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56 lines
1.3 KiB
Markdown
56 lines
1.3 KiB
Markdown
## sorting
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<br>
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* **inversions** in a sequence is a pair of elements that are out of order with respect to the ordering relation. a sorting algorithm is a sequence of operations that reduces inversions to zero.
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* a **topological sort** of a directed graph is a way of ordering the list of nodes such that if `(a, b)` is a edge of the graph, then `a` appears before `b`. this type of sorting does not work if a graph has cycles or is not directed.
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* because of their efficiencies, you usually want to use either merge sort or quick sort (`O(N log (N)`).
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* other type of sorting algorithms can be seen below and in this directory's source code:
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<br>
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<p align="center">
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<img src="https://github.com/go-outside-labs/master-algorithms-py/assets/138340846/54ab4d2c-a8b7-4e5c-9e98-5d7d2e627007" width="60%" align="center" style="padding:1px;border:1px solid black;">
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</p>
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<br>
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---
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### merge sort
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<br>
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```python
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def ms(array):
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if len(array) < 2:
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return array
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mid = len(array) // 2
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left = array[:mid]
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right = array[mid:]
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result, i, j = [], 0, 0
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while i < len(left) and j < len(right):
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if left[i] <= right[j]:
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result.append(left[i])
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i += 1
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else:
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result.append(right[j])
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j += 1
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if left[i:]:
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result.extend(left[i:])
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if right[j:]:
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result.extend(right[j:])
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return result
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```
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