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👍

Comment on lines +24 to 26
# Time Complexity: O(log n)
# Space Complexity: O(log n)
def remove()

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👍

Comment on lines +48 to 50
# Time complexity: o(1)
# Space complexity: o(1)
def empty?

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👍

Comment on lines +59 to 61
# Time complexity: O(log n)
# Space complexity: O(log n)
def heap_up(index)

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👍

Comment on lines 77 to 79
# moves it up the heap if it's smaller
# than it's parent node.
def heap_down(index)

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👍

temp = @store[index_1]
@store[index_1] = @store[index_2]
@store[index_2] = temp
@store[index_1], @store[index_2] = @store[index_2], @store[index_1]

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Fancy

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