Largest Share from the Circular Pizza Selection Game
Company: Infosys
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Other
### Problem
The circular slices array has length 3*n. Repeatedly choose any remaining slice for yourself; Alice then takes its immediate remaining anticlockwise neighbor and Bob its immediate remaining clockwise neighbor. Continue until no slices remain. Return the largest total size you can collect.
```cpp
class Solution {
public:
int maxSizeSlices(vector<int>& slices);
};
```
### Examples
**Example 1:**
```text
Input: slices = [2,1,2,1,2,1]
Output: 4
Explanation: Choose the size2 at index0, removing its neighboring ones; then choose either remaining size2. You collect4, the sum of the two largest possible chosen sizes.
```
**Example 2:**
```text
Input: slices = [1,4,2]
Output: 4
Explanation: There is one round; taking the size4 leaves the other two slices for Alice and Bob.
```
### Constraints
- slices.length equals 3*n, lies between 1 and 500,and is divisible by 3.
- `1 <= slices[i] <= 1000`.
### Contract considerations
Alice and Bob take neighbors in the remaining circle after each choice, not arbitrary slices.
```hint Read the boundary condition
Follow both neighbors in the remaining circle after every choice. The objective is your total over the complete game.
```
### Boundary reminders
Alice and Bob take neighbors in the remaining circle after each choice, not arbitrary slices.
Overview: Largest Share from the Circular Pizza Selection Game. The circular slices array has length3*n. Repeatedly choose any remaining slice for yourself; Alice then takes its immediate remaining anticlockwise neighbor and Bob its immediate remaining clockwise neighbor.