Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 1 | :mod:`itertools` --- Functions creating iterators for efficient looping |
| 2 | ======================================================================= |
| 3 | |
| 4 | .. module:: itertools |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 5 | :synopsis: Functions creating iterators for efficient looping. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 6 | .. moduleauthor:: Raymond Hettinger <python@rcn.com> |
| 7 | .. sectionauthor:: Raymond Hettinger <python@rcn.com> |
| 8 | |
| 9 | |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 10 | .. testsetup:: |
| 11 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 12 | from itertools import * |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 13 | |
| 14 | |
Raymond Hettinger | f76b920 | 2009-02-17 20:00:59 +0000 | [diff] [blame] | 15 | This module implements a number of :term:`iterator` building blocks inspired |
| 16 | by constructs from APL, Haskell, and SML. Each has been recast in a form |
| 17 | suitable for Python. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 18 | |
| 19 | The module standardizes a core set of fast, memory efficient tools that are |
Raymond Hettinger | f76b920 | 2009-02-17 20:00:59 +0000 | [diff] [blame] | 20 | useful by themselves or in combination. Together, they form an "iterator |
| 21 | algebra" making it possible to construct specialized tools succinctly and |
| 22 | efficiently in pure Python. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 23 | |
| 24 | For instance, SML provides a tabulation tool: ``tabulate(f)`` which produces a |
Ezio Melotti | b660599 | 2010-01-21 20:57:24 +0000 | [diff] [blame] | 25 | sequence ``f(0), f(1), ...``. The same effect can be achieved in Python |
Raymond Hettinger | a6c6037 | 2008-03-13 01:26:19 +0000 | [diff] [blame] | 26 | by combining :func:`map` and :func:`count` to form ``map(f, count())``. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 27 | |
Raymond Hettinger | 2c109ab | 2009-03-12 00:29:44 +0000 | [diff] [blame] | 28 | These tools and their built-in counterparts also work well with the high-speed |
| 29 | functions in the :mod:`operator` module. For example, the multiplication |
| 30 | operator can be mapped across two vectors to form an efficient dot-product: |
| 31 | ``sum(map(operator.mul, vector1, vector2))``. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 32 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 33 | |
Raymond Hettinger | f76b920 | 2009-02-17 20:00:59 +0000 | [diff] [blame] | 34 | **Infinite Iterators:** |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 35 | |
Raymond Hettinger | 5bfd8ce | 2009-04-10 19:02:36 +0000 | [diff] [blame] | 36 | ================== ================= ================================================= ========================================= |
| 37 | Iterator Arguments Results Example |
| 38 | ================== ================= ================================================= ========================================= |
| 39 | :func:`count` start, [step] start, start+step, start+2*step, ... ``count(10) --> 10 11 12 13 14 ...`` |
| 40 | :func:`cycle` p p0, p1, ... plast, p0, p1, ... ``cycle('ABCD') --> A B C D A B C D ...`` |
| 41 | :func:`repeat` elem [,n] elem, elem, elem, ... endlessly or up to n times ``repeat(10, 3) --> 10 10 10`` |
| 42 | ================== ================= ================================================= ========================================= |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 43 | |
Raymond Hettinger | f76b920 | 2009-02-17 20:00:59 +0000 | [diff] [blame] | 44 | **Iterators terminating on the shortest input sequence:** |
| 45 | |
Raymond Hettinger | 5bfd8ce | 2009-04-10 19:02:36 +0000 | [diff] [blame] | 46 | ==================== ============================ ================================================= ============================================================= |
| 47 | Iterator Arguments Results Example |
| 48 | ==================== ============================ ================================================= ============================================================= |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 49 | :func:`accumulate` p [,func] p0, p0+p1, p0+p1+p2, ... ``accumulate([1,2,3,4,5]) --> 1 3 6 10 15`` |
Raymond Hettinger | 5bfd8ce | 2009-04-10 19:02:36 +0000 | [diff] [blame] | 50 | :func:`chain` p, q, ... p0, p1, ... plast, q0, q1, ... ``chain('ABC', 'DEF') --> A B C D E F`` |
| 51 | :func:`compress` data, selectors (d[0] if s[0]), (d[1] if s[1]), ... ``compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F`` |
| 52 | :func:`dropwhile` pred, seq seq[n], seq[n+1], starting when pred fails ``dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1`` |
Georg Brandl | c2da5ce | 2009-08-13 09:16:39 +0000 | [diff] [blame] | 53 | :func:`filterfalse` pred, seq elements of seq where pred(elem) is False ``filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8`` |
Raymond Hettinger | 5bfd8ce | 2009-04-10 19:02:36 +0000 | [diff] [blame] | 54 | :func:`groupby` iterable[, keyfunc] sub-iterators grouped by value of keyfunc(v) |
| 55 | :func:`islice` seq, [start,] stop [, step] elements from seq[start:stop:step] ``islice('ABCDEFG', 2, None) --> C D E F G`` |
| 56 | :func:`starmap` func, seq func(\*seq[0]), func(\*seq[1]), ... ``starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000`` |
| 57 | :func:`takewhile` pred, seq seq[0], seq[1], until pred fails ``takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4`` |
| 58 | :func:`tee` it, n it1, it2 , ... itn splits one iterator into n |
Georg Brandl | c2da5ce | 2009-08-13 09:16:39 +0000 | [diff] [blame] | 59 | :func:`zip_longest` p, q, ... (p[0], q[0]), (p[1], q[1]), ... ``zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-`` |
Raymond Hettinger | 5bfd8ce | 2009-04-10 19:02:36 +0000 | [diff] [blame] | 60 | ==================== ============================ ================================================= ============================================================= |
Raymond Hettinger | f76b920 | 2009-02-17 20:00:59 +0000 | [diff] [blame] | 61 | |
| 62 | **Combinatoric generators:** |
| 63 | |
Raymond Hettinger | 7f587cd | 2009-04-10 19:43:50 +0000 | [diff] [blame] | 64 | ============================================== ==================== ============================================================= |
| 65 | Iterator Arguments Results |
| 66 | ============================================== ==================== ============================================================= |
| 67 | :func:`product` p, q, ... [repeat=1] cartesian product, equivalent to a nested for-loop |
| 68 | :func:`permutations` p[, r] r-length tuples, all possible orderings, no repeated elements |
Raymond Hettinger | 36c3c02 | 2009-11-19 01:20:07 +0000 | [diff] [blame] | 69 | :func:`combinations` p, r r-length tuples, in sorted order, no repeated elements |
| 70 | :func:`combinations_with_replacement` p, r r-length tuples, in sorted order, with repeated elements |
Raymond Hettinger | 7f587cd | 2009-04-10 19:43:50 +0000 | [diff] [blame] | 71 | ``product('ABCD', repeat=2)`` ``AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD`` |
| 72 | ``permutations('ABCD', 2)`` ``AB AC AD BA BC BD CA CB CD DA DB DC`` |
| 73 | ``combinations('ABCD', 2)`` ``AB AC AD BC BD CD`` |
| 74 | ``combinations_with_replacement('ABCD', 2)`` ``AA AB AC AD BB BC BD CC CD DD`` |
| 75 | ============================================== ==================== ============================================================= |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 76 | |
| 77 | |
| 78 | .. _itertools-functions: |
| 79 | |
| 80 | Itertool functions |
| 81 | ------------------ |
| 82 | |
| 83 | The following module functions all construct and return iterators. Some provide |
| 84 | streams of infinite length, so they should only be accessed by functions or |
| 85 | loops that truncate the stream. |
| 86 | |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 87 | .. function:: accumulate(iterable[, func]) |
Raymond Hettinger | adb8146 | 2010-12-01 22:50:36 +0000 | [diff] [blame] | 88 | |
Raymond Hettinger | 2d93e6e | 2010-12-03 02:33:53 +0000 | [diff] [blame] | 89 | Make an iterator that returns accumulated sums. Elements may be any addable |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 90 | type including :class:`Decimal` or :class:`Fraction`. If the optional |
| 91 | *func* argument is supplied, it should be a function of two arguments |
| 92 | and it will be used instead of addition. |
Raymond Hettinger | adb8146 | 2010-12-01 22:50:36 +0000 | [diff] [blame] | 93 | |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 94 | Equivalent to:: |
| 95 | |
| 96 | def accumulate(iterable, func=operator.add): |
Raymond Hettinger | adb8146 | 2010-12-01 22:50:36 +0000 | [diff] [blame] | 97 | 'Return running totals' |
Raymond Hettinger | d8ff465 | 2010-12-03 02:09:34 +0000 | [diff] [blame] | 98 | # accumulate([1,2,3,4,5]) --> 1 3 6 10 15 |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 99 | # accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120 |
Raymond Hettinger | d8ff465 | 2010-12-03 02:09:34 +0000 | [diff] [blame] | 100 | it = iter(iterable) |
| 101 | total = next(it) |
| 102 | yield total |
| 103 | for element in it: |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 104 | total = func(total, element) |
Raymond Hettinger | d8ff465 | 2010-12-03 02:09:34 +0000 | [diff] [blame] | 105 | yield total |
Raymond Hettinger | adb8146 | 2010-12-01 22:50:36 +0000 | [diff] [blame] | 106 | |
Raymond Hettinger | 295c1d4 | 2011-04-21 11:09:28 -0700 | [diff] [blame] | 107 | There are a number of uses for the *func* argument. It can be set to |
| 108 | :func:`min` for a running minimum, :func:`max` for a running maximum, or |
| 109 | :func:`operator.mul` for a running product. Amortization tables can be |
| 110 | built by accumulating interest and applying payments. First-order |
| 111 | `recurrence relations <http://en.wikipedia.org/wiki/Recurrence_relation>`_ |
| 112 | can be modeled by supplying the initial value in the iterable and using only |
| 113 | the accumulated total in *func* argument:: |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 114 | |
| 115 | >>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8] |
| 116 | >>> list(accumulate(data, operator.mul)) # running product |
| 117 | [3, 12, 72, 144, 144, 1296, 0, 0, 0, 0] |
| 118 | >>> list(accumulate(data, max)) # running maximum |
| 119 | [3, 4, 6, 6, 6, 9, 9, 9, 9, 9] |
| 120 | |
| 121 | # Amortize a 5% loan of 1000 with 4 annual payments of 90 |
| 122 | >>> cashflows = [1000, -90, -90, -90, -90] |
| 123 | >>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt)) |
| 124 | [1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001] |
| 125 | |
Raymond Hettinger | 295c1d4 | 2011-04-21 11:09:28 -0700 | [diff] [blame] | 126 | # Chaotic recurrence relation http://en.wikipedia.org/wiki/Logistic_map |
| 127 | >>> logistic_map = lambda x, _: r * x * (1 - x) |
| 128 | >>> r = 3.8 |
| 129 | >>> x0 = 0.4 |
| 130 | >>> inputs = repeat(x0, 36) # only the initial value is used |
| 131 | >>> [format(x, '.2f') for x in accumulate(inputs, logistic_map)] |
| 132 | ['0.40', '0.91', '0.30', '0.81', '0.60', '0.92', '0.29', '0.79', '0.63', |
| 133 | '0.88' ,'0.39', '0.90', '0.33', '0.84', '0.52', '0.95', '0.18', '0.57', |
| 134 | '0.93', '0.25', '0.71', '0.79', '0.63', '0.88', '0.39', '0.91', '0.32', |
| 135 | '0.83', '0.54', '0.95', '0.20', '0.60', '0.91', '0.30', '0.80', '0.60'] |
| 136 | |
Raymond Hettinger | adb8146 | 2010-12-01 22:50:36 +0000 | [diff] [blame] | 137 | .. versionadded:: 3.2 |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 138 | |
Raymond Hettinger | 5d44613 | 2011-03-27 18:52:10 -0700 | [diff] [blame] | 139 | .. versionchanged:: 3.3 |
| 140 | Added the optional *func* parameter. |
| 141 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 142 | .. function:: chain(*iterables) |
| 143 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 144 | Make an iterator that returns elements from the first iterable until it is |
| 145 | exhausted, then proceeds to the next iterable, until all of the iterables are |
| 146 | exhausted. Used for treating consecutive sequences as a single sequence. |
| 147 | Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 148 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 149 | def chain(*iterables): |
| 150 | # chain('ABC', 'DEF') --> A B C D E F |
| 151 | for it in iterables: |
| 152 | for element in it: |
| 153 | yield element |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 154 | |
| 155 | |
Georg Brandl | 933b974 | 2010-07-29 14:36:11 +0000 | [diff] [blame] | 156 | .. classmethod:: chain.from_iterable(iterable) |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 157 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 158 | Alternate constructor for :func:`chain`. Gets chained inputs from a |
| 159 | single iterable argument that is evaluated lazily. Equivalent to:: |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 160 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 161 | @classmethod |
| 162 | def from_iterable(iterables): |
| 163 | # chain.from_iterable(['ABC', 'DEF']) --> A B C D E F |
| 164 | for it in iterables: |
| 165 | for element in it: |
| 166 | yield element |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 167 | |
Christian Heimes | 7864476 | 2008-03-04 23:39:23 +0000 | [diff] [blame] | 168 | |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 169 | .. function:: combinations(iterable, r) |
| 170 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 171 | Return *r* length subsequences of elements from the input *iterable*. |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 172 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 173 | Combinations are emitted in lexicographic sort order. So, if the |
| 174 | input *iterable* is sorted, the combination tuples will be produced |
| 175 | in sorted order. |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 176 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 177 | Elements are treated as unique based on their position, not on their |
| 178 | value. So if the input elements are unique, there will be no repeat |
| 179 | values in each combination. |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 180 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 181 | Equivalent to:: |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 182 | |
| 183 | def combinations(iterable, r): |
Raymond Hettinger | dd1150e | 2008-03-13 02:39:40 +0000 | [diff] [blame] | 184 | # combinations('ABCD', 2) --> AB AC AD BC BD CD |
| 185 | # combinations(range(4), 3) --> 012 013 023 123 |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 186 | pool = tuple(iterable) |
Christian Heimes | 380f7f2 | 2008-02-28 11:19:05 +0000 | [diff] [blame] | 187 | n = len(pool) |
Raymond Hettinger | 5bad41e | 2009-01-08 21:01:54 +0000 | [diff] [blame] | 188 | if r > n: |
| 189 | return |
| 190 | indices = list(range(r)) |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 191 | yield tuple(pool[i] for i in indices) |
Raymond Hettinger | cf984ce | 2009-02-18 20:56:51 +0000 | [diff] [blame] | 192 | while True: |
Christian Heimes | 380f7f2 | 2008-02-28 11:19:05 +0000 | [diff] [blame] | 193 | for i in reversed(range(r)): |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 194 | if indices[i] != i + n - r: |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 195 | break |
Christian Heimes | 380f7f2 | 2008-02-28 11:19:05 +0000 | [diff] [blame] | 196 | else: |
| 197 | return |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 198 | indices[i] += 1 |
Christian Heimes | 380f7f2 | 2008-02-28 11:19:05 +0000 | [diff] [blame] | 199 | for j in range(i+1, r): |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 200 | indices[j] = indices[j-1] + 1 |
| 201 | yield tuple(pool[i] for i in indices) |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 202 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 203 | The code for :func:`combinations` can be also expressed as a subsequence |
| 204 | of :func:`permutations` after filtering entries where the elements are not |
| 205 | in sorted order (according to their position in the input pool):: |
Christian Heimes | 7864476 | 2008-03-04 23:39:23 +0000 | [diff] [blame] | 206 | |
| 207 | def combinations(iterable, r): |
| 208 | pool = tuple(iterable) |
| 209 | n = len(pool) |
| 210 | for indices in permutations(range(n), r): |
| 211 | if sorted(indices) == list(indices): |
| 212 | yield tuple(pool[i] for i in indices) |
| 213 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 214 | The number of items returned is ``n! / r! / (n-r)!`` when ``0 <= r <= n`` |
| 215 | or zero when ``r > n``. |
Christian Heimes | 836baa5 | 2008-02-26 08:18:30 +0000 | [diff] [blame] | 216 | |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 217 | .. function:: combinations_with_replacement(iterable, r) |
| 218 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 219 | Return *r* length subsequences of elements from the input *iterable* |
| 220 | allowing individual elements to be repeated more than once. |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 221 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 222 | Combinations are emitted in lexicographic sort order. So, if the |
| 223 | input *iterable* is sorted, the combination tuples will be produced |
| 224 | in sorted order. |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 225 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 226 | Elements are treated as unique based on their position, not on their |
| 227 | value. So if the input elements are unique, the generated combinations |
| 228 | will also be unique. |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 229 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 230 | Equivalent to:: |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 231 | |
| 232 | def combinations_with_replacement(iterable, r): |
| 233 | # combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC |
| 234 | pool = tuple(iterable) |
| 235 | n = len(pool) |
| 236 | if not n and r: |
| 237 | return |
| 238 | indices = [0] * r |
| 239 | yield tuple(pool[i] for i in indices) |
Raymond Hettinger | cf984ce | 2009-02-18 20:56:51 +0000 | [diff] [blame] | 240 | while True: |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 241 | for i in reversed(range(r)): |
| 242 | if indices[i] != n - 1: |
| 243 | break |
| 244 | else: |
| 245 | return |
| 246 | indices[i:] = [indices[i] + 1] * (r - i) |
| 247 | yield tuple(pool[i] for i in indices) |
| 248 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 249 | The code for :func:`combinations_with_replacement` can be also expressed as |
| 250 | a subsequence of :func:`product` after filtering entries where the elements |
| 251 | are not in sorted order (according to their position in the input pool):: |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 252 | |
| 253 | def combinations_with_replacement(iterable, r): |
| 254 | pool = tuple(iterable) |
| 255 | n = len(pool) |
| 256 | for indices in product(range(n), repeat=r): |
| 257 | if sorted(indices) == list(indices): |
| 258 | yield tuple(pool[i] for i in indices) |
| 259 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 260 | The number of items returned is ``(n+r-1)! / r! / (n-1)!`` when ``n > 0``. |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 261 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 262 | .. versionadded:: 3.1 |
Raymond Hettinger | d07d939 | 2009-01-27 04:20:44 +0000 | [diff] [blame] | 263 | |
Georg Brandl | 67b21b7 | 2010-08-17 15:07:14 +0000 | [diff] [blame] | 264 | |
Raymond Hettinger | 6b3b0fc | 2009-01-26 02:56:58 +0000 | [diff] [blame] | 265 | .. function:: compress(data, selectors) |
| 266 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 267 | Make an iterator that filters elements from *data* returning only those that |
| 268 | have a corresponding element in *selectors* that evaluates to ``True``. |
| 269 | Stops when either the *data* or *selectors* iterables has been exhausted. |
| 270 | Equivalent to:: |
Raymond Hettinger | 6b3b0fc | 2009-01-26 02:56:58 +0000 | [diff] [blame] | 271 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 272 | def compress(data, selectors): |
| 273 | # compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F |
| 274 | return (d for d, s in zip(data, selectors) if s) |
Raymond Hettinger | 6b3b0fc | 2009-01-26 02:56:58 +0000 | [diff] [blame] | 275 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 276 | .. versionadded:: 3.1 |
Raymond Hettinger | 6b3b0fc | 2009-01-26 02:56:58 +0000 | [diff] [blame] | 277 | |
| 278 | |
Raymond Hettinger | 9e8dbbc | 2009-02-14 04:21:49 +0000 | [diff] [blame] | 279 | .. function:: count(start=0, step=1) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 280 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 281 | Make an iterator that returns evenly spaced values starting with *n*. Often |
| 282 | used as an argument to :func:`map` to generate consecutive data points. |
| 283 | Also, used with :func:`zip` to add sequence numbers. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 284 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 285 | def count(start=0, step=1): |
| 286 | # count(10) --> 10 11 12 13 14 ... |
Georg Brandl | 37a80dc | 2011-01-13 07:31:18 +0000 | [diff] [blame] | 287 | # count(2.5, 0.5) -> 2.5 3.0 3.5 ... |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 288 | n = start |
| 289 | while True: |
| 290 | yield n |
| 291 | n += step |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 292 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 293 | When counting with floating point numbers, better accuracy can sometimes be |
| 294 | achieved by substituting multiplicative code such as: ``(start + step * i |
| 295 | for i in count())``. |
Raymond Hettinger | 5bc472a | 2009-06-17 01:40:52 +0000 | [diff] [blame] | 296 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 297 | .. versionchanged:: 3.1 |
| 298 | Added *step* argument and allowed non-integer arguments. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 299 | |
| 300 | .. function:: cycle(iterable) |
| 301 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 302 | Make an iterator returning elements from the iterable and saving a copy of each. |
| 303 | When the iterable is exhausted, return elements from the saved copy. Repeats |
| 304 | indefinitely. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 305 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 306 | def cycle(iterable): |
| 307 | # cycle('ABCD') --> A B C D A B C D A B C D ... |
| 308 | saved = [] |
| 309 | for element in iterable: |
| 310 | yield element |
| 311 | saved.append(element) |
| 312 | while saved: |
| 313 | for element in saved: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 314 | yield element |
| 315 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 316 | Note, this member of the toolkit may require significant auxiliary storage |
| 317 | (depending on the length of the iterable). |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 318 | |
| 319 | |
| 320 | .. function:: dropwhile(predicate, iterable) |
| 321 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 322 | Make an iterator that drops elements from the iterable as long as the predicate |
| 323 | is true; afterwards, returns every element. Note, the iterator does not produce |
| 324 | *any* output until the predicate first becomes false, so it may have a lengthy |
| 325 | start-up time. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 326 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 327 | def dropwhile(predicate, iterable): |
| 328 | # dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1 |
| 329 | iterable = iter(iterable) |
| 330 | for x in iterable: |
| 331 | if not predicate(x): |
| 332 | yield x |
| 333 | break |
| 334 | for x in iterable: |
| 335 | yield x |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 336 | |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 337 | .. function:: filterfalse(predicate, iterable) |
| 338 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 339 | Make an iterator that filters elements from iterable returning only those for |
| 340 | which the predicate is ``False``. If *predicate* is ``None``, return the items |
| 341 | that are false. Equivalent to:: |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 342 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 343 | def filterfalse(predicate, iterable): |
| 344 | # filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8 |
| 345 | if predicate is None: |
| 346 | predicate = bool |
| 347 | for x in iterable: |
| 348 | if not predicate(x): |
| 349 | yield x |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 350 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 351 | |
Georg Brandl | 3dd3388 | 2009-06-01 17:35:27 +0000 | [diff] [blame] | 352 | .. function:: groupby(iterable, key=None) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 353 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 354 | Make an iterator that returns consecutive keys and groups from the *iterable*. |
| 355 | The *key* is a function computing a key value for each element. If not |
| 356 | specified or is ``None``, *key* defaults to an identity function and returns |
| 357 | the element unchanged. Generally, the iterable needs to already be sorted on |
| 358 | the same key function. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 359 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 360 | The operation of :func:`groupby` is similar to the ``uniq`` filter in Unix. It |
| 361 | generates a break or new group every time the value of the key function changes |
| 362 | (which is why it is usually necessary to have sorted the data using the same key |
| 363 | function). That behavior differs from SQL's GROUP BY which aggregates common |
| 364 | elements regardless of their input order. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 365 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 366 | The returned group is itself an iterator that shares the underlying iterable |
| 367 | with :func:`groupby`. Because the source is shared, when the :func:`groupby` |
| 368 | object is advanced, the previous group is no longer visible. So, if that data |
| 369 | is needed later, it should be stored as a list:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 370 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 371 | groups = [] |
| 372 | uniquekeys = [] |
| 373 | data = sorted(data, key=keyfunc) |
| 374 | for k, g in groupby(data, keyfunc): |
| 375 | groups.append(list(g)) # Store group iterator as a list |
| 376 | uniquekeys.append(k) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 377 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 378 | :func:`groupby` is equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 379 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 380 | class groupby: |
| 381 | # [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B |
| 382 | # [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D |
| 383 | def __init__(self, iterable, key=None): |
| 384 | if key is None: |
| 385 | key = lambda x: x |
| 386 | self.keyfunc = key |
| 387 | self.it = iter(iterable) |
| 388 | self.tgtkey = self.currkey = self.currvalue = object() |
| 389 | def __iter__(self): |
| 390 | return self |
| 391 | def __next__(self): |
| 392 | while self.currkey == self.tgtkey: |
| 393 | self.currvalue = next(self.it) # Exit on StopIteration |
| 394 | self.currkey = self.keyfunc(self.currvalue) |
| 395 | self.tgtkey = self.currkey |
| 396 | return (self.currkey, self._grouper(self.tgtkey)) |
| 397 | def _grouper(self, tgtkey): |
| 398 | while self.currkey == tgtkey: |
| 399 | yield self.currvalue |
| 400 | self.currvalue = next(self.it) # Exit on StopIteration |
| 401 | self.currkey = self.keyfunc(self.currvalue) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 402 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 403 | |
Ezio Melotti | e0add76 | 2012-09-14 06:32:35 +0300 | [diff] [blame] | 404 | .. function:: islice(iterable, stop) |
| 405 | islice(iterable, start, stop[, step]) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 406 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 407 | Make an iterator that returns selected elements from the iterable. If *start* is |
| 408 | non-zero, then elements from the iterable are skipped until start is reached. |
| 409 | Afterward, elements are returned consecutively unless *step* is set higher than |
| 410 | one which results in items being skipped. If *stop* is ``None``, then iteration |
| 411 | continues until the iterator is exhausted, if at all; otherwise, it stops at the |
| 412 | specified position. Unlike regular slicing, :func:`islice` does not support |
| 413 | negative values for *start*, *stop*, or *step*. Can be used to extract related |
| 414 | fields from data where the internal structure has been flattened (for example, a |
| 415 | multi-line report may list a name field on every third line). Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 416 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 417 | def islice(iterable, *args): |
| 418 | # islice('ABCDEFG', 2) --> A B |
| 419 | # islice('ABCDEFG', 2, 4) --> C D |
| 420 | # islice('ABCDEFG', 2, None) --> C D E F G |
| 421 | # islice('ABCDEFG', 0, None, 2) --> A C E G |
| 422 | s = slice(*args) |
| 423 | it = iter(range(s.start or 0, s.stop or sys.maxsize, s.step or 1)) |
| 424 | nexti = next(it) |
| 425 | for i, element in enumerate(iterable): |
| 426 | if i == nexti: |
| 427 | yield element |
| 428 | nexti = next(it) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 429 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 430 | If *start* is ``None``, then iteration starts at zero. If *step* is ``None``, |
| 431 | then the step defaults to one. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 432 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 433 | |
Georg Brandl | 3dd3388 | 2009-06-01 17:35:27 +0000 | [diff] [blame] | 434 | .. function:: permutations(iterable, r=None) |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 435 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 436 | Return successive *r* length permutations of elements in the *iterable*. |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 437 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 438 | If *r* is not specified or is ``None``, then *r* defaults to the length |
| 439 | of the *iterable* and all possible full-length permutations |
| 440 | are generated. |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 441 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 442 | Permutations are emitted in lexicographic sort order. So, if the |
| 443 | input *iterable* is sorted, the permutation tuples will be produced |
| 444 | in sorted order. |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 445 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 446 | Elements are treated as unique based on their position, not on their |
| 447 | value. So if the input elements are unique, there will be no repeat |
| 448 | values in each permutation. |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 449 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 450 | Equivalent to:: |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 451 | |
| 452 | def permutations(iterable, r=None): |
Raymond Hettinger | dd1150e | 2008-03-13 02:39:40 +0000 | [diff] [blame] | 453 | # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC |
| 454 | # permutations(range(3)) --> 012 021 102 120 201 210 |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 455 | pool = tuple(iterable) |
| 456 | n = len(pool) |
| 457 | r = n if r is None else r |
Raymond Hettinger | 5bad41e | 2009-01-08 21:01:54 +0000 | [diff] [blame] | 458 | if r > n: |
| 459 | return |
| 460 | indices = list(range(n)) |
Sandro Tosi | 7386662 | 2011-12-25 17:25:45 +0100 | [diff] [blame] | 461 | cycles = list(range(n, n-r, -1)) |
Christian Heimes | b558a2e | 2008-03-02 22:46:37 +0000 | [diff] [blame] | 462 | yield tuple(pool[i] for i in indices[:r]) |
| 463 | while n: |
| 464 | for i in reversed(range(r)): |
| 465 | cycles[i] -= 1 |
| 466 | if cycles[i] == 0: |
| 467 | indices[i:] = indices[i+1:] + indices[i:i+1] |
| 468 | cycles[i] = n - i |
| 469 | else: |
| 470 | j = cycles[i] |
| 471 | indices[i], indices[-j] = indices[-j], indices[i] |
| 472 | yield tuple(pool[i] for i in indices[:r]) |
| 473 | break |
| 474 | else: |
| 475 | return |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 476 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 477 | The code for :func:`permutations` can be also expressed as a subsequence of |
| 478 | :func:`product`, filtered to exclude entries with repeated elements (those |
| 479 | from the same position in the input pool):: |
Christian Heimes | 7864476 | 2008-03-04 23:39:23 +0000 | [diff] [blame] | 480 | |
| 481 | def permutations(iterable, r=None): |
| 482 | pool = tuple(iterable) |
| 483 | n = len(pool) |
| 484 | r = n if r is None else r |
| 485 | for indices in product(range(n), repeat=r): |
| 486 | if len(set(indices)) == r: |
| 487 | yield tuple(pool[i] for i in indices) |
| 488 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 489 | The number of items returned is ``n! / (n-r)!`` when ``0 <= r <= n`` |
| 490 | or zero when ``r > n``. |
Christian Heimes | 70e7ea2 | 2008-02-28 20:02:27 +0000 | [diff] [blame] | 491 | |
Georg Brandl | 3dd3388 | 2009-06-01 17:35:27 +0000 | [diff] [blame] | 492 | .. function:: product(*iterables, repeat=1) |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 493 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 494 | Cartesian product of input iterables. |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 495 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 496 | Equivalent to nested for-loops in a generator expression. For example, |
| 497 | ``product(A, B)`` returns the same as ``((x,y) for x in A for y in B)``. |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 498 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 499 | The nested loops cycle like an odometer with the rightmost element advancing |
| 500 | on every iteration. This pattern creates a lexicographic ordering so that if |
| 501 | the input's iterables are sorted, the product tuples are emitted in sorted |
| 502 | order. |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 503 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 504 | To compute the product of an iterable with itself, specify the number of |
| 505 | repetitions with the optional *repeat* keyword argument. For example, |
| 506 | ``product(A, repeat=4)`` means the same as ``product(A, A, A, A)``. |
Christian Heimes | 9e7f1d2 | 2008-02-28 12:27:11 +0000 | [diff] [blame] | 507 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 508 | This function is equivalent to the following code, except that the |
| 509 | actual implementation does not build up intermediate results in memory:: |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 510 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 511 | def product(*args, repeat=1): |
| 512 | # product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy |
| 513 | # product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111 |
| 514 | pools = [tuple(pool) for pool in args] * repeat |
| 515 | result = [[]] |
| 516 | for pool in pools: |
| 517 | result = [x+[y] for x in result for y in pool] |
| 518 | for prod in result: |
| 519 | yield tuple(prod) |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 520 | |
| 521 | |
Raymond Hettinger | d75ad44 | 2009-06-01 19:16:52 +0000 | [diff] [blame] | 522 | .. function:: repeat(object[, times]) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 523 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 524 | Make an iterator that returns *object* over and over again. Runs indefinitely |
| 525 | unless the *times* argument is specified. Used as argument to :func:`map` for |
| 526 | invariant parameters to the called function. Also used with :func:`zip` to |
| 527 | create an invariant part of a tuple record. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 528 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 529 | def repeat(object, times=None): |
| 530 | # repeat(10, 3) --> 10 10 10 |
| 531 | if times is None: |
| 532 | while True: |
| 533 | yield object |
| 534 | else: |
| 535 | for i in range(times): |
| 536 | yield object |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 537 | |
Raymond Hettinger | fc3ba6b | 2012-02-01 09:07:40 -0800 | [diff] [blame] | 538 | A common use for *repeat* is to supply a stream of constant values to *map* |
| 539 | or *zip*:: |
| 540 | |
| 541 | >>> list(map(pow, range(10), repeat(2))) |
| 542 | [0, 1, 4, 9, 16, 25, 36, 49, 64, 81] |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 543 | |
| 544 | .. function:: starmap(function, iterable) |
| 545 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 546 | Make an iterator that computes the function using arguments obtained from |
| 547 | the iterable. Used instead of :func:`map` when argument parameters are already |
| 548 | grouped in tuples from a single iterable (the data has been "pre-zipped"). The |
| 549 | difference between :func:`map` and :func:`starmap` parallels the distinction |
| 550 | between ``function(a,b)`` and ``function(*c)``. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 551 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 552 | def starmap(function, iterable): |
| 553 | # starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000 |
| 554 | for args in iterable: |
| 555 | yield function(*args) |
Christian Heimes | 679db4a | 2008-01-18 09:56:22 +0000 | [diff] [blame] | 556 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 557 | |
| 558 | .. function:: takewhile(predicate, iterable) |
| 559 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 560 | Make an iterator that returns elements from the iterable as long as the |
| 561 | predicate is true. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 562 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 563 | def takewhile(predicate, iterable): |
| 564 | # takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4 |
| 565 | for x in iterable: |
| 566 | if predicate(x): |
| 567 | yield x |
| 568 | else: |
| 569 | break |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 570 | |
| 571 | |
Georg Brandl | 3dd3388 | 2009-06-01 17:35:27 +0000 | [diff] [blame] | 572 | .. function:: tee(iterable, n=2) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 573 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 574 | Return *n* independent iterators from a single iterable. Equivalent to:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 575 | |
Raymond Hettinger | cf984ce | 2009-02-18 20:56:51 +0000 | [diff] [blame] | 576 | def tee(iterable, n=2): |
| 577 | it = iter(iterable) |
| 578 | deques = [collections.deque() for i in range(n)] |
| 579 | def gen(mydeque): |
| 580 | while True: |
| 581 | if not mydeque: # when the local deque is empty |
| 582 | newval = next(it) # fetch a new value and |
| 583 | for d in deques: # load it to all the deques |
| 584 | d.append(newval) |
| 585 | yield mydeque.popleft() |
| 586 | return tuple(gen(d) for d in deques) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 587 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 588 | Once :func:`tee` has made a split, the original *iterable* should not be |
| 589 | used anywhere else; otherwise, the *iterable* could get advanced without |
| 590 | the tee objects being informed. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 591 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 592 | This itertool may require significant auxiliary storage (depending on how |
| 593 | much temporary data needs to be stored). In general, if one iterator uses |
| 594 | most or all of the data before another iterator starts, it is faster to use |
| 595 | :func:`list` instead of :func:`tee`. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 596 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 597 | |
Georg Brandl | 3dd3388 | 2009-06-01 17:35:27 +0000 | [diff] [blame] | 598 | .. function:: zip_longest(*iterables, fillvalue=None) |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 599 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 600 | Make an iterator that aggregates elements from each of the iterables. If the |
| 601 | iterables are of uneven length, missing values are filled-in with *fillvalue*. |
| 602 | Iteration continues until the longest iterable is exhausted. Equivalent to:: |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 603 | |
Raymond Hettinger | 6f45d18 | 2011-10-30 15:06:14 -0700 | [diff] [blame] | 604 | class ZipExhausted(Exception): |
| 605 | pass |
| 606 | |
| 607 | def zip_longest(*args, **kwds): |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 608 | # zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D- |
Raymond Hettinger | 6f45d18 | 2011-10-30 15:06:14 -0700 | [diff] [blame] | 609 | fillvalue = kwds.get('fillvalue') |
| 610 | counter = len(args) - 1 |
| 611 | def sentinel(): |
| 612 | nonlocal counter |
| 613 | if not counter: |
| 614 | raise ZipExhausted |
| 615 | counter -= 1 |
| 616 | yield fillvalue |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 617 | fillers = repeat(fillvalue) |
Raymond Hettinger | 6f45d18 | 2011-10-30 15:06:14 -0700 | [diff] [blame] | 618 | iterators = [chain(it, sentinel(), fillers) for it in args] |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 619 | try: |
Raymond Hettinger | 6f45d18 | 2011-10-30 15:06:14 -0700 | [diff] [blame] | 620 | while iterators: |
| 621 | yield tuple(map(next, iterators)) |
| 622 | except ZipExhausted: |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 623 | pass |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 624 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 625 | If one of the iterables is potentially infinite, then the :func:`zip_longest` |
| 626 | function should be wrapped with something that limits the number of calls |
| 627 | (for example :func:`islice` or :func:`takewhile`). If not specified, |
| 628 | *fillvalue* defaults to ``None``. |
Raymond Hettinger | 749761e | 2009-01-27 04:42:48 +0000 | [diff] [blame] | 629 | |
| 630 | |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 631 | .. _itertools-recipes: |
| 632 | |
Raymond Hettinger | 1fa7682 | 2010-12-06 23:31:36 +0000 | [diff] [blame] | 633 | Itertools Recipes |
| 634 | ----------------- |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 635 | |
| 636 | This section shows recipes for creating an extended toolset using the existing |
| 637 | itertools as building blocks. |
| 638 | |
| 639 | The extended tools offer the same high performance as the underlying toolset. |
| 640 | The superior memory performance is kept by processing elements one at a time |
| 641 | rather than bringing the whole iterable into memory all at once. Code volume is |
| 642 | kept small by linking the tools together in a functional style which helps |
| 643 | eliminate temporary variables. High speed is retained by preferring |
Georg Brandl | 9afde1c | 2007-11-01 20:32:30 +0000 | [diff] [blame] | 644 | "vectorized" building blocks over the use of for-loops and :term:`generator`\s |
Christian Heimes | fe337bf | 2008-03-23 21:54:12 +0000 | [diff] [blame] | 645 | which incur interpreter overhead. |
| 646 | |
| 647 | .. testcode:: |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 648 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 649 | def take(n, iterable): |
| 650 | "Return first n items of the iterable as a list" |
| 651 | return list(islice(iterable, n)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 652 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 653 | def tabulate(function, start=0): |
| 654 | "Return function(0), function(1), ..." |
| 655 | return map(function, count(start)) |
Raymond Hettinger | dd1150e | 2008-03-13 02:39:40 +0000 | [diff] [blame] | 656 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 657 | def consume(iterator, n): |
| 658 | "Advance the iterator n-steps ahead. If n is none, consume entirely." |
| 659 | # Use functions that consume iterators at C speed. |
| 660 | if n is None: |
| 661 | # feed the entire iterator into a zero-length deque |
| 662 | collections.deque(iterator, maxlen=0) |
| 663 | else: |
| 664 | # advance to the empty slice starting at position n |
| 665 | next(islice(iterator, n, n), None) |
Raymond Hettinger | fa00796 | 2009-03-09 11:55:25 +0000 | [diff] [blame] | 666 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 667 | def nth(iterable, n, default=None): |
| 668 | "Returns the nth item or a default value" |
| 669 | return next(islice(iterable, n, None), default) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 670 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 671 | def quantify(iterable, pred=bool): |
| 672 | "Count how many times the predicate is true" |
| 673 | return sum(map(pred, iterable)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 674 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 675 | def padnone(iterable): |
| 676 | """Returns the sequence elements and then returns None indefinitely. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 677 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 678 | Useful for emulating the behavior of the built-in map() function. |
| 679 | """ |
| 680 | return chain(iterable, repeat(None)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 681 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 682 | def ncycles(iterable, n): |
| 683 | "Returns the sequence elements n times" |
| 684 | return chain.from_iterable(repeat(tuple(iterable), n)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 685 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 686 | def dotproduct(vec1, vec2): |
| 687 | return sum(map(operator.mul, vec1, vec2)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 688 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 689 | def flatten(listOfLists): |
| 690 | "Flatten one level of nesting" |
| 691 | return chain.from_iterable(listOfLists) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 692 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 693 | def repeatfunc(func, times=None, *args): |
| 694 | """Repeat calls to func with specified arguments. |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 695 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 696 | Example: repeatfunc(random.random) |
| 697 | """ |
| 698 | if times is None: |
| 699 | return starmap(func, repeat(args)) |
| 700 | return starmap(func, repeat(args, times)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 701 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 702 | def pairwise(iterable): |
| 703 | "s -> (s0,s1), (s1,s2), (s2, s3), ..." |
| 704 | a, b = tee(iterable) |
| 705 | next(b, None) |
| 706 | return zip(a, b) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 707 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 708 | def grouper(n, iterable, fillvalue=None): |
Raymond Hettinger | 9ae9473 | 2012-07-08 16:04:03 -0700 | [diff] [blame] | 709 | "Collect data into fixed-length chunks or blocks" |
| 710 | # grouper(3, 'ABCDEFG', 'x') --> ABC DEF Gxx" |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 711 | args = [iter(iterable)] * n |
| 712 | return zip_longest(*args, fillvalue=fillvalue) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 713 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 714 | def roundrobin(*iterables): |
| 715 | "roundrobin('ABC', 'D', 'EF') --> A D E B F C" |
| 716 | # Recipe credited to George Sakkis |
| 717 | pending = len(iterables) |
| 718 | nexts = cycle(iter(it).__next__ for it in iterables) |
| 719 | while pending: |
| 720 | try: |
| 721 | for next in nexts: |
| 722 | yield next() |
| 723 | except StopIteration: |
| 724 | pending -= 1 |
| 725 | nexts = cycle(islice(nexts, pending)) |
Georg Brandl | 116aa62 | 2007-08-15 14:28:22 +0000 | [diff] [blame] | 726 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 727 | def partition(pred, iterable): |
| 728 | 'Use a predicate to partition entries into false entries and true entries' |
| 729 | # partition(is_odd, range(10)) --> 0 2 4 6 8 and 1 3 5 7 9 |
| 730 | t1, t2 = tee(iterable) |
| 731 | return filterfalse(pred, t1), filter(pred, t2) |
Raymond Hettinger | 5ce0aa2 | 2010-12-01 10:49:19 +0000 | [diff] [blame] | 732 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 733 | def powerset(iterable): |
| 734 | "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)" |
| 735 | s = list(iterable) |
| 736 | return chain.from_iterable(combinations(s, r) for r in range(len(s)+1)) |
Raymond Hettinger | 08d01ee | 2010-08-07 05:36:53 +0000 | [diff] [blame] | 737 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 738 | def unique_everseen(iterable, key=None): |
| 739 | "List unique elements, preserving order. Remember all elements ever seen." |
| 740 | # unique_everseen('AAAABBBCCDAABBB') --> A B C D |
| 741 | # unique_everseen('ABBCcAD', str.lower) --> A B C D |
| 742 | seen = set() |
| 743 | seen_add = seen.add |
| 744 | if key is None: |
| 745 | for element in filterfalse(seen.__contains__, iterable): |
| 746 | seen_add(element) |
| 747 | yield element |
| 748 | else: |
| 749 | for element in iterable: |
| 750 | k = key(element) |
| 751 | if k not in seen: |
| 752 | seen_add(k) |
| 753 | yield element |
Christian Heimes | 90c3d9b | 2008-02-23 13:18:03 +0000 | [diff] [blame] | 754 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 755 | def unique_justseen(iterable, key=None): |
| 756 | "List unique elements, preserving order. Remember only the element just seen." |
| 757 | # unique_justseen('AAAABBBCCDAABBB') --> A B C D A B |
| 758 | # unique_justseen('ABBCcAD', str.lower) --> A B C A D |
| 759 | return map(next, map(itemgetter(1), groupby(iterable, key))) |
Raymond Hettinger | ad9d96b | 2009-01-02 21:39:07 +0000 | [diff] [blame] | 760 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 761 | def iter_except(func, exception, first=None): |
| 762 | """ Call a function repeatedly until an exception is raised. |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 763 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 764 | Converts a call-until-exception interface to an iterator interface. |
| 765 | Like __builtin__.iter(func, sentinel) but uses an exception instead |
| 766 | of a sentinel to end the loop. |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 767 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 768 | Examples: |
| 769 | iter_except(functools.partial(heappop, h), IndexError) # priority queue iterator |
| 770 | iter_except(d.popitem, KeyError) # non-blocking dict iterator |
| 771 | iter_except(d.popleft, IndexError) # non-blocking deque iterator |
| 772 | iter_except(q.get_nowait, Queue.Empty) # loop over a producer Queue |
| 773 | iter_except(s.pop, KeyError) # non-blocking set iterator |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 774 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 775 | """ |
| 776 | try: |
| 777 | if first is not None: |
| 778 | yield first() # For database APIs needing an initial cast to db.first() |
| 779 | while 1: |
| 780 | yield func() |
| 781 | except exception: |
| 782 | pass |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 783 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 784 | def random_product(*args, repeat=1): |
| 785 | "Random selection from itertools.product(*args, **kwds)" |
| 786 | pools = [tuple(pool) for pool in args] * repeat |
| 787 | return tuple(random.choice(pool) for pool in pools) |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 788 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 789 | def random_permutation(iterable, r=None): |
| 790 | "Random selection from itertools.permutations(iterable, r)" |
| 791 | pool = tuple(iterable) |
| 792 | r = len(pool) if r is None else r |
| 793 | return tuple(random.sample(pool, r)) |
Raymond Hettinger | 063a4b6 | 2010-04-02 04:18:18 +0000 | [diff] [blame] | 794 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 795 | def random_combination(iterable, r): |
| 796 | "Random selection from itertools.combinations(iterable, r)" |
| 797 | pool = tuple(iterable) |
| 798 | n = len(pool) |
| 799 | indices = sorted(random.sample(range(n), r)) |
| 800 | return tuple(pool[i] for i in indices) |
Raymond Hettinger | 063a4b6 | 2010-04-02 04:18:18 +0000 | [diff] [blame] | 801 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 802 | def random_combination_with_replacement(iterable, r): |
| 803 | "Random selection from itertools.combinations_with_replacement(iterable, r)" |
| 804 | pool = tuple(iterable) |
| 805 | n = len(pool) |
| 806 | indices = sorted(random.randrange(n) for i in range(r)) |
| 807 | return tuple(pool[i] for i in indices) |
Raymond Hettinger | 063a4b6 | 2010-04-02 04:18:18 +0000 | [diff] [blame] | 808 | |
Raymond Hettinger | fc91aa2 | 2010-03-28 18:27:13 +0000 | [diff] [blame] | 809 | Note, many of the above recipes can be optimized by replacing global lookups |
| 810 | with local variables defined as default values. For example, the |
| 811 | *dotproduct* recipe can be written as:: |
| 812 | |
Raymond Hettinger | 30c7362 | 2010-12-01 23:45:20 +0000 | [diff] [blame] | 813 | def dotproduct(vec1, vec2, sum=sum, map=map, mul=operator.mul): |
| 814 | return sum(map(mul, vec1, vec2)) |