Modelling GTU's 4-backlog detain rule in 15 lines of Python

I keep seeing GTU (Gujarat Technological University) juniors panic about the "4 backlog" rule, and half of them count it wrong. The rule has one twist that makes it a nice little exercise in code.

The rule

• A backlog is a subject with an FF grade (below 35 marks). Missing the exam also counts as not cleared.
• At any time you can carry at most 4 pending backlogs. More than 4 and you can be detained for one year.
• Backlogs from the semester just before your current one are not counted.

That last line is the bug in most people's mental model.

The code

def detention_check(current_sem: int, pending: dict[int, int]) -> tuple[int, bool]:
    """pending maps semester -> number of FF subjects still not cleared."""
    just_previous = current_sem - 1
    counted = sum(
        n for sem, n in pending.items()
        if sem < just_previous
    )
    return counted, counted > 4


# Sem 4 student: 2 in Sem 1, 1 in Sem 2, 3 in Sem 3 (6 total)
print(detention_check(4, {1: 2, 2: 1, 3: 3}))  # (3, False) -> safe

# Same student moves to Sem 5 and clears nothing
print(detention_check(5, {1: 2, 2: 1, 3: 3}))  # (6, True) -> detained

Same backlogs, different semester, opposite result. A backlog that is "free" today gets counted the moment you move up, so the real deadline for clearing a paper is one semester later than it looks.

What the function does not cover

• Students admitted from 2018-19 onward follow a stricter table from GTU circular 5440 (19 July 2018), where certain semesters must be fully cleared before you enter the semester two years ahead.
• Attendance: you need at least 75% to fill the exam form at all.

So treat this as a sanity check, not a verdict. Your college exam cell has the final word for your batch.

The full write-up, with the 2018 table, fees and a semester-by-semester plan, is on GTU Hero. Disclosure: I build GTU Hero.