Decide Whether Four Cards Can Form Twenty-Four
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
Use all four cards exactly once in a parenthesized expression with binary +, -, *, /. Division is real division. Unary minus and concatenating card digits are forbidden. Return whether any permitted expression has exact value 24.
```cpp
class Solution {
public:
bool judgePoint24(vector<int>& cards);
};
```
### Examples
**Example 1:**
```text
cards = [3,3,8,8]
Output: true
Explanation: 8/(3-8/3) = 24 uses real division.
```
**Example 2:**
```text
cards = [1,1,1,1]
Output: false
Explanation: A pair of ones can only produce 0,1,2 (or undefined division); combining the resulting two pairs reaches at most 4, and the three-plus-one parenthesizations likewise cannot reach 24.
```
### Constraints
- Exactly four card entries are supplied; each integer lies in 1..9.
### Clarifying Questions
Use every card once, support noninteger intermediates and reject division by zero.
```hint Read the boundary condition
Can combining two available values recursively cover every parenthesized binary expression?
```
### Contract considerations
Use every card once, support noninteger intermediates and reject division by zero.
Overview: Decide Whether Four Cards Can Form Twenty-Four. Use all four cards exactly once in a parenthesized expression with binary +, -, *, /.