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
Input
cards = [4,1,8,7]Output
trueThe expression
(8 - 4) * (7 - 1) evaluates to 24.Example 2
Input
cards = [1,2,1,2]Output
falseNo valid expression using all four cards and the allowed operators evaluates to
24.Constraints
- cards.length == 4
- 1 <= cards[i] <= 9