Final answer:
The student's code using regex_search fails to capture all matching substrings because it only finds the first match. A loop is required to find and print all matching patterns as per the DFA designed to match the regular expression A(A+T+G+C)*T.
Step-by-step explanation:
The issue at hand is that the regex_search function captures only the first match of the regular expression within the input DNA sequence. In order to find all the occurrences of the substring that match your regular expression, you need to use regex_search in a loop, recursively finding subsequent matches starting from the end of the previous match.
To implement this using a deterministic finite automata (DFA) approach in C++, you should keep track of the state you're in (starting, middle, or accepting) and iterate over each character of the DNA sequence, looking for a match by transitioning through the states according to your DFA design. For each 'A' you encounter, start a new state-tracking iteration that checks if it is followed by a sequence of DNA letters and ends in a 'T', constituting a match. Print the match and continue scanning. You will need a nested loop—one scanning the entire input string and an inner loop checking each possible substring starting with 'A' and ending with 'T'.