Solve this programming problem:
Question: Suppose that a bag contains strings that represent various grocery items. Write a C++ function that removes and counts all occurrences of a given string from such a bag. Your function should return this number. Use comments in javadoc style to fully specify your function. Accommodate the possibility that the given bag is either empty or does not contain any occurrences of the given string.
Can you write this program in c++ language? Define every function.