Python實現快速排序算法

Python 算法 快速排序

# -- coding: utf-8 --

from random import randint, shuffle
def _partition(seq, p, r):
    """數組劃分，偽碼如下：
    PARTITION(A, p, r)
    1  x ← A[r] // 作為劃分主元
    2  i ← p-1
    3  for j ← p to r-1
    4    do if A[j] <= x
    5         then i ← i + 1 // 前劃分區域的索引
    6              exchange A[i] ?A[j] // 小值交換到前面
    7 exchange A[i+1] ?A[r] // A[r]交換到前區域結尾
    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):
    """遞歸調用，偽碼如下：
    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): 一個序列對象。
    """
    _quick_sort(seq, 0, len(seq) - 1)
def _rand_partition(seq, p, r):
    """隨機取樣交換后再劃分，偽碼如下：
    RANDOMIZED-PARTITION(A, p, r)
    1  i ← RANDOM(p, r)  // 從A[p..r]中隨機選出一個
    2  exchange A[r] ? A[i] // A[r]與其交換
    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):
    """隨機取樣劃分方式的遞歸調用，偽碼如下：
    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（隨機化版本）"""
    _rand_qsort(seq, 0, len(seq) - 1)
def qsort(L):
    """快速排序（簡易版本）
    更多: Python Cookbook 2nd Edition 第5.11章節
    """
    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))</pre><br />