C16 Digital - Gabe K

[GabeKelemen]

Heaps Practice

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Comprehension Questions

Question	Answer
How is a Heap different from a Binary Search Tree?	A heap has to be a complete binary tree. It has a faster insertion and deletion -- O(log n) -- than a BST, O(n). A can be ordered as a max or min heap where the root/parent is either greater or smaller than the child, whereas in a BST all nodes in the left subtree are smaller, and all nodes in the right subtree are larger.
Could you build a heap with linked nodes?	A heap can implement a priority queue using a singly linked list but it makes more sense to implement a heap with an array because you can iterate over the array and use the array's index for the children / nodes.
Why is adding a node to a heap an O(log n) operation?	A new node is always added at the bottom of the heap and bubbles up. The number of comparisons and swaps to move the new element to its correct position will be at worst-case one swap per level of the heap. Since there Log n levels to the heap, then adding a node is 𝑂(log𝑛).
Were the heap_up & heap_down methods useful? Why?	These methods make the comparison and swapping between the child and parent easier per level until the node in question ends up in its correct position.

[kyra-patton]

✨💫 Very nice! I left a few comments on space complexity below. Let me know what questions you have.

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[kyra-patton]

✨

[kyra-patton]

✨ Nice, however the space complexity is O(log n) because of the recursive call stack of heap_up

[kyra-patton]

✨ Nice, however like above, space complexity is O(log n) because of the recursive call stack of heap_down

[kyra-patton]

✨

[kyra-patton]

✨ What does the recursive call imply the space complexity should be??

[kyra-patton]

✨ Very clean!