Final answer:
The time complexity for counting occurrences of a character in a vector of unsorted strings is O(n * m), where n is the number of strings and m is the length of the longest string. Since m is capped by n, the worst-case time complexity becomes O(n^2).
Step-by-step explanation:
To determine the time complexity of counting occurrences of a character c in a vector of unsorted strings, you need to consider the operations performed on every element of the input. The task involves iterating over each string in the vector and then iterating over each character in the string to check for matches with the character c.
Let n be the number of strings in the vector and let m be the maximum length of any string within the vector. You perform a constant-time check for each character in each string, resulting in a time complexity of O(n * m). Because you are not performing any other operations that would significantly impact the time complexity, such as sorting or searching a data structure with more complex look-up times, the overall time complexity remains O(n * m).
Given that the largest string will not contain more characters than there are strings in the vector, m can also be thought of as not exceeding n, thereby simplifying the complexity to O(n2) in the worst case scenario. Remember that Big O notation describes the upper limit of the time complexity, so while it is possible that the actual time to count occurrences could be less, depending on the lengths of the strings, we affirm the worst-case time complexity as O(n2).