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)) 
