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[英]What is the fastest way to represent number as the sum of powers of two in python
[英]Python - Combination of powers of two to obtain target sum
我需要找到两个幂的所有组合,以获得具有特定长度的单个组合的目标总和
例如
target_sum = 10
target_len = 3 # (number of powers of two to use)
input_list = [1, 1, 2, 2, 2, 4, 4, 8]
值 1、2、4 等的重复是可变的,但总是<= target_len
生产中的实际输入是 ~10k 个元素,target_sum 5/50000,target_len 高达 1000
另一种表示输入的方式是[(1, 2), (2, 3), (4, 2), (8, 1)]
(与collections.Counter(input_list)
相同)
解决方案是: [(1, 1, 8), (2, 4, 4)]
或[((1, 2), (8, 1)), ((2, 1), (4, 2))]
在后一种符号中
假设:
这个函数会被多次调用并且必须很快,我无法使用 itertools 探索所有解决方案。*
我已经找到了一个解决方案,速度快但不优雅,我想知道是否有人有好主意。
(欢迎使用 cython 或类似 c 的代码)
编辑
用作参考的函数是
def pow2_to_target_len_sum_reference(x: (list, tuple), target_sum, target_len):
return [i for i in set(itertools.combinations(x, target_len)) if sum(i) == target_sum]
这是〜10k快但丑陋
def _make_first_guess(t, target_sum, target_len):
guess , valid = [], []
v, n = t
for i in range(1, n + 1):
s = v * i
if s > target_sum:
break
reach_sum = s == target_sum
reach_len = i == target_len
if reach_sum & (i < target_len):
break
if reach_len & (s < reach_sum):
break
if reach_sum and reach_len:
valid.append((v, i))
break
guess.append(([(v, i)], s, i))
return guess, valid
def _evaluate_next_guess(t, target_sum, target_len, cur_sum, cur_len):
guess, valid = [], []
v, n = t
for i in range(1, n + 1):
temp_len = cur_len + i
temp_sum = cur_sum + (v * i)
reach_sum = temp_sum == target_sum
reach_len = temp_len == target_len
if reach_sum & reach_len:
valid.append((v, i))
break
elif reach_sum | reach_len:
break
else:
if temp_sum > target_sum:
break
if temp_len > target_len:
break
guess.append(((v, i), temp_sum, temp_len))
return guess, valid
def _append_guess(comb, list_prev_guess, target_sum, target_len):
list_new_guess, ret_valid = [], []
for cur_guess, cur_sum, cur_len in list_prev_guess:
list_guess_to_append, list_valid = _evaluate_next_guess(comb, target_sum, target_len, cur_sum, cur_len)
for valid in list_valid:
ret_valid.append(cur_guess + [valid])
for new_guess, new_sum, new_len in list_guess_to_append:
concat_guess = cur_guess + [new_guess]
list_new_guess.append((concat_guess, new_sum, new_len))
return list_new_guess, ret_valid
def pow2_to_target_len_sum(li, target_sum: int, target_len: int):
# list like [1,1,1,2,2,4,4,4,8,8,16,16,16,16]
list_counts = list(Counter(li).items())
rev_counts = list_counts[::-1]
ret = []
for i in range(len(rev_counts)):
starting_list = rev_counts[i:]
list_guess, valid = _make_first_guess(starting_list[0], target_sum, target_len)
# ret += valid
if not list_guess:
continue
found_solution = False
for tup in starting_list[1:]:
new_guess, valid_after = _append_guess(tup, list_guess, target_sum, target_len)
if valid_after:
found_solution = True
valid += valid_after
# ret += valid
list_guess += new_guess
if valid:
# ret at first guess: List[Tuple[int, int]]
# ret after first guess: List[List[Tuple[int, int]]]
# if the right solution is found at first guess ret must be fixed
ret += valid if found_solution else [valid]
list_readable = []
for solution in ret:
nested = [[i] * j for i, j in solution[::-1]]
list_readable.append(tuple([i for j in nested for i in j]))
return list_readable
有效地找到与给定结果相加的值组合的一种方法是迭代每个值的频率范围,从而仅在单个递归调用中填充输出列表一定次数:
from collections import Counter
target_sum = 10
max_len = 3
input_list = [1, 1, 2, 2, 2, 4, 4, 4, 8]
def ajax_solution1(target_sum, max_len, input_list):
def get_combos(d, l = 0, c = [], cl = 0):
if l == target_sum and cl == max_len:
yield tuple(c)
elif d and d[0][0] + l <= target_sum:
for i in range(1, d[0][-1]+1):
if d[0][0]*i + l <= target_sum and cl + i <= max_len:
yield from get_combos(d[1:], l=l+(d[0][0]*i), c = c+([d[0][0]]*i), cl = cl+i)
yield from get_combos(d[1:], l = l, c = c, cl= cl)
[(_, x), *vals], r = Counter(input_list).items(), []
for i in range(1, x+1):
if target_sum%2 == i%2:
if i <= max_len and i <= target_sum:
r.extend(list(get_combos(vals, l = i, c=([1]*i), cl = i)))
r.extend(list(get_combos(vals)))
return r
print(ajax_solution1(target_sum, max_len, input_list))
输出:
[(1, 1, 8), (2, 4, 4)]
时间:
下图说明了函数ajax_solution1
的更高效率,而不是针对同一问题的基本itertools
实现以及 OP 代码。 可以在此处找到带有计时源代码的 Gist。
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