如何生成与数组替换变量的所有组合？

def generate_combinations(arr, variables, index, current_combination, combinations):
    if index == len(variables):
        combinations.append(current_combination.copy())
        return

    for value in arr:
        current_combination[variables[index]] = value
        generate_combinations(arr, variables, index + 1, current_combination, combinations)

def generate_all_combinations(arr, variables):
    combinations = []
    generate_combinations(arr, variables, 0, {}, combinations)
    return combinations

arr = [1, 2, 3]
variables = ['var1', 'var2', 'var3']
combinations = generate_all_combinations(arr, variables)
for combination in combinations:
    print(combination)

{'var1': 1, 'var2': 1, 'var3': 1}
{'var1': 1, 'var2': 1, 'var3': 2}
{'var1': 1, 'var2': 1, 'var3': 3}
{'var1': 1, 'var2': 2, 'var3': 1}
{'var1': 1, 'var2': 2, 'var3': 2}
{'var1': 1, 'var2': 2, 'var3': 3}
{'var1': 1, 'var2': 3, 'var3': 1}
{'var1': 1, 'var2': 3, 'var3': 2}
{'var1': 1, 'var2': 3, 'var3': 3}
{'var1': 2, 'var2': 1, 'var3': 1}
{'var1': 2, 'var2': 1, 'var3': 2}
{'var1': 2, 'var2': 1, 'var3': 3}
{'var1': 2, 'var2': 2, 'var3': 1}
{'var1': 2, 'var2': 2, 'var3': 2}
{'var1': 2, 'var2': 2, 'var3': 3}
{'var1': 2, 'var2': 3, 'var3': 1}
{'var1': 2, 'var2': 3, 'var3': 2}
{'var1': 2, 'var2': 3, 'var3': 3}
{'var1': 3, 'var2': 1, 'var3': 1}
{'var1': 3, 'var2': 1, 'var3': 2}
{'var1': 3, 'var2': 1, 'var3': 3}
{'var1': 3, 'var2': 2, 'var3': 1}
{'var1': 3, 'var2': 2, 'var3': 2}
{'var1': 3, 'var2': 2, 'var3': 3}
{'var1': 3, 'var2': 3, 'var3': 1}
{'var1': 3, 'var2': 3, 'var3': 2}
{'var1': 3, 'var2': 3, 'var3': 3}