我构建此代码是为了完成数学挑战，我必须找到一个组合来给出目标结果。
我必须替换“？”对于“+”、“-”、“/”或“*”，并在需要给我们答案的地方添加“( )”。
6 ? 6 ? 6 ? 6 = 5
6 ? 6 ? 6 ? 6 = 6
6 ? 6 ? 6 ? 6 = 8
6 ? 6 ? 6 ? 6 = 30
6 ? 6 ? 6 ? 6 = 24
6 ? 6 ? 6 ? 6 = 48
6 ? 6 ? 6 ? 6 = 66
6 ? 6 ? 6 ? 6 = 180
但是下面的代码找不到 30 的答案，应该是：
(6-(6/6))*6 = 30
这是代码
import itertools # Import itertools module for combinations
import datetime # Import datetime module for timing
# Function to evaluate mathematical expression
def evaluate_expression(expression):
try:
return eval(expression) # Use eval to compute the expression's value
except:
return None
# Function to resolve using combinatorics
def solve_with_combinatorics(target_results, factor):
operators = ['+', '-', '*', '/'] # List of mathematical operators
numbers = [factor, factor, factor, factor] # List of input numbers
found_solutions = [] # List to store found solutions
all_possibilities = [] # List to store all expression possibilities
# Iterate over target results
for target_result in target_results:
found = False # Flag to track if solution is found
attempts = 0 # Counter for attempts
expression_possibilities = [] # List to store expression possibilities
# Iterate over operator combinations
for operator_combination in itertools.product(operators, repeat=3):
attempts += 1 # Increment attempts counter
expression = str(numbers[0]) # Initialize expression with first number
for i in range(3):
expression = f"({expression} {operator_combination[i]} {numbers[i+1]})"
result = evaluate_expression(expression) # Evaluate the expression
if result == target_result: # Check if the result matches the target
found_solutions.append((expression, result, attempts)) # Store solution
found = True
break
expression_possibilities.append(expression) # Store expression possibility
all_possibilities.append((target_result, expression_possibilities)) # Store possibilities
if not found:
for possibility in expression_possibilities:
if evaluate_expression(possibility) == target_result: # Check if possibility matches target
found_solutions.append((possibility, target_result, attempts)) # Store solution
found = True
break
if not found:
found_solutions.append(("No solution found", None, attempts)) # Store no solution
# Print and return results
for solution, result, attempts in found_solutions:
if result is not None:
print(f"Expression: {solution} = {int(result)}") # Print solution expression and result
else:
print("Expression:", solution) # Print no solution message
print("Attempts:", attempts) # Print number of attempts
return all_possibilities
# Target results and factor
target_results = [5, 6, 8, 30, 24, 48, 66, 180]
factor = 6
print("\n[ACHIEVE EQUALITY FOR THE MATHEMATICAL EXPRESSIONS BELOW]")
for i, result in enumerate(target_results):
print(f"{factor} ? {factor} ? {factor} ? {factor} = {result}") # Print target expressions
print()
start_time = datetime.datetime.now()
print(f'## Program started at: {start_time}\n') # Print start time
all_possibilities = solve_with_combinatorics(target_results, factor) # Call the solver function
end_time = datetime.datetime.now()
total_time = end_time - start_time
print(f'## Program ended at: {end_time}') # Print end time
print(f'## Total time: {total_time}\n') # Print total execution time
print("\n[All possible combinations and combination results]")
largest_target_result = max(target_results)
for target_result, possibilities in all_possibilities:
if target_result <= largest_target_result:
print(f"\nTarget Result {target_result}:") # Print target result label
for possibility in possibilities:
print(possibility) # Print each expression possibility
print()
这是输出的一部分：
## Program started at: 2023-08-26 14:30:45.595289
Expression: (((6 * 6) - 6) / 6) = 5
Attempts: 40
Expression: (((6 - 6) * 6) + 6) = 6
Attempts: 25
Expression: (((6 + 6) / 6) + 6) = 8
Attempts: 13
Expression: No solution found
Attempts: 64
Expression: (((6 + 6) + 6) + 6) = 24
Attempts: 1
Expression: (((6 * 6) + 6) + 6) = 48
Attempts: 33
Expression: (((6 + 6) * 6) - 6) = 66
Attempts: 10
Expression: (((6 * 6) - 6) * 6) = 180
Attempts: 39
## Program ended at: 2023-08-26 14:30:45.604267
## Total time: 0:00:00.008978
那么，问题是：除了64种可能性之外，如何增加组合的可能性？
我尝试在屏幕上绘制所有可能性，看看代码中是否有问题，但没有。我相信这是 intertool 库的限制。
为了增加 64 种可能性，您应该创建数字的可能括号组。
这是一种查找数字可能的括号组的算法：
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
def product(*iterables):
if not iterables:
yield []
return
for i in iterables[0]:
for p in product(*iterables[1:]):
yield [i, *p]
def find_numbers(s: str):
return list(map(int, "".join(map(lambda i: i if i.isnumeric() else " ", s)).split()))
def find_chars(s: str):
return list(filter(lambda i: not i.isnumeric(), s))
def group_numbers(x):
step = 2
result = [x]
while step < len(x):
for i in range(len(x) - 1):
left = x[:i]
mid = x[i: i + step]
right = x[i + step:]
if len(mid) == step:
result.append([*left, mid, *right])
if len(left) == step:
result.append([left, mid, *right])
if len(mid) > 2:
for mid_group in group_numbers(mid):
item = [*left, mid_group, *right]
if item not in result:
result.append(item)
step += 1
return result
def insert_operators(x, y):
expr = ""
for i in range(len(x)):
if isinstance(x[i], list):
expr += "(" + insert_operators(x[i], y) + ")"
try:
if expr[-1] != x[i + 1]:
expr += next(y)
except IndexError:
pass
else:
expr += str(x[i])
if i != len(x) - 1:
try:
expr += next(y)
except StopIteration:
pass
return expr
def get_products(factor, ops, number):
products = []
for i in range(number):
if i == number - 1:
products += [factor]
else:
products += [factor] + [ops]
return products
def main():
ops = "+-/*"
factor = "6"
number = 4
targets = [5, 6, 8, 30, 24, 48, 66, 180]
for i in product(*get_products(factor, ops, number)):
expr = "".join(i)
for group in group_numbers(find_numbers(expr)):
equation = insert_operators(group, iter(find_chars(expr)))
try:
res = eval(equation)
if res in targets:
print(equation, res)
targets.remove(res)
except ZeroDivisionError:
pass
main()
输出：
6+6+6+6 24
6+(6+6)/6 8.0
6+6+6*6 48
6+(6-6)/6 6.0
(6+6)*6-6 66
(6-6/6)*6 30.0
(6*6-6)/6 5.0
(6*6-6)*6 180