Cs50 - Tideman Solution !!link!!

Algorithmic Implementation of the Tideman Voting System

A Comprehensive Analysis of the CS50 Solution

The Helper Function: will_create_cycle

We will write a helper that answers: "Starting from the loser, can I eventually reach the winner using existing locked edges?"

If yes → cycle → don’t lock. If no → safe to lock.

Key Insight for the Difficult Part: Detecting Cycles

The hardest part is lock_pairs() — locking a pair if it doesn’t create a cycle.

Think of locked pairs as directed edges from winner to loser.

A cycle occurs if:

Adding edge A → B would create a path from B back to A using already locked edges.

So to check if locking (winner, loser) is safe:

• Temporarily add the edge.
• Check if there’s a path from loser to winner in the current locked graph.
• If yes → cycle would form → don’t lock.
• If no → safe to lock.

4.1 Sorting Complexity

A common mistake students make is sorting based only on the raw number of votes for the winner, rather than the margin of victory. However, the Tideman specification dictates sorting by victory strength (margin), which requires accessing both preferences[winner][loser] and preferences[loser][winner].