Maple - Karishma Johnson #17
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✨💫 Nice job Karishma. I left some comments on your implementation below.
In response to your comprehension questions, note that heaps are _semi_ordered not unordered, and that a heap can be implemented using a linked list it's just not the ideal structure as linked lists are quite expensive to traverse.
Let me know what questions you have!
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| """ This method uses a heap to sort an array. | ||
| Time Complexity: ? | ||
| Space Complexity: ? | ||
| Time Complexity: o(n^2) |
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✨ However time complexity is actually O(n log n) because remove and add are O(log n) operations instead of O(n). Because you are creating a heap of size n, space complexity will be O(n)
| Time complexity: ? | ||
| Space complexity: ? | ||
| Time complexity: o(1) | ||
| Space complexity: o(0-1) |
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| def heap_down(self, index): | ||
| """ This helper method takes an index and | ||
| moves the corresponding element down the heap if it's | ||
| larger than either of its children and continues until | ||
| the heap property is reestablished. | ||
| """ | ||
| pass | ||
| left = index * 2 + 1 |
| i = 0 | ||
| while not heap.empty(): | ||
| arr[i] = heap.remove() |
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👀 remove is actually an O(log n) operation - see additional comments in your remove implementation
| self.store.append(node) | ||
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| index = len(self.store) -1 | ||
| while index != None and index != 0: |
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Interesting to do this iteratively! Because you are halving the index with each call to heap_up, this loop should actually run O(log n) times
| @@ -19,18 +19,36 @@ def __init__(self): | |||
| def add(self, key, value = None): | |||
| """ This method adds a HeapNode instance to the heap | |||
| If value == None the new node's value should be set to key | |||
| Time Complexity: ? | |||
| Space Complexity: ? | |||
| Time Complexity: o(n) | |||
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✨ However space complexity is O(log n). See comment below ⬇️
| Time Complexity: ? | ||
| Space Complexity: ? | ||
| Time Complexity: o(n) | ||
| Space Complexity: o(1) |
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✨ Because of the recursive heap_down operation, space and time complexity will actually be O(log n) here.
| Time complexity: ? | ||
| Space complexity: ? | ||
| Time complexity: o(1) | ||
| Space complexity: o(1) |
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✨ Creative to use this in conjunction with iteration in your add function. For consistency style wise, I would recommend sticking to either an iterative or recursive solution between heap_up and heap_down. Technically the specification does say heap_up should perform its operation "until the Heap property is reestablished" which indicates recursion, but I'm not too concerned with that.
Heaps Practice
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Comprehension Questions
heap_up&heap_downmethods useful? Why?heap_upwas good for checking if a node should be moved up and swapping if that was the case; the same in reverse,heap_downwas good for removing a node at the root and then choosing the replacement child and sliding the respective children upward