## 2018年12月18日火曜日

### Algorithm - Python - 整理が苦手な修理屋(移動数、計算量、ループの回数、再帰分割統治クイックソート、インプレースピボット決め、再帰インプレースソート)

コード(Emacs)

Python 3

```#!/usr/bin/env python3
def pivot_partition_clever(lst: list, start: int, end: int) -> (int, int):
pivot = lst[end]
bottom = start - 1
top = end
done = False
move_count = 0
while not done:
while not done:
move_count += 1
bottom += 1
if bottom == top:
done = True
break
if lst[bottom] > pivot:
lst[top] = lst[bottom]
break
while not done:
move_count += 1
top -= 1
if top == bottom:
done = True
break
if lst[top] <= pivot:
lst[bottom] = lst[top]
break
lst[top] = pivot

def quick_sort(lst: list, start: int, end: int) -> None:
'''
>>> a = [4, 65, 2, -31, 0, 99, 83, 782, 1]
>>> quick_sort(a, 0, len(a) - 1)
24
'''
move_count = 0
if start < end:
pivot_index, count = pivot_partition_clever(lst, start, end)
move_count += count
move_count += quick_sort(lst, start, pivot_index - 1)
move_count += quick_sort(lst, pivot_index + 1, end)
return move_count

if __name__ == '__main__':
import doctest
doctest.testmod()
r = [0] * 100
r[0] = 19
for i in range(100):
r[i] = (9679 * r[i-1] + 12637 * i) % 2287
count = quick_sort(r, 0, len(r) - 1)
print(r)
print(count)
d = list(range(99, -1, -1))
count = quick_sort(d, 0, len(d) - 1)
print(d)
print(count)
'''

'''
import random
import math
n = 50
m = 10000
print(f'近似値: {n * math.log2(n)}')
l = list(range(n))
total = 0
for _ in range(m):
random.shuffle(l)
total += quick_sort(l, 0, n - 1)
print(total / m)
```

```\$ ./sample2.py -v
Trying:
a = [4, 65, 2, -31, 0, 99, 83, 782, 1]
Expecting nothing
ok
Trying:
quick_sort(a, 0, len(a) - 1)
Expecting:
24
ok
__main__
__main__.pivot_partition_clever
1 items passed all tests:
2 tests in __main__.quick_sort
2 tests in 3 items.
2 passed and 0 failed.
Test passed.
[0, 38, 50, 116, 122, 141, 146, 220, 240, 240, 243, 275, 288, 305, 306, 306, 307, 387, 419, 431, 433, 446, 450, 493, 538, 548, 595, 598, 711, 764, 804, 812, 829, 844, 879, 910, 929, 942, 955, 967, 1038, 1041, 1049, 1078, 1083, 1102, 1105, 1150, 1153, 1154, 1172, 1202, 1208, 1221, 1244, 1266, 1266, 1290, 1320, 1384, 1386, 1425, 1428, 1476, 1505, 1517, 1520, 1523, 1553, 1582, 1609, 1613, 1625, 1639, 1691, 1696, 1725, 1818, 1845, 1884, 1927, 1938, 1946, 1949, 1980, 1991, 1995, 2006, 2029, 2038, 2047, 2085, 2107, 2115, 2119, 2125, 2188, 2215, 2269, 2284]
682
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]
5049

291.9067
\$
```

DとRでループの回数が異なる理由は、Dの場合、ピボットが最小値で、分割の偏りがもっとも大きい場合に該当するから。