Count Students Left When Lunch Service Stops

### Problem Students queue with preferences 0 or 1. `sandwiches` lists a stack from top to bottom, using the same two types. A front student takes a matching top sandwich and leaves; otherwise the student moves to the back. Stop when no remaining student wants the top sandwich. Return how many students cannot eat. ```cpp class Solution { public: int countStudents(vector<int>& students, vector<int>& sandwiches); }; ``` ### Examples **Example 1:** ```text students = [0,1,0], sandwiches = [1,0,0] Output: 0 Explanation: Rotation brings the type-1 student forward, then both type-0 students eat. ``` **Example 2:** ```text students = [1,0,1], sandwiches = [0,0,1] Output: 2 Explanation: The only type-0 student takes the first sandwich; the next type-0 sandwich blocks both remaining students. ``` ### Constraints - The arrays have equal length in `[1,100]`. - Every student preference and sandwich type is either 0 or 1. - Index zero is the queue front or the stack top, respectively. ### Clarifying Questions Sandwich order cannot change. Queue rotation can reach any remaining student but cannot skip an unwanted top sandwich. ```hint Inspect the structure When does the stated queue process stop, and can a later sandwich be considered before the top one? ``` ### Reasoning checkpoints - Show that each served sandwich follows the fixed stack order and the queue rules. - Justify the stopping condition and the exact remaining-student count. ### Optional extensions How would the counting method extend to more than two sandwich types?