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@ -10,7 +10,7 @@
<br>
* heap is a data structure capable of giving you the smallest (or the largest) element in constant time, while adding or removing the smallest (or the largest) element on logarithmic time.
* heap is a data structure capable of giving you the smallest (or the largest) element in constant time, while adding or removing the smallest (or the largest) element in logarithmic time.
* heaps guarantees both insertion and deletion to have time complexity `O(log N)` (while maintaining get_max/get_min at `O(1)`).
@ -93,13 +93,13 @@ class Heap:
<br>
* it's cheaper to heapify an array of data (`O(N)`) than creating an empty heap and inserting each element (`O(N log(N))`).
* heapify means create a binary tree and then comparing each nodes with their child (and swapping when necessary).
* it's cheaper to heapify an array of data (`O(N)`) than create an empty heap and inserting each element (`O(N log(N))`).
* heapify means create a binary tree and then comparing each nodes with their children (and swapping when necessary).
* parents node can simply exchange with their smallest child (so the max number of exchanges is `N/2`) and leaves are left out.
* python's built-in heap differs from the standard implementation of a heap in two ways:
* firstly, it uses zero-based indexing, so it stores the root node at index zero instead of the size of the heap.
* secondly, the built-in module does not offer a direct way to create a max heap, instead, we must modify the values of each eelement when inserting in the heap, and when removing it from the heap.
* secondly, the built-in module does not offer a direct way to create a max heap, instead, we must modify the values of each element when inserting in the heap, and when removing it from the heap.
<br>
@ -155,7 +155,7 @@ size_max_heap = len(max_heap)
- then compare this node to each parent, exchanging them until the tree's properties are correct.
* `extract_min`:
- first, remove/return the top and then replace the tree's top with its latest element (the bottom most rightmost).
- first, remove/return the top and then replace the tree's top with its latest element (the bottom-most rightmost).
- then bubble down, swapping it with one of its children until the min-heap is properly restored
- there is no need for order between right and left, so this operation would only take `O(log N)` runtime.