Python 算法 快速排序
# -*- coding: utf-8 -*- from random import randint, shuffle def _partition(seq, p, r): """数组划分，伪码如下： PARTITION(A, p, r) 1 x ← A[r] // 作为划分主元 2 i ← p-1 3 for j ← p to r-1 4 do if A[j] <= x 5 then i ← i + 1 // 前划分区域的索引 6 exchange A[i] ↔A[j] // 小值交换到前面 7 exchange A[i+1] ↔A[r] // A[r]交换到前区域结尾 8 return i + 1 T(n) = θ(n) """ x = seq[r] i = p - 1 for j in range(p, r): if seq[j] <= x: i += 1 seq[i], seq[j] = seq[j], seq[i] i += 1 seq[i], seq[r] = seq[r], seq[i] return i def _quick_sort(seq, p, r): """递归调用，伪码如下： QUICKSORT(A, p, r) 1 if p < r 2 then q ← PARTITION(A, p, r) 3 QUICKSORT(A, p, q-1) 4 QUICKSORT(A, q+1, r) T(n) = θ(n^2) """ if p >= r: return q = _partition(seq, p, r) _quick_sort(seq, p, q - 1) _quick_sort(seq, q + 1, r) def quick_sort(seq): """快速排序 Args: seq (Sequence): 一个序列对象。 """ _quick_sort(seq, 0, len(seq) - 1) def _rand_partition(seq, p, r): """随机取样交换后再划分，伪码如下： RANDOMIZED-PARTITION(A, p, r) 1 i ← RANDOM(p, r) // 从A[p..r]中随机选出一个 2 exchange A[r] ↔ A[i] // A[r]与其交换 3 return PARTITION(A, p, r) T(n) = O(n) """ i = randint(p, r) seq[r], seq[i] = seq[i], seq[r] return _partition(seq, p, r) def _rand_qsort(seq, p, r): """随机取样划分方式的递归调用，伪码如下： RANDOMIZED-QUICKSORT(A, p, r) 1 if p < r 2 then q ← RANDOMIZED-PARTITION(A, p, r) 3 RANDOMIZED-QUICKSORT(A, p, q-1) 4 RANDOMIZED-QUICKSORT(A, q+1, r) T(n) = O(n^2) """ if p >= r: return q = _rand_partition(seq, p, r) _rand_qsort(seq, p, q - 1) _rand_qsort(seq, q + 1, r) def rand_qsort(seq): """快速排序（随机化版本）""" _rand_qsort(seq, 0, len(seq) - 1) def qsort(L): """快速排序（简易版本） 更多: Python Cookbook 2nd Edition 第5.11章节 """ if not L: return [] return qsort([x for x in L[1:] if x < L[0]]) + L[0:1] + qsort([x for x in L[1:] if x >= L[0]]) if __name__ == '__main__': import timeit items = range(10000) shuffle(items) def test_sorted(): print(items) sorted_items = sorted(items) print(sorted_items) def test_quick_sort(): print(items) quick_sort(items) print(items) test_methods = [test_sorted, test_quick_sort] # test_rand_qsort, test_qsort for test in test_methods: name = test.__name__ # test.func_name t = timeit.Timer(name + '()', 'from __main__ import ' + name) print(name + ' takes time : %f' % t.timeit(1))
