@@ -1188,6 +1188,8 @@ msgid ""
1188
1188
"If the input is an iterator, then fully consuming the *islice* advances the "
1189
1189
"input iterator by ``max(start, stop)`` steps regardless of the *step* value."
1190
1190
msgstr ""
1191
+ "若輸入為疊代器,則完整耗盡 *islice* 會使輸入的疊代器向前移動 ``max(start, "
1192
+ "stop)`` 步,與 *step* 的值無關。"
1191
1193
1192
1194
#: ../../library/itertools.rst:513
1193
1195
msgid "Return successive overlapping pairs taken from the input *iterable*."
@@ -1332,6 +1334,8 @@ msgid ""
1332
1334
"`Cartesian product <https://en.wikipedia.org/wiki/Cartesian_product>`_ of "
1333
1335
"the input iterables."
1334
1336
msgstr ""
1337
+ "輸入可疊代物的 `笛卡爾乘積 <https://en.wikipedia.org/wiki/"
1338
+ "Cartesian_product>`_"
1335
1339
1336
1340
#: ../../library/itertools.rst:592
1337
1341
msgid ""
@@ -1601,10 +1605,14 @@ msgid ""
1601
1605
"`tee` calls to share the same underlying data chain and to have a single "
1602
1606
"update step rather than a chain of calls."
1603
1607
msgstr ""
1608
+ "當輸入的 *iterable* 已經是一個 tee 疊代物件時,回傳的 tuple(元組)中所有成員"
1609
+ "都會被建立,就如同它們是由上游的 :func:`tee` 呼叫所產生的一樣。這個「展平步"
1610
+ "驟 (flattening step)」讓巢狀的 :func:`tee` 呼叫能共享相同的底層資料鏈,並以單"
1611
+ "一的更新步驟取代一連串的呼叫。"
1604
1612
1605
1613
#: ../../library/itertools.rst:734
1606
1614
msgid "The flattening property makes tee iterators efficiently peekable:"
1607
- msgstr ""
1615
+ msgstr "展平特性讓 tee 疊代器具備高效的預覽能力: "
1608
1616
1609
1617
#: ../../library/itertools.rst:736
1610
1618
msgid ""
@@ -1613,6 +1621,10 @@ msgid ""
1613
1621
" [forked_iterator] = tee(tee_iterator, 1)\n"
1614
1622
" return next(forked_iterator)"
1615
1623
msgstr ""
1624
+ "def lookahead(tee_iterator):\n"
1625
+ " \" 回傳下一個值,但不推進輸入\" \n"
1626
+ " [forked_iterator] = tee(tee_iterator, 1)\n"
1627
+ " return next(forked_iterator)"
1616
1628
1617
1629
#: ../../library/itertools.rst:743
1618
1630
msgid ""
@@ -1969,6 +1981,171 @@ msgid ""
1969
1981
" while True:\n"
1970
1982
" yield function()"
1971
1983
msgstr ""
1984
+ "from collections import Counter, deque\n"
1985
+ "from contextlib import suppress\n"
1986
+ "from functools import reduce\n"
1987
+ "from math import comb, prod, sumprod, isqrt\n"
1988
+ "from operator import itemgetter, getitem, mul, neg\n"
1989
+ "\n"
1990
+ "def take(n, iterable):\n"
1991
+ " \" 回傳可疊代物件的前 n 個元素為串列。\" \n"
1992
+ " return list(islice(iterable, n))\n"
1993
+ "\n"
1994
+ "def prepend(value, iterable):\n"
1995
+ " \" 在可疊代物件開頭插入單一值。\" \n"
1996
+ " # prepend(1, [2, 3, 4]) → 1 2 3 4\n"
1997
+ " return chain([value], iterable)\n"
1998
+ "\n"
1999
+ "def tabulate(function, start=0):\n"
2000
+ " \" 回傳 function(0), function(1), ...\" \n"
2001
+ " return map(function, count(start))\n"
2002
+ "\n"
2003
+ "def repeatfunc(function, times=None, *args):\n"
2004
+ " \" 重複呼叫一個帶指定引數的函式。\" \n"
2005
+ " if times is None:\n"
2006
+ " return starmap(function, repeat(args))\n"
2007
+ " return starmap(function, repeat(args, times))\n"
2008
+ "\n"
2009
+ "def flatten(list_of_lists):\n"
2010
+ " \" 將巢狀結構攤平一層。\" \n"
2011
+ " return chain.from_iterable(list_of_lists)\n"
2012
+ "\n"
2013
+ "def ncycles(iterable, n):\n"
2014
+ " \" 回傳序列的元素重複 n 次。\" \n"
2015
+ " return chain.from_iterable(repeat(tuple(iterable), n))\n"
2016
+ "\n"
2017
+ "def loops(n):\n"
2018
+ " \" 執行 n 次的迴圈。類似 range(n) 但不建立整數序列。\" \n"
2019
+ " # for _ in loops(100): ...\n"
2020
+ " return repeat(None, n)\n"
2021
+ "\n"
2022
+ "def tail(n, iterable):\n"
2023
+ " \" 回傳一個疊代器,疊代最後 n 個元素。\" \n"
2024
+ " # tail(3, 'ABCDEFG') → E F G\n"
2025
+ " return iter(deque(iterable, maxlen=n))\n"
2026
+ "\n"
2027
+ "def consume(iterator, n=None):\n"
2028
+ " \" 將疊代器往前推進 n 步。如果 n 為 None,則完全消耗。\" \n"
2029
+ " # 使用以 C 語言的速度消耗疊代器的函式。\n"
2030
+ " if n is None:\n"
2031
+ " deque(iterator, maxlen=0)\n"
2032
+ " else:\n"
2033
+ " next(islice(iterator, n, n), None)\n"
2034
+ "\n"
2035
+ "def nth(iterable, n, default=None):\n"
2036
+ " \" 回傳第 n 個元素或預設值。\" \n"
2037
+ " return next(islice(iterable, n, None), default)\n"
2038
+ "\n"
2039
+ "def quantify(iterable, predicate=bool):\n"
2040
+ " \" 給定一個回傳 True 或 False 的判斷函式,計算為 True 的結果。\" \n"
2041
+ " return sum(map(predicate, iterable))\n"
2042
+ "\n"
2043
+ "def first_true(iterable, default=False, predicate=None):\n"
2044
+ " \" 回傳第一個為 true 的值,若無則回傳*預設值*。\" \n"
2045
+ " # first_true([a,b,c], x) → a or b or c or x\n"
2046
+ " # first_true([a,b], x, f) → a if f(a) else b if f(b) else x\n"
2047
+ " return next(filter(predicate, iterable), default)\n"
2048
+ "\n"
2049
+ "def all_equal(iterable, key=None):\n"
2050
+ " \" 回傳 True,如果所有元素兩兩相等。\" \n"
2051
+ " # all_equal('4٤௪౪໔', key=int) → True\n"
2052
+ " return len(take(2, groupby(iterable, key))) <= 1\n"
2053
+ "\n"
2054
+ "def unique_justseen(iterable, key=None):\n"
2055
+ " \" 產生唯一的元素,並保留原始順序。只記住剛看見的元素。\" \n"
2056
+ " # unique_justseen('AAAABBBCCDAABBB') → A B C D A B\n"
2057
+ " # unique_justseen('ABBcCAD', str.casefold) → A B c A D\n"
2058
+ " if key is None:\n"
2059
+ " return map(itemgetter(0), groupby(iterable))\n"
2060
+ " return map(next, map(itemgetter(1), groupby(iterable, key)))\n"
2061
+ "\n"
2062
+ "def unique_everseen(iterable, key=None):\n"
2063
+ " \" 產生唯一的元素,並保留原始順序。記住所有曾見過的元素。\" \n"
2064
+ " # unique_everseen('AAAABBBCCDAABBB') → A B C D\n"
2065
+ " # unique_everseen('ABBcCAD', str.casefold) → A B c D\n"
2066
+ " seen = set()\n"
2067
+ " if key is None:\n"
2068
+ " for element in filterfalse(seen.__contains__, iterable):\n"
2069
+ " seen.add(element)\n"
2070
+ " yield element\n"
2071
+ " else:\n"
2072
+ " for element in iterable:\n"
2073
+ " k = key(element)\n"
2074
+ " if k not in seen:\n"
2075
+ " seen.add(k)\n"
2076
+ " yield element\n"
2077
+ "\n"
2078
+ "def unique(iterable, key=None, reverse=False):\n"
2079
+ " \" 產生排序後的不重複元素。支援不可雜湊的輸入。\" \n"
2080
+ " # unique([[1, 2], [3, 4], [1, 2]]) → [1, 2] [3, 4]\n"
2081
+ " sequenced = sorted(iterable, key=key, reverse=reverse)\n"
2082
+ " return unique_justseen(sequenced, key=key)\n"
2083
+ "\n"
2084
+ "def sliding_window(iterable, n):\n"
2085
+ " \" 將資料收集成重疊的固定長度區段或區塊。\" \n"
2086
+ " # sliding_window('ABCDEFG', 4) → ABCD BCDE CDEF DEFG\n"
2087
+ " iterator = iter(iterable)\n"
2088
+ " window = deque(islice(iterator, n - 1), maxlen=n)\n"
2089
+ " for x in iterator:\n"
2090
+ " window.append(x)\n"
2091
+ " yield tuple(window)\n"
2092
+ "\n"
2093
+ "def grouper(iterable, n, *, incomplete='fill', fillvalue=None):\n"
2094
+ " \" 將資料收集成不重疊的固定長度區段或區塊。\" \n"
2095
+ " # grouper('ABCDEFG', 3, fillvalue='x') → ABC DEF Gxx\n"
2096
+ " # grouper('ABCDEFG', 3, incomplete='strict') → ABC DEF ValueError\n"
2097
+ " # grouper('ABCDEFG', 3, incomplete='ignore') → ABC DEF\n"
2098
+ " iterators = [iter(iterable)] * n\n"
2099
+ " match incomplete:\n"
2100
+ " case 'fill':\n"
2101
+ " return zip_longest(*iterators, fillvalue=fillvalue)\n"
2102
+ " case 'strict':\n"
2103
+ " return zip(*iterators, strict=True)\n"
2104
+ " case 'ignore':\n"
2105
+ " return zip(*iterators)\n"
2106
+ " case _:\n"
2107
+ " raise ValueError('Expected fill, strict, or ignore')\n"
2108
+ "\n"
2109
+ "def roundrobin(*iterables):\n"
2110
+ " \" 以循環方式依序輸入可疊代物件,直到全部耗盡。\" \n"
2111
+ " # roundrobin('ABC', 'D', 'EF') → A D E B F C\n"
2112
+ " # 演算法出自 George Sakkis\n"
2113
+ " iterators = map(iter, iterables)\n"
2114
+ " for num_active in range(len(iterables), 0, -1):\n"
2115
+ " iterators = cycle(islice(iterators, num_active))\n"
2116
+ " yield from map(next, iterators)\n"
2117
+ "\n"
2118
+ "def subslices(seq):\n"
2119
+ " \" 回傳序列的所有連續非空子切片。\" \n"
2120
+ " # subslices('ABCD') → A AB ABC ABCD B BC BCD C CD D\n"
2121
+ " slices = starmap(slice, combinations(range(len(seq) + 1), 2))\n"
2122
+ " return map(getitem, repeat(seq), slices)\n"
2123
+ "\n"
2124
+ "def iter_index(iterable, value, start=0, stop=None):\n"
2125
+ " \" 回傳在序列或可疊代物件中某值出現的索引位置。\" \n"
2126
+ " # iter_index('AABCADEAF', 'A') → 0 1 4 7\n"
2127
+ " seq_index = getattr(iterable, 'index', None)\n"
2128
+ " if seq_index is None:\n"
2129
+ " iterator = islice(iterable, start, stop)\n"
2130
+ " for i, element in enumerate(iterator, start):\n"
2131
+ " if element is value or element == value:\n"
2132
+ " yield i\n"
2133
+ " else:\n"
2134
+ " stop = len(iterable) if stop is None else stop\n"
2135
+ " i = start\n"
2136
+ " with suppress(ValueError):\n"
2137
+ " while True:\n"
2138
+ " yield (i := seq_index(value, i, stop))\n"
2139
+ " i += 1\n"
2140
+ "\n"
2141
+ "def iter_except(function, exception, first=None):\n"
2142
+ " \" 將一個 call-until-exception 轉換為疊代器介面。\" \n"
2143
+ " # iter_except(d.popitem, KeyError) → 非阻塞的字典疊代器\n"
2144
+ " with suppress(exception):\n"
2145
+ " if first is not None:\n"
2146
+ " yield first()\n"
2147
+ " while True:\n"
2148
+ " yield function()"
1972
2149
1973
2150
#: ../../library/itertools.rst:1008
1974
2151
msgid "The following recipes have a more mathematical flavor:"
@@ -2100,3 +2277,125 @@ msgid ""
2100
2277
" n -= n // prime\n"
2101
2278
" return n"
2102
2279
msgstr ""
2280
+ "def multinomial(*counts):\n"
2281
+ " \" 多重集合的不同排列數。\" \n"
2282
+ " # Counter('abracadabra').values() → 5 2 2 1 1\n"
2283
+ " # multinomial(5, 2, 2, 1, 1) → 83160\n"
2284
+ " return prod(map(comb, accumulate(counts), counts))\n"
2285
+ "\n"
2286
+ "def powerset(iterable):\n"
2287
+ " \" 來自可疊代物件的子序列,從最短到最長。\" \n"
2288
+ " # powerset([1,2,3]) → () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)\n"
2289
+ " s = list(iterable)\n"
2290
+ " return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))\n"
2291
+ "\n"
2292
+ "def sum_of_squares(iterable):\n"
2293
+ " \" 將輸入值的平方加總。\" \n"
2294
+ " # sum_of_squares([10, 20, 30]) → 1400\n"
2295
+ " return sumprod(*tee(iterable))\n"
2296
+ "\n"
2297
+ "def reshape(matrix, columns):\n"
2298
+ " \" 將 2 維矩陣重新塑形為指定的行數。\" \n"
2299
+ " # reshape([(0, 1), (2, 3), (4, 5)], 3) → (0, 1, 2), (3, 4, 5)\n"
2300
+ " return batched(chain.from_iterable(matrix), columns, strict=True)\n"
2301
+ "\n"
2302
+ "def transpose(matrix):\n"
2303
+ " \" 交換 2 維矩陣的列和行。\" \n"
2304
+ " # transpose([(1, 2, 3), (11, 22, 33)]) → (1, 11) (2, 22) (3, 33)\n"
2305
+ " return zip(*matrix, strict=True)\n"
2306
+ "\n"
2307
+ "def matmul(m1, m2):\n"
2308
+ " \" 矩陣相乘。\" \n"
2309
+ " # matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]) → (49, 80), (41, 60)\n"
2310
+ " n = len(m2[0])\n"
2311
+ " return batched(starmap(sumprod, product(m1, transpose(m2))), n)\n"
2312
+ "\n"
2313
+ "def convolve(signal, kernel):\n"
2314
+ " \"\"\" 兩個可疊代物件的離散線性捲積。\n"
2315
+ " 等同於多項式相乘。\n"
2316
+ "\n"
2317
+ " 在數學上捲積是可交換的;但輸入的處理方式不同。\n"
2318
+ " 訊號以惰性方式被讀取,且可以是無限;核心會在計算開始前被全部讀取。\n"
2319
+ "\n"
2320
+ " 文章:https://betterexplained.com/articles/intuitive-convolution/\n"
2321
+ " 影片:https://www.youtube.com/watch?v=KuXjwB4LzSA\n"
2322
+ " \"\"\" \n"
2323
+ " # convolve([1, -1, -20], [1, -3]) → 1 -4 -17 60\n"
2324
+ " # convolve(data, [0.25, 0.25, 0.25, 0.25]) → 移動平均(模糊)\n"
2325
+ " # convolve(data, [1/2, 0, -1/2]) → 一階導數估計\n"
2326
+ " # convolve(data, [1, -2, 1]) → 二階導數估計\n"
2327
+ " kernel = tuple(kernel)[::-1]\n"
2328
+ " n = len(kernel)\n"
2329
+ " padded_signal = chain(repeat(0, n-1), signal, repeat(0, n-1))\n"
2330
+ " windowed_signal = sliding_window(padded_signal, n)\n"
2331
+ " return map(sumprod, repeat(kernel), windowed_signal)\n"
2332
+ "\n"
2333
+ "def polynomial_from_roots(roots):\n"
2334
+ " \"\"\" 由多項式的根計算其係數。\n"
2335
+ "\n"
2336
+ " (x - 5) (x + 4) (x - 3) 展開為: x³ -4x² -17x + 60\n"
2337
+ " \"\"\" \n"
2338
+ " # polynomial_from_roots([5, -4, 3]) → [1, -4, -17, 60]\n"
2339
+ " factors = zip(repeat(1), map(neg, roots))\n"
2340
+ " return list(reduce(convolve, factors, [1]))\n"
2341
+ "\n"
2342
+ "def polynomial_eval(coefficients, x):\n"
2343
+ " \"\"\" 在指定值計算多項式的值。\n"
2344
+ "\n"
2345
+ " 此方法在數值穩定性上比 Horner 方法更好。\n"
2346
+ " \"\"\" \n"
2347
+ " # 計算 x³ -4x² -17x + 60 在 x = 5 時的值\n"
2348
+ " # polynomial_eval([1, -4, -17, 60], x=5) → 0\n"
2349
+ " n = len(coefficients)\n"
2350
+ " if not n:\n"
2351
+ " return type(x)(0)\n"
2352
+ " powers = map(pow, repeat(x), reversed(range(n)))\n"
2353
+ " return sumprod(coefficients, powers)\n"
2354
+ "\n"
2355
+ "def polynomial_derivative(coefficients):\n"
2356
+ " \"\"\" 計算多項式的一階導數。\n"
2357
+ "\n"
2358
+ " f(x) = x³ -4x² -17x + 60\n"
2359
+ " f'(x) = 3x² -8x -17\n"
2360
+ " \"\"\" \n"
2361
+ " # polynomial_derivative([1, -4, -17, 60]) → [3, -8, -17]\n"
2362
+ " n = len(coefficients)\n"
2363
+ " powers = reversed(range(1, n))\n"
2364
+ " return list(map(mul, coefficients, powers))\n"
2365
+ "\n"
2366
+ "def sieve(n):\n"
2367
+ " \" 小於 n 的質數。\" \n"
2368
+ " # sieve(30) → 2 3 5 7 11 13 17 19 23 29\n"
2369
+ " if n > 2:\n"
2370
+ " yield 2\n"
2371
+ " data = bytearray((0, 1)) * (n // 2)\n"
2372
+ " for p in iter_index(data, 1, start=3, stop=isqrt(n) + 1):\n"
2373
+ " data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))\n"
2374
+ " yield from iter_index(data, 1, start=3)\n"
2375
+ "\n"
2376
+ "def factor(n):\n"
2377
+ " \" n 的質因數。\" \n"
2378
+ " # factor(99) → 3 3 11\n"
2379
+ " # factor(1_000_000_000_000_007) → 47 59 360620266859\n"
2380
+ " # factor(1_000_000_000_000_403) → 1000000000000403\n"
2381
+ " for prime in sieve(isqrt(n) + 1):\n"
2382
+ " while not n % prime:\n"
2383
+ " yield prime\n"
2384
+ " n //= prime\n"
2385
+ " if n == 1:\n"
2386
+ " return\n"
2387
+ " if n > 1:\n"
2388
+ " yield n\n"
2389
+ "\n"
2390
+ "def is_prime(n):\n"
2391
+ " \" 回傳 True,若 n 為質數。\" \n"
2392
+ " # is_prime(1_000_000_000_000_403) → True\n"
2393
+ " return n > 1 and next(factor(n)) == n\n"
2394
+ "\n"
2395
+ "def totient(n):\n"
2396
+ " \" 計算不大於 n 且與 n 互質的自然數個數。\" \n"
2397
+ " # https://mathworld.wolfram.com/TotientFunction.html\n"
2398
+ " # totient(12) → 4 因爲 len([1, 5, 7, 11]) == 4\n"
2399
+ " for prime in set(factor(n)):\n"
2400
+ " n -= n // prime\n"
2401
+ " return n"
0 commit comments