Union-based heaps - Speaker Deck

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Union-based heaps Alexey Kachayev KyivPy #11 Sunday, October 27, 13

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•@kachayev •github: kachayev •kachayev@gmail.com •attendify.com Sunday, October 27, 13

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Problem extract min (quickly) Sunday, October 27, 13

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•priority queue •bounded leadership •greedy algorithms •.. and more Sunday, October 27, 13

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Solution heaps Sunday, October 27, 13

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•binary •binominal •2/3 •ﬁbonacci •leftist •skew •pairing Heaps Sunday, October 27, 13

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In Python heapq.* Sunday, October 27, 13

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•binary heap •push •pop •heapify •nlargest •merge heapq. Sunday, October 27, 13

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Sunday, October 27, 13

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Use: Dijkstra Sunday, October 27, 13

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•push = O(log N) •pop = O(log N) •merge = O(N+M) •build = O(N) Binary Sunday, October 27, 13

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•union :( •size bounding •array resizing •mutable But.. Sunday, October 27, 13

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Union-based Sunday, October 27, 13

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•still one tree •union is a King •low branching •persistent Idea Sunday, October 27, 13

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Persistent each operation returns new structure Sunday, October 27, 13

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Skew heaps Sunday, October 27, 13

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Sunday, October 27, 13

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Haskell Sunday, October 27, 13

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Skew Python 2.* only Sunday, October 27, 13

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•push= O(log N)* •pop= O(log N)* •union= O(log N)* Skew Sunday, October 27, 13

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Pairing heaps Sunday, October 27, 13

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Sunday, October 27, 13

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Haskell Sunday, October 27, 13

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Pairing Python 2.* only Sunday, October 27, 13

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•push= O(1) •pop= O(1)* •union= O(1) Pairing Sunday, October 27, 13

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More more persistent structure Sunday, October 27, 13

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More fn.py module Sunday, October 27, 13

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Links http://en.wikipedia.org/wiki/Heap_(data_structure) http://en.wikipedia.org/wiki/Skew_heap http://interactivepython.org/runestone/static/ pythonds/Trees/heap.html https://gist.github.com/kachayev/7161521 https://gist.github.com/kachayev/6081643 https://gist.github.com/kachayev/7167046 Sunday, October 27, 13

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Q/A Sunday, October 27, 13