I am working on the Tideman problem from the CS50 course (see Problem Set 3 – Tideman), and I am having an issue with my lock_pairs function. The function is intended to lock pairs of candidates without creating cycles, but I am encountering unexpected behavior.

I have implemented the function to iterate over pairs and attempt to lock them in a way that prevents cycles. While my implementation passes certain test cases, I am not confident that it is robust enough to handle all scenarios. I suspect I might be missing something related to cycles.

I have tried to check for cycles manually in my code without recursion (I only realized recursion might be needed after Googling post-implementation), and I was working under the assumption that I could not modify the code outside the provided function definitions (i.e., no additional helper functions).

The course specification allows modifying the lock_pairs function as long as no cycles are introduced. However, I am unsure if my approach is correct or if I am just getting lucky with my test cases and the candidate orders I’ve tried. I would greatly appreciate feedback on whether this implementation is correct or if there’s a flaw in the logic.

Background:

• Problem set: CS50 Tideman
• The function must lock pairs of candidates into a graph without creating cycles.
• I initially forgot about recursion for cycle detection.

Here’s my current implementation of lock_pairs:

// Lock pairs into the candidate graph in order, without creating cycles
void lock_pairs(void)
{
    int lastloser;
    int winnerloser = MAX + 1;

    for (int r = 0; r < pair_count; r++)
    {
        int losercheck[MAX] = {0};

        // Check each locked pair if false (empty), store only the loser index
        for (int i = 0; i < candidate_count; i++)
        {
            for (int j = 0; j < candidate_count; j++)
            {
                if (locked[i][j] == false)
                {
                    losercheck[j]++;
                }
            }
        }

        lastloser = 0;

        // Check how many currently are all empty by comparing to candidate count
        for (int j = 0; j < candidate_count; j++)
        {
            if (losercheck[j] == candidate_count)
            {
                // Store quantity of empty loser columns in lastloser
                lastloser++;
            }
        }

        // If last loser == 1, leave it blank to declare a winner
        if (lastloser == 1)
        {
            for (int j = 0; j < candidate_count; j++)
            {
                if (losercheck[j] == candidate_count)
                {
                    winnerloser = j;
                }
            }
        }

        if (pairs[r].loser != winnerloser)
        {
            locked[pairs[r].winner][pairs[r].loser] = true;
        }
    }

    return;
}

My Question:

1. Is this implementation correct for ensuring no cycles are created while locking pairs?
2. Is the manual checking method I’ve employed effective, or is recursion necessary for checking cycles, as suggested in the problem hints?
3. Are there any edge cases where this implementation might fail that I might not have tested?

I am happy to provide additional context if necessary. Thanks in advance for your help!