translation: Update heap.md #1604
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K3v123
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Jan 21, 2025
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| As mentioned in the "Binary Trees" section, complete binary trees are well-suited for array representation. Since heaps are a type of complete binary tree, **we will use arrays to store heaps**. | ||
| As mentioned in the "Binary Trees" section, a complete binary tree can be efficiently represented with an array. Since heaps are a type of complete binary tree, **we will use arrays to store heaps**. |
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(please let me know if im wrong)
I think the original may be better, i did a little tweak on it
"a complete binary tree can be efficiently represented with an array"
to
-> "complete binary trees are highly suitable for array representation"
also we removed the "a" and added "trees" because again its more general.
| 3. Starting from the root node, **perform heapify from top to bottom**. | ||
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| As shown in the figure below, **the direction of "heapify from top to bottom" is opposite to "heapify from bottom to top"**. We compare the value of the root node with its two children and swap it with the largest child. Then repeat this operation until passing the leaf node or encountering a node that does not need to be swapped. | ||
| As shown in the figure below, **the direction of "heapify from top to bottom" is opposite to "heapify from bottom to top"**. We compare the value of the root node with its two children and swap it with the largest child. Then, repeat this operation until reaching the leaf node or encountering a node that does not need to be swapped. |
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"does not need to be swapped." -> "does not need swapping."
this is more concise and more consistent with the previous changes (eg "repairing each node in the heap from bottom to top until reaching the root or a node that does not need swapping.")
| @@ -534,5 +534,5 @@ Similar to the element insertion operation, the time complexity of the top eleme | |||
| ## Common applications of heaps | |||
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| - **Priority Queue**: Heaps are often the preferred data structure for implementing priority queues, with both enqueue and dequeue operations having a time complexity of $O(\log n)$, and building a queue having a time complexity of $O(n)$, all of which are very efficient. | |||
| - **Heap Sort**: Given a set of data, we can create a heap from them and then continually perform element removal operations to obtain ordered data. However, we usually use a more elegant method to implement heap sort, as detailed in the "Heap Sort" section. | |||
| - **Finding the Largest $k$ Elements**: This is a classic algorithm problem and also a typical application, such as selecting the top 10 hot news for Weibo hot search, picking the top 10 selling products, etc. | |||
| - **Heap Sort**: Given a set of data, we can create a heap from them and then continually perform element removal operations to obtain ordered data. However, there is a more elegant way to implement heap sort, which is explained in the "Heap Sort" chapter. | |||
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"which is explained" -> "as explained" this is more concise
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