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July 15, 2019 20:40
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Python implementation of weighted quick-union with path compression algorithm
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| class WeightedQuickUnionWithPathCompressionUF(): | |
| """Weighted quick-union with path compression algorithm | |
| The original Java implementation is introduced at: | |
| https://algs4.cs.princeton.edu/15uf/index.php#1.5 | |
| https://www.cs.princeton.edu/~rs/AlgsDS07/01UnionFind.pdf | |
| Time complexity: | |
| constructor: O(n) | |
| union: amortized ~O(1) | |
| find: amortized ~O(1) | |
| >>> uf = WeightedQuickUnionWithPathCompressionUF(10) | |
| >>> for (p, q) in [(4, 3), (3, 8), (6, 5), (9, 4), (2, 1), | |
| ... (8, 9), (5, 0), (7, 2), (6, 1)]: | |
| ... uf.union(p, q) | |
| >>> uf | |
| {'roots': [6, 2, 6, 4, 4, 6, 6, 2, 4, 4], 'count': 2} | |
| >>> uf.find(1) | |
| 6 | |
| >>> uf | |
| {'roots': [6, 6, 6, 4, 4, 6, 6, 2, 4, 4], 'count': 2} | |
| >>> uf.connected(7, 0) | |
| True | |
| >>> uf | |
| {'roots': [6, 6, 6, 4, 4, 6, 6, 6, 4, 4], 'count': 2} | |
| """ | |
| def __init__(self, n): | |
| self.items = list(range(n)) | |
| self.sizes = [1] * n | |
| self.count = len(self.items) | |
| def __repr__(self): | |
| return "{'roots': %s, 'count': %d}" % (self.items, self.count) | |
| def union(self, p, q): | |
| if p == q: | |
| return | |
| p_root = self._root(p) | |
| q_root = self._root(q) | |
| if p_root == q_root: | |
| return | |
| if self.sizes[p_root] < self.sizes[q_root]: | |
| self.items[p_root] = q_root | |
| self.sizes[q_root] += self.sizes[p_root] | |
| else: | |
| self.items[q_root] = p_root | |
| self.sizes[p_root] += self.sizes[q_root] | |
| self.count -= 1 | |
| def _root(self, p): | |
| root = self.items[p] | |
| while not root == self.items[root]: | |
| self.items[root] = self.items[self.items[root]] | |
| root = self.items[root] | |
| self.items[p] = root | |
| return root | |
| def find(self, p): | |
| return self._root(p) | |
| def connected(self, p, q): | |
| return p == q or self.find(p) == self.find(q) | |
| def count(self): | |
| return self.count | |
| if __name__ == '__main__': | |
| import doctest | |
| doctest.testmod() |
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Thanks for the class :)