Maya ran check50 . Green smiles across the board. She leaned back.
"You’re not just looking for a loop," Kai said. "You’re looking for a chain . Before you lock a new edge from winner to loser , ask yourself: is there any path from the loser back to the winner using the edges already locked? If yes, this new edge would complete the cycle. Skip it."
Her friend, an old sysadmin named Kai, peered over her shoulder. "You're trying to lock every pair in order of strength, right?"
"Show me your cycle detection," Kai said. Cs50 Tideman Solution
The story is useful because the narrative (the cycle, the DFS, the "path back") sticks in your brain longer than any pseudocode. Next time you face Tideman, remember Maya and the Orchard.
"It's not about the edge you're adding," she whispered. "It's about the path that already exists beneath it."
Maya was the new programmer tasked with tabulating the votes. She had the first part down: counting each ballot to build a 2D array of preferences . It told her that Alice beat Bob (5 votes to 2), Bob beat Charlie (4 to 3), and Charlie beat Alice (3 to 2). A perfect, frustrating cycle. Maya ran check50
Kai chuckled. "That's not just Tideman, Maya. That's life. Don't create cycles. Always check if the person you're stepping on has a hidden path back to you."
Kai nodded slowly. "You are looking for a direct path back to the winner. But what if the path is three steps? Four? Your recursion only goes two levels deep."
Maya submitted her solution. And in the real election that followed, Alice became Keeper of the Orchard—not because she was the strongest in every head-to-head match, but because when paradoxes arose, the village had a coder wise enough to know which locks to leave open. Don't just check for a two-step loop. Use depth-first search to see if the loser has any path to the winner in the existing locked graph. If yes, skip the pair. That’s the entire secret of Tideman. "You’re not just looking for a loop," Kai said
"Yes," Maya sighed. "I sort the pairs. Strongest first. Alice over Bob? Lock it. Bob over Charlie? Lock it. Charlie over Alice? Don't lock it because it creates a cycle. But my cycle detection is wrong."
Maya pointed. "I wrote a recursive function creates_cycle(winner, loser) . It checks if the loser has any locked edges pointing to another candidate. Then it checks if that candidate points back to the original winner. If yes, it’s a cycle."
Her job was to "lock in" the strongest edges of victory to create a directed graph of the winner—without creating a cycle.
Every year, the village of Coderidge held an election for the Keeper of the Orchard. Unlike other villages, they used a complex ranked voting system designed by a long-dead mathematician named Tideman. The rule was simple: if there was a way to trace a circle of preference (A beats B, B beats C, C beats A), that circle was a paradox, and the weakest link in that circle must be ignored.
He drew on the whiteboard: