# -*- 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))