# 679. 24 Game
You are given an integer array cards of length 4. You have four cards, each containing a number in the range [1, 9]. You should arrange the numbers on these cards in a mathematical expression using the operators ['+', '-', '*', '/'] and the parentheses '(' and ')' to get the value 24.
You are restricted with the following rules:
The division operator '/' represents real division, not integer division.
For example, 4 / (1 - 2 / 3) = 4 / (1 / 3) = 12.
Every operation done is between two numbers. In particular, we cannot use '-' as a unary operator.
For example, if cards = [1, 1, 1, 1], the expression "-1 - 1 - 1 - 1" is not allowed.
You cannot concatenate numbers together. For example, if cards = [1, 2, 1, 2], the expression "12 + 12" is not valid.
Return true if you can get such expression that evaluates to 24, and false otherwise.
Example 1:
Input: cards = [4,1,8,7]
Output: true
Explanation: (8-4) * (7-1) = 24
Example 2:
Input: cards = [1,2,1,2]
Output: false
# Solution
Approach 1: keeps picking two numbers and merge them with the rest, until there's one number left.
# Code (Python)
Approach 1:
ERROR_BOUND = 0.001
class Solution:
def judgePoint24(self, cards: List[int]) -> bool:
return any(abs(item - 24) < ERROR_BOUND for item in self._all_results(cards))
def _all_results(self, nums):
# keeps picking two numbers and merge them with the rest, until there's one number left
if len(nums) == 1:
return set([nums[0]])
results = set()
for i in range(len(nums)):
for j in range(i + 1, len(nums)):
a, b = nums[i], nums[j]
merge_result = [a + b, a - b, b - a, a * b]
if a != 0:
merge_result.append(b / a)
if b != 0:
merge_result.append(a / b)
for result in merge_result:
results = results.union(self._all_results(nums[:i] + nums[i+1:j] + nums[j+1:] + [result]))
return results
# Code (C++)
Approach 1:
Approach 2: