该问题表述为：给定一个仅包含数字 0-9 和一个目标值的字符串，返回通过在数字之间添加一些二元运算符（+、- 或 *）创建的所有表达式，以便它们计算为目标值。在某些情况下，可能没有任何二元运算符可以创建有效的表达式，在这种情况下，函数应返回空数组。新表达式中的数字不应包含前导零。
该函数应返回计算结果为目标的所有有效表达式，并按字典顺序排序。
例如：
数字="123"和目标=6，应该返回：["1*2*3", "1+2+3"]
我当前的算法如下。它有点慢，所以我正在寻找一种更有效的方法来解决这个问题。我当前的算法生成操作数和运算符的所有组合。对于上面的例子，它产生
操作数：
[['1', '2', '3'], ['1', '23'], ['12', '3'], ['123']]
运营商：
{0: [()], 1: [('+',), ('-',), ('*',)], 2: [('+', '+'), ('+', '-'), ('+', '*'), ('-', '+'), ('-', '-'), ('-', '*'), ('*', '+'), ('*', '-'), ('*', '*')]}
然后，它组合操作数和运算符的所有可能组合并评估每个组合。
数字有一个约束2 ≤ digits.length ≤ 10.所以它并没有那么糟糕，但是使用这个算法，长度为 10 的数字需要大约 4.3 秒，而它应该只需要 4 秒（最大值）。
我还尝试使用以下替代方案来加速 eval() 函数：
if eval(temp) == target:
or
exp_as_func = eval('lambda: ' + temp)
if exp_as_func() == target:
or
compiled = compile(temp, '<string>', 'eval')
if compiled == target:
使用 Python 3，所有这些仍然需要大约相同的时间。
Code:
import itertools
import time
def getValidExp(digits, target):
def getSign_combination(length):
signCombo = {}
for i in range(0, length):
signCombo[i] = [c for c in itertools.product(('+', '-', '*'), repeat=i)]
return signCombo
def generate_combination(source, comb):
res = []
for x, action in zip(source, comb + (0,)):
res.append(x)
if action == 0:
#####IF ITS A 0, YIELD STRING. IF NOT COMBINE NEXT ONE
yield "".join(res)
res = []
#####PRODUCT GENERATES (0,0,1). ALL COMBINATIONS. 0 MEANS BY ITSELF, 1 APPEND NEXT ITEM.
elementCombo = [list(generate_combination(digits, c)) for c in itertools.product((0, 1), repeat=len(digits) - 1)]
signCombo = getSign_combination(len(digits))
result = []
for e in elementCombo:
signs = signCombo[len(e)-1]
for i,sign in enumerate(signs):
temp = [ item for tple in zip(e, sign) for item in tple ]
temp.append(e[-1])
temp = "".join(temp)
try:
if eval(temp) == target:
result.append(temp)
except:
pass
return sorted(result)
digits = "3456237490"
target = 9180
print("Answer:", getValidExp(digits, target))
使用计算器函数（无 eval()）的代码几乎具有相同的速度：
from itertools import combinations, permutations
import itertools
import time
def getValidExp(digits, target):
def calculate(s):
operands, operators = [], []
operand = ""
for i in reversed(range(len(s))):
if s[i].isdigit():
operand += s[i]
if i == 0 or not s[i - 1].isdigit():
operands.append(int(operand[::-1]))
operand = ""
elif s[i] == '*':
operators.append(s[i])
elif s[i] == '+' or s[i] == '-':
while operators and operators[-1] == '*':
compute(operands, operators)
operators.append(s[i])
while operators:
compute(operands, operators)
return operands[-1]
def compute(operands, operators):
left, right = operands.pop(), operands.pop()
op = operators.pop()
if op == '+':
operands.append(left + right)
elif op == '-':
operands.append(left - right)
elif op == '*':
operands.append(left * right)
def getSign_combination(length):
signCombo = {}
for i in range(0, length):
signCombo[i] = [c for c in itertools.product(('+', '-', '*'), repeat=i)]
return signCombo
def generate_combination(source, comb):
res = []
for x, action in zip(source, comb + (0,)):
res.append(x)
if action == 0:
yield "".join(res)
res = []
start = time.clock()
#####PRODUCT GENERATES (0,0,1). ALL COMBINATIONS. 0 MEANS BY ITSELF, 1 APPEND NEXT ITEM.
elementCombo = [list(generate_combination(digits, c)) for c in itertools.product((0, 1), repeat=len(digits) - 1)]
signCombo = getSign_combination(len(digits))
result = []
for e in elementCombo:
signs = signCombo[len(e)-1]
for i,sign in enumerate(signs):
temp = ""
valid = True
for num in e:
if num[0] == '0' and len(num) > 1:
valid = False
break
if valid:
for num,operator in zip(e,sign):
temp += num
temp += operator
temp += e[-1]
####USING CALCULATOR CODE
if calculate(temp) == target:
result.append(temp)
print(time.clock() - start)
return sorted(result)
digits = "3456237490"
target = 9180
print("Answer:", getValidExp(digits, target))
