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 an expression that evaluates to 24, and false otherwise.

Example 1
Inputcards = [4,1,8,7]
Outputtrue
The expression (8 - 4) * (7 - 1) evaluates to 24.
Example 2
Inputcards = [1,2,1,2]
Outputfalse
No valid expression using all four cards and the allowed operators evaluates to 24.

Constraints

  • cards.length == 4
  • 1 <= cards[i] <= 9

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