Kim <3 <3 <3

[Kimberly-Fasbender]

Heaps Practice

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Comprehension Questions

Question	Answer
How is a Heap different from a Binary Search Tree?	It isn't! J/K, gotcha! In a BST the left child of a parent node always has a value less than the parent, and the right child always has a value greater than the parent. In a Heap both children of a parent are either less than the parent (maxHeap) or greater than the parent (minHeap). Also, in a BST a parent could have a right child node, and no left child node (not the case in a Heap where each level is filled in left to right).
Could you build a heap with linked nodes?	Yes, if you hated yourself. It would be much more difficult without being able to access the indices like you can with an array.
Why is adding a node to a heap an O(log n) operation?	Because when you add a node to the Heap you compare it to its parent's value, swap if necessary, and then repeat until you reach the root of the tree. This means the depth of the tree is the max number of swaps you will ever need to preform. The depth is also 1/2 of the nodes in any given subtree of the heap, hence O(log n) time complexity.
Were the heap_up & heap_down methods useful? Why?	Yes, they made the add and remove methods much more readable, and are also essential parts of maintaining the heap.

[CheezItMan]

Nice work! You hit all the learning goals here. Well done.

[CheezItMan]

Very clear and elegant.

[CheezItMan]

Since heap_up is recursive... You do have some space complexity here. The system stack.

[CheezItMan]

Ditto

[CheezItMan]

Since m is likely to be constant in size, this is O(n)