# `itertools` --- 为高效循环而创建迭代器的函数¶

These tools and their built-in counterparts also work well with the high-speed functions in the `operator` module. For example, the multiplication operator can be mapped across two vectors to form an efficient dot-product: `sum(starmap(operator.mul, zip(vec1, vec2, strict=True)))`.

`count()`

start, [step]

start, start+step, start+2*step, ...

`count(10) --> 10 11 12 13 14 ...`

`cycle()`

p

p0, p1, ... plast, p0, p1, ...

`cycle('ABCD') --> A B C D A B C D ...`

`repeat()`

elem [,n]

elem, elem, elem, ... 重复无限次或n次

`repeat(10, 3) --> 10 10 10`

`accumulate()`

p [,func]

p0, p0+p1, p0+p1+p2, ...

`accumulate([1,2,3,4,5]) --> 1 3 6 10 15`

`batched()`

p, n

(p0, p1, ..., p_n-1), ...

`batched('ABCDEFG', n=3) --> ABC DEF G`

`chain()`

p, q, ...

p0, p1, ... plast, q0, q1, ...

`chain('ABC', 'DEF') --> A B C D E F`

`chain.from_iterable()`

iterable -- 可迭代对象

p0, p1, ... plast, q0, q1, ...

`chain.from_iterable(['ABC', 'DEF']) --> A B C D E F`

`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`

`dropwhile()`

pred, seq

seq[n], seq[n+1], ... 从pred首次真值测试失败开始

`dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1`

`filterfalse()`

pred, seq

seq中pred(x)为假值的元素，x是seq中的元素。

`filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8`

`groupby()`

iterable[, key]

`islice()`

seq, [start,] stop [, step]

seq[start:stop:step]中的元素

`islice('ABCDEFG', 2, None) --> C D E F G`

`pairwise()`

iterable -- 可迭代对象

(p[0], p[1]), (p[1], p[2])

`pairwise('ABCDEFG') --> AB BC CD DE EF FG`

`starmap()`

func, seq

func(*seq[0]), func(*seq[1]), ...

`starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000`

`takewhile()`

pred, seq

seq[0], seq[1], ..., 直到pred真值测试失败

`takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4`

`tee()`

it, n

it1, it2, ... itn 将一个迭代器拆分为n个迭代器

`zip_longest()`

p, q, ...

(p[0], q[0]), (p[1], q[1]), ...

`zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-`

`product()`

p, q, ... [repeat=1]

`permutations()`

p[, r]

`combinations()`

p, r

`combinations_with_replacement()`

p, r

`product('ABCD', repeat=2)`

`AA AB AC AD BA BB BC BD CA CB CC CD DA DB DC DD`

`permutations('ABCD', 2)`

`AB AC AD BA BC BD CA CB CD DA DB DC`

`combinations('ABCD', 2)`

`AB AC AD BC BD CD`

`combinations_with_replacement('ABCD', 2)`

`AA AB AC AD BB BC BD CC CD DD`

## Itertool函数¶

itertools.accumulate(iterable[, func, *, initial=None])

```def accumulate(iterable, func=operator.add, *, initial=None):
'Return running totals'
# accumulate([1,2,3,4,5]) --> 1 3 6 10 15
# accumulate([1,2,3,4,5], initial=100) --> 100 101 103 106 110 115
# accumulate([1,2,3,4,5], operator.mul) --> 1 2 6 24 120
it = iter(iterable)
total = initial
if initial is None:
try:
total = next(it)
except StopIteration:
return
yield total
for element in it:
total = func(total, element)
yield total
```

There are a number of uses for the func argument. It can be set to `min()` for a running minimum, `max()` for a running maximum, or `operator.mul()` for a running product. Amortization tables can be built by accumulating interest and applying payments:

```>>> data = [3, 4, 6, 2, 1, 9, 0, 7, 5, 8]
>>> list(accumulate(data, operator.mul))     # running product
[3, 12, 72, 144, 144, 1296, 0, 0, 0, 0]
>>> list(accumulate(data, max))              # running maximum
[3, 4, 6, 6, 6, 9, 9, 9, 9, 9]

# Amortize a 5% loan of 1000 with 4 annual payments of 90
>>> cashflows = [1000, -90, -90, -90, -90]
>>> list(accumulate(cashflows, lambda bal, pmt: bal*1.05 + pmt))
[1000, 960.0, 918.0, 873.9000000000001, 827.5950000000001]
```

3.2 新版功能.

itertools.batched(iterable, n)

Batch data from the iterable into tuples of length n. The last batch may be shorter than n.

Loops over the input iterable and accumulates data into tuples up to size n. The input is consumed lazily, just enough to fill a batch. The result is yielded as soon as the batch is full or when the input iterable is exhausted:

```>>> flattened_data = ['roses', 'red', 'violets', 'blue', 'sugar', 'sweet']
>>> unflattened = list(batched(flattened_data, 2))
>>> unflattened
[('roses', 'red'), ('violets', 'blue'), ('sugar', 'sweet')]

>>> for batch in batched('ABCDEFG', 3):
...     print(batch)
...
('A', 'B', 'C')
('D', 'E', 'F')
('G',)
```

```def batched(iterable, n):
# batched('ABCDEFG', 3) --> ABC DEF G
if n < 1:
raise ValueError('n must be at least one')
it = iter(iterable)
while batch := tuple(islice(it, n)):
yield batch
```

3.12 新版功能.

itertools.chain(*iterables)

```def chain(*iterables):
# chain('ABC', 'DEF') --> A B C D E F
for it in iterables:
for element in it:
yield element
```
classmethod chain.from_iterable(iterable)

```def from_iterable(iterables):
# chain.from_iterable(['ABC', 'DEF']) --> A B C D E F
for it in iterables:
for element in it:
yield element
```
itertools.combinations(iterable, r)

The combination tuples are emitted in lexicographic ordering according to the order of the input iterable. So, if the input iterable is sorted, the output tuples will be produced in sorted order.

Elements are treated as unique based on their position, not on their value. So if the input elements are unique, there will be no repeated values in each combination.

```def combinations(iterable, r):
# combinations('ABCD', 2) --> AB AC AD BC BD CD
# combinations(range(4), 3) --> 012 013 023 123
pool = tuple(iterable)
n = len(pool)
if r > n:
return
indices = list(range(r))
yield tuple(pool[i] for i in indices)
while True:
for i in reversed(range(r)):
if indices[i] != i + n - r:
break
else:
return
indices[i] += 1
for j in range(i+1, r):
indices[j] = indices[j-1] + 1
yield tuple(pool[i] for i in indices)
```

`combinations()` 的代码可被改写为 `permutations()` 过滤后的子序列，（相对于元素在输入中的位置）元素不是有序的。

```def combinations(iterable, r):
pool = tuple(iterable)
n = len(pool)
for indices in permutations(range(n), r):
if sorted(indices) == list(indices):
yield tuple(pool[i] for i in indices)
```

`0 <= r <= n` 时，返回项的个数是 `n! / r! / (n-r)!`；当 `r > n` 时，返回项个数为0。

itertools.combinations_with_replacement(iterable, r)

The combination tuples are emitted in lexicographic ordering according to the order of the input iterable. So, if the input iterable is sorted, the output tuples will be produced in sorted order.

```def combinations_with_replacement(iterable, r):
# combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
pool = tuple(iterable)
n = len(pool)
if not n and r:
return
indices = [0] * r
yield tuple(pool[i] for i in indices)
while True:
for i in reversed(range(r)):
if indices[i] != n - 1:
break
else:
return
indices[i:] = [indices[i] + 1] * (r - i)
yield tuple(pool[i] for i in indices)
```

`combinations_with_replacement()` 的代码可被改写为 `production()` 过滤后的子序列，（相对于元素在输入中的位置）元素不是有序的。

```def combinations_with_replacement(iterable, r):
pool = tuple(iterable)
n = len(pool)
for indices in product(range(n), repeat=r):
if sorted(indices) == list(indices):
yield tuple(pool[i] for i in indices)
```

`n > 0` 时，返回项个数为 `(n+r-1)! / r! / (n-1)!`.

3.1 新版功能.

itertools.compress(data, selectors)

```def compress(data, selectors):
# compress('ABCDEF', [1,0,1,0,1,1]) --> A C E F
return (d for d, s in zip(data, selectors) if s)
```

3.1 新版功能.

itertools.count(start=0, step=1)

```def count(start=0, step=1):
# count(10) --> 10 11 12 13 14 ...
# count(2.5, 0.5) --> 2.5 3.0 3.5 ...
n = start
while True:
yield n
n += step
```

itertools.cycle(iterable)

```def cycle(iterable):
# cycle('ABCD') --> A B C D A B C D A B C D ...
saved = []
for element in iterable:
yield element
saved.append(element)
while saved:
for element in saved:
yield element
```

itertools.dropwhile(predicate, iterable)

```def dropwhile(predicate, iterable):
# dropwhile(lambda x: x<5, [1,4,6,4,1]) --> 6 4 1
iterable = iter(iterable)
for x in iterable:
if not predicate(x):
yield x
break
for x in iterable:
yield x
```
itertools.filterfalse(predicate, iterable)

Make an iterator that filters elements from iterable returning only those for which the predicate is false. If predicate is `None`, return the items that are false. Roughly equivalent to:

```def filterfalse(predicate, iterable):
# filterfalse(lambda x: x%2, range(10)) --> 0 2 4 6 8
if predicate is None:
predicate = bool
for x in iterable:
if not predicate(x):
yield x
```
itertools.groupby(iterable, key=None)

`groupby()` 操作类似于Unix中的 `uniq`。当每次 key 函数产生的键值改变时，迭代器会分组或生成一个新组（这就是为什么通常需要使用同一个键值函数先对数据进行排序）。这种行为与SQL的GROUP BY操作不同，SQL的操作会忽略输入的顺序将相同键值的元素分在同组中。

```groups = []
uniquekeys = []
data = sorted(data, key=keyfunc)
for k, g in groupby(data, keyfunc):
groups.append(list(g))      # Store group iterator as a list
uniquekeys.append(k)
```

`groupby()` 大致相当于：

```class groupby:
# [k for k, g in groupby('AAAABBBCCDAABBB')] --> A B C D A B
# [list(g) for k, g in groupby('AAAABBBCCD')] --> AAAA BBB CC D

def __init__(self, iterable, key=None):
if key is None:
key = lambda x: x
self.keyfunc = key
self.it = iter(iterable)
self.tgtkey = self.currkey = self.currvalue = object()

def __iter__(self):
return self

def __next__(self):
self.id = object()
while self.currkey == self.tgtkey:
self.currvalue = next(self.it)    # Exit on StopIteration
self.currkey = self.keyfunc(self.currvalue)
self.tgtkey = self.currkey
return (self.currkey, self._grouper(self.tgtkey, self.id))

def _grouper(self, tgtkey, id):
while self.id is id and self.currkey == tgtkey:
yield self.currvalue
try:
self.currvalue = next(self.it)
except StopIteration:
return
self.currkey = self.keyfunc(self.currvalue)
```
itertools.islice(iterable, stop)
itertools.islice(iterable, start, stop[, step])

Make an iterator that returns selected elements from the iterable. If start is non-zero, then elements from the iterable are skipped until start is reached. Afterward, elements are returned consecutively unless step is set higher than one which results in items being skipped. If stop is `None`, then iteration continues until the iterator is exhausted, if at all; otherwise, it stops at the specified position.

Unlike regular slicing, `islice()` does not support negative values for start, stop, or step. Can be used to extract related fields from data where the internal structure has been flattened (for example, a multi-line report may list a name field on every third line).

```def islice(iterable, *args):
# islice('ABCDEFG', 2) --> A B
# islice('ABCDEFG', 2, 4) --> C D
# islice('ABCDEFG', 2, None) --> C D E F G
# islice('ABCDEFG', 0, None, 2) --> A C E G
s = slice(*args)
start, stop, step = s.start or 0, s.stop or sys.maxsize, s.step or 1
it = iter(range(start, stop, step))
try:
nexti = next(it)
except StopIteration:
# Consume *iterable* up to the *start* position.
for i, element in zip(range(start), iterable):
pass
return
try:
for i, element in enumerate(iterable):
if i == nexti:
yield element
nexti = next(it)
except StopIteration:
# Consume to *stop*.
for i, element in zip(range(i + 1, stop), iterable):
pass
```
itertools.pairwise(iterable)

```def pairwise(iterable):
# pairwise('ABCDEFG') --> AB BC CD DE EF FG
a, b = tee(iterable)
next(b, None)
return zip(a, b)
```

3.10 新版功能.

itertools.permutations(iterable, r=None)

The permutation tuples are emitted in lexicographic order according to the order of the input iterable. So, if the input iterable is sorted, the output tuples will be produced in sorted order.

Elements are treated as unique based on their position, not on their value. So if the input elements are unique, there will be no repeated values within a permutation.

```def permutations(iterable, r=None):
# permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC
# permutations(range(3)) --> 012 021 102 120 201 210
pool = tuple(iterable)
n = len(pool)
r = n if r is None else r
if r > n:
return
indices = list(range(n))
cycles = list(range(n, n-r, -1))
yield tuple(pool[i] for i in indices[:r])
while n:
for i in reversed(range(r)):
cycles[i] -= 1
if cycles[i] == 0:
indices[i:] = indices[i+1:] + indices[i:i+1]
cycles[i] = n - i
else:
j = cycles[i]
indices[i], indices[-j] = indices[-j], indices[i]
yield tuple(pool[i] for i in indices[:r])
break
else:
return
```

`permutations()` 的代码也可被改写为 `product()` 的子序列，只要将含有重复元素（来自输入中同一位置的）的项排除。

```def permutations(iterable, r=None):
pool = tuple(iterable)
n = len(pool)
r = n if r is None else r
for indices in product(range(n), repeat=r):
if len(set(indices)) == r:
yield tuple(pool[i] for i in indices)
```

`0 <= r <= n` ，返回项个数为 `n! / (n-r)!` ；当 `r > n` ，返回项个数为0。

itertools.product(*iterables, repeat=1)

```def product(*args, repeat=1):
# product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
# product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
pools = [tuple(pool) for pool in args] * repeat
result = [[]]
for pool in pools:
result = [x+[y] for x in result for y in pool]
for prod in result:
yield tuple(prod)
```

`product()` 运行之前，它会完全耗尽输入的可迭代对象，在内存中保留值的临时池以生成结果积。 相应地，它只适用于有限的输入。

itertools.repeat(object[, times])

Make an iterator that returns object over and over again. Runs indefinitely unless the times argument is specified.

```def repeat(object, times=None):
# repeat(10, 3) --> 10 10 10
if times is None:
while True:
yield object
else:
for i in range(times):
yield object
```

A common use for repeat is to supply a stream of constant values to map or zip:

```>>> list(map(pow, range(10), repeat(2)))
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
```
itertools.starmap(function, iterable)

Make an iterator that computes the function using arguments obtained from the iterable. Used instead of `map()` when argument parameters are already grouped in tuples from a single iterable (when the data has been "pre-zipped").

The difference between `map()` and `starmap()` parallels the distinction between `function(a,b)` and `function(*c)`. Roughly equivalent to:

```def starmap(function, iterable):
# starmap(pow, [(2,5), (3,2), (10,3)]) --> 32 9 1000
for args in iterable:
yield function(*args)
```
itertools.takewhile(predicate, iterable)

```def takewhile(predicate, iterable):
# takewhile(lambda x: x<5, [1,4,6,4,1]) --> 1 4
for x in iterable:
if predicate(x):
yield x
else:
break
```
itertools.tee(iterable, n=2)

The following Python code helps explain what tee does (although the actual implementation is more complex and uses only a single underlying FIFO queue):

```def tee(iterable, n=2):
it = iter(iterable)
deques = [collections.deque() for i in range(n)]
def gen(mydeque):
while True:
if not mydeque:             # when the local deque is empty
try:
newval = next(it)   # fetch a new value and
except StopIteration:
return
for d in deques:        # load it to all the deques
d.append(newval)
yield mydeque.popleft()
return tuple(gen(d) for d in deques)
```

Once a `tee()` has been created, the original iterable should not be used anywhere else; otherwise, the iterable could get advanced without the tee objects being informed.

`tee` iterators are not threadsafe. A `RuntimeError` may be raised when simultaneously using iterators returned by the same `tee()` call, even if the original iterable is threadsafe.

itertools.zip_longest(*iterables, fillvalue=None)

```def zip_longest(*args, fillvalue=None):
# zip_longest('ABCD', 'xy', fillvalue='-') --> Ax By C- D-
iterators = [iter(it) for it in args]
num_active = len(iterators)
if not num_active:
return
while True:
values = []
for i, it in enumerate(iterators):
try:
value = next(it)
except StopIteration:
num_active -= 1
if not num_active:
return
iterators[i] = repeat(fillvalue)
value = fillvalue
values.append(value)
yield tuple(values)
```

## itertools 配方¶

The primary purpose of the itertools recipes is educational. The recipes show various ways of thinking about individual tools — for example, that `chain.from_iterable` is related to the concept of flattening. The recipes also give ideas about ways that the tools can be combined — for example, how `compress()` and `range()` can work together. The recipes also show patterns for using itertools with the `operator` and `collections` modules as well as with the built-in itertools such as `map()`, `filter()`, `reversed()`, and `enumerate()`.

A secondary purpose of the recipes is to serve as an incubator. The `accumulate()`, `compress()`, and `pairwise()` itertools started out as recipes. Currently, the `iter_index()` recipe is being tested to see whether it proves its worth.

```python -m pip install more-itertools
```

Many of the recipes offer the same high performance as the underlying toolset. Superior memory performance is kept by processing elements one at a time rather than bringing the whole iterable into memory all at once. Code volume is kept small by linking the tools together in a functional style which helps eliminate temporary variables. High speed is retained by preferring "vectorized" building blocks over the use of for-loops and generators which incur interpreter overhead.

```import collections
import math
import operator
import random

def take(n, iterable):
"Return first n items of the iterable as a list"
return list(islice(iterable, n))

def prepend(value, iterator):
"Prepend a single value in front of an iterator"
# prepend(1, [2, 3, 4]) --> 1 2 3 4
return chain([value], iterator)

def tabulate(function, start=0):
"Return function(0), function(1), ..."
return map(function, count(start))

def tail(n, iterable):
"Return an iterator over the last n items"
# tail(3, 'ABCDEFG') --> E F G
return iter(collections.deque(iterable, maxlen=n))

def consume(iterator, n=None):
"Advance the iterator n-steps ahead. If n is None, consume entirely."
# Use functions that consume iterators at C speed.
if n is None:
# feed the entire iterator into a zero-length deque
collections.deque(iterator, maxlen=0)
else:
# advance to the empty slice starting at position n
next(islice(iterator, n, n), None)

def nth(iterable, n, default=None):
"Returns the nth item or a default value"
return next(islice(iterable, n, None), default)

def all_equal(iterable):
"Returns True if all the elements are equal to each other"
g = groupby(iterable)
return next(g, True) and not next(g, False)

def quantify(iterable, pred=bool):
"Count how many times the predicate is True"
return sum(map(pred, iterable))

def ncycles(iterable, n):
"Returns the sequence elements n times"
return chain.from_iterable(repeat(tuple(iterable), n))

def sum_of_squares(it):
"Add up the squares of the input values."
# sum_of_squares([10, 20, 30]) -> 1400
return math.sumprod(*tee(it))

def transpose(it):
"Swap the rows and columns of the input."
# transpose([(1, 2, 3), (11, 22, 33)]) --> (1, 11) (2, 22) (3, 33)
return zip(*it, strict=True)

def matmul(m1, m2):
"Multiply two matrices."
# matmul([(7, 5), (3, 5)], [[2, 5], [7, 9]]) --> (49, 80), (41, 60)
n = len(m2[0])
return batched(starmap(math.sumprod, product(m1, transpose(m2))), n)

def convolve(signal, kernel):
# See:  https://betterexplained.com/articles/intuitive-convolution/
# convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
# convolve(data, [1, -1]) --> 1st finite difference (1st derivative)
# convolve(data, [1, -2, 1]) --> 2nd finite difference (2nd derivative)
kernel = tuple(kernel)[::-1]
n = len(kernel)
window = collections.deque([0], maxlen=n) * n
for x in chain(signal, repeat(0, n-1)):
window.append(x)
yield math.sumprod(kernel, window)

def polynomial_from_roots(roots):
"""Compute a polynomial's coefficients from its roots.

(x - 5) (x + 4) (x - 3)  expands to:   x³ -4x² -17x + 60
"""
# polynomial_from_roots([5, -4, 3]) --> [1, -4, -17, 60]
expansion = [1]
for r in roots:
expansion = convolve(expansion, (1, -r))
return list(expansion)

def polynomial_eval(coefficients, x):
"""Evaluate a polynomial at a specific value.

Computes with better numeric stability than Horner's method.
"""
# Evaluate x³ -4x² -17x + 60 at x = 2.5
# polynomial_eval([1, -4, -17, 60], x=2.5) --> 8.125
n = len(coefficients)
if n == 0:
return x * 0  # coerce zero to the type of x
powers = map(pow, repeat(x), reversed(range(n)))
return math.sumprod(coefficients, powers)

def iter_index(iterable, value, start=0):
"Return indices where a value occurs in a sequence or iterable."
# iter_index('AABCADEAF', 'A') --> 0 1 4 7
try:
seq_index = iterable.index
except AttributeError:
# Slow path for general iterables
it = islice(iterable, start, None)
i = start - 1
try:
while True:
yield (i := i + operator.indexOf(it, value) + 1)
except ValueError:
pass
else:
# Fast path for sequences
i = start - 1
try:
while True:
yield (i := seq_index(value, i+1))
except ValueError:
pass

def sieve(n):
"Primes less than n"
# sieve(30) --> 2 3 5 7 11 13 17 19 23 29
data = bytearray((0, 1)) * (n // 2)
data[:3] = 0, 0, 0
limit = math.isqrt(n) + 1
for p in compress(range(limit), data):
data[p*p : n : p+p] = bytes(len(range(p*p, n, p+p)))
data[2] = 1
return iter_index(data, 1) if n > 2 else iter([])

def factor(n):
"Prime factors of n."
# factor(99) --> 3 3 11
for prime in sieve(math.isqrt(n) + 1):
while True:
quotient, remainder = divmod(n, prime)
if remainder:
break
yield prime
n = quotient
if n == 1:
return
if n > 1:
yield n

def flatten(list_of_lists):
"Flatten one level of nesting"
return chain.from_iterable(list_of_lists)

def repeatfunc(func, times=None, *args):
"""Repeat calls to func with specified arguments.

Example:  repeatfunc(random.random)
"""
if times is None:
return starmap(func, repeat(args))
return starmap(func, repeat(args, times))

def grouper(iterable, n, *, incomplete='fill', fillvalue=None):
"Collect data into non-overlapping fixed-length chunks or blocks"
# grouper('ABCDEFG', 3, fillvalue='x') --> ABC DEF Gxx
# grouper('ABCDEFG', 3, incomplete='strict') --> ABC DEF ValueError
# grouper('ABCDEFG', 3, incomplete='ignore') --> ABC DEF
args = [iter(iterable)] * n
if incomplete == 'fill':
return zip_longest(*args, fillvalue=fillvalue)
if incomplete == 'strict':
return zip(*args, strict=True)
if incomplete == 'ignore':
return zip(*args)
else:
raise ValueError('Expected fill, strict, or ignore')

def triplewise(iterable):
"Return overlapping triplets from an iterable"
# triplewise('ABCDEFG') --> ABC BCD CDE DEF EFG
for (a, _), (b, c) in pairwise(pairwise(iterable)):
yield a, b, c

def sliding_window(iterable, n):
# sliding_window('ABCDEFG', 4) --> ABCD BCDE CDEF DEFG
it = iter(iterable)
window = collections.deque(islice(it, n), maxlen=n)
if len(window) == n:
yield tuple(window)
for x in it:
window.append(x)
yield tuple(window)

def roundrobin(*iterables):
"roundrobin('ABC', 'D', 'EF') --> A D E B F C"
# Recipe credited to George Sakkis
num_active = len(iterables)
nexts = cycle(iter(it).__next__ for it in iterables)
while num_active:
try:
for next in nexts:
yield next()
except StopIteration:
# Remove the iterator we just exhausted from the cycle.
num_active -= 1
nexts = cycle(islice(nexts, num_active))

def partition(pred, iterable):
"Use a predicate to partition entries into false entries and true entries"
# partition(is_odd, range(10)) --> 0 2 4 6 8   and  1 3 5 7 9
t1, t2 = tee(iterable)
return filterfalse(pred, t1), filter(pred, t2)

def before_and_after(predicate, it):
""" Variant of takewhile() that allows complete
access to the remainder of the iterator.

>>> it = iter('ABCdEfGhI')
>>> all_upper, remainder = before_and_after(str.isupper, it)
>>> ''.join(all_upper)
'ABC'
>>> ''.join(remainder)     # takewhile() would lose the 'd'
'dEfGhI'

Note that the first iterator must be fully
consumed before the second iterator can
generate valid results.
"""
it = iter(it)
transition = []
def true_iterator():
for elem in it:
if predicate(elem):
yield elem
else:
transition.append(elem)
return
def remainder_iterator():
yield from transition
yield from it
return true_iterator(), remainder_iterator()

def subslices(seq):
"Return all contiguous non-empty subslices of a sequence"
# subslices('ABCD') --> A AB ABC ABCD B BC BCD C CD D
slices = starmap(slice, combinations(range(len(seq) + 1), 2))
return map(operator.getitem, repeat(seq), slices)

def powerset(iterable):
"powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

def unique_everseen(iterable, key=None):
"List unique elements, preserving order. Remember all elements ever seen."
# unique_everseen('AAAABBBCCDAABBB') --> A B C D
# unique_everseen('ABBcCAD', str.lower) --> A B c D
seen = set()
if key is None:
for element in filterfalse(seen.__contains__, iterable):
yield element
# For order preserving deduplication,
# a faster but non-lazy solution is:
#     yield from dict.fromkeys(iterable)
else:
for element in iterable:
k = key(element)
if k not in seen:
yield element
# For use cases that allow the last matching element to be returned,
# a faster but non-lazy solution is:
#      t1, t2 = tee(iterable)
#      yield from dict(zip(map(key, t1), t2)).values()

def unique_justseen(iterable, key=None):
"List unique elements, preserving order. Remember only the element just seen."
# unique_justseen('AAAABBBCCDAABBB') --> A B C D A B
# unique_justseen('ABBcCAD', str.lower) --> A B c A D
return map(next, map(operator.itemgetter(1), groupby(iterable, key)))

def iter_except(func, exception, first=None):
""" Call a function repeatedly until an exception is raised.

Converts a call-until-exception interface to an iterator interface.
Like builtins.iter(func, sentinel) but uses an exception instead
of a sentinel to end the loop.

Examples:
iter_except(functools.partial(heappop, h), IndexError)   # priority queue iterator
iter_except(d.popitem, KeyError)                         # non-blocking dict iterator
iter_except(d.popleft, IndexError)                       # non-blocking deque iterator
iter_except(q.get_nowait, Queue.Empty)                   # loop over a producer Queue
iter_except(s.pop, KeyError)                             # non-blocking set iterator

"""
try:
if first is not None:
yield first()            # For database APIs needing an initial cast to db.first()
while True:
yield func()
except exception:
pass

def first_true(iterable, default=False, pred=None):
"""Returns the first true value in the iterable.

If no true value is found, returns *default*

If *pred* is not None, returns the first item
for which pred(item) is true.

"""
# first_true([a,b,c], x) --> a or b or c or x
# first_true([a,b], x, f) --> a if f(a) else b if f(b) else x
return next(filter(pred, iterable), default)

def nth_combination(iterable, r, index):
"Equivalent to list(combinations(iterable, r))[index]"
pool = tuple(iterable)
n = len(pool)
c = math.comb(n, r)
if index < 0:
index += c
if index < 0 or index >= c:
raise IndexError
result = []
while r:
c, n, r = c*r//n, n-1, r-1
while index >= c:
index -= c
c, n = c*(n-r)//n, n-1
result.append(pool[-1-n])
return tuple(result)
```