Cs50 Tideman Solution -

Feature: "Ranked Choice Voting with Tideman's Algorithm"

Description: Implement a ranked-choice voting system using Tideman's algorithm, a well-known method for determining the winner of an election based on ranked preferences. This feature will allow users to input their ranked preferences for a set of candidates and then determine the winner based on Tideman's algorithm.

Requirements:

Candidate Input: Allow users to input a list of candidates for the election.
Voter Input: Allow users to input their ranked preferences for the candidates, with the ability to specify their top choice, second choice, third choice, and so on.
Tideman's Algorithm Implementation: Implement Tideman's algorithm to determine the winner of the election based on the ranked preferences.
Results Output: Display the results of the election, including the winner and the ranked order of the candidates.

Tideman's Algorithm Overview:

Tideman's algorithm works by:

Pairwise Comparisons: Comparing each pair of candidates to determine which one is preferred by more voters.
Win Counts: Keeping track of the number of wins for each candidate.
Ranking: Ranking the candidates based on their win counts.

Example Use Case:

Suppose we have an election with three candidates: Alice, Bob, and Charlie. The voters input their ranked preferences as follows:

Voter 1: Alice > Bob > Charlie
Voter 2: Bob > Charlie > Alice
Voter 3: Charlie > Alice > Bob

The Tideman algorithm would then:

Compare Alice and Bob: Alice wins (2/3)
Compare Alice and Charlie: Charlie wins (2/3)
Compare Bob and Charlie: Bob wins (2/3)

The algorithm would then rank the candidates as follows: Cs50 Tideman Solution

Bob (2 wins)
Alice (1 win)
Charlie (0 wins)

Code Implementation:

Here is a potential implementation in Python:

def tideman_election(candidates, voter_preferences):
    """
    Run a Tideman election with the given candidates and voter preferences.
:param candidates: List of candidate names
    :param voter_preferences: List of voter preferences, where each preference is a list of candidate names in ranked order
    :return: The winner of the election and the ranked order of the candidates
    """
    # Initialize win counts for each candidate
    win_counts = candidate: 0 for candidate in candidates
# Perform pairwise comparisons
    for i in range(len(candidates)):
        for j in range(i + 1, len(candidates)):
            # Determine which candidate wins the comparison
            winner = compare_candidates(candidates[i], candidates[j], voter_preferences)
            if winner == candidates[i]:
                win_counts[candidates[i]] += 1
            else:
                win_counts[candidates[j]] += 1
# Rank candidates by win count
    ranked_candidates = sorted(candidates, key=lambda x: win_counts[x], reverse=True)
# Determine the winner
    winner = ranked_candidates[0]
return winner, ranked_candidates
def compare_candidates(candidate1, candidate2, voter_preferences):
    """
    Compare two candidates and determine which one is preferred by more voters.
:param candidate1: Name of the first candidate
    :param candidate2: Name of the second candidate
    :param voter_preferences: List of voter preferences, where each preference is a list of candidate names in ranked order
    :return: The candidate that is preferred by more voters
    """
    # Count the number of voters who prefer each candidate
    count1 = sum(1 for preference in voter_preferences if candidate1 in preference and candidate2 not in preference[:preference.index(candidate1)])
    count2 = sum(1 for preference in voter_preferences if candidate2 in preference and candidate1 not in preference[:preference.index(candidate2)])
# Return the candidate with the higher count
    if count1 > count2:
        return candidate1
    else:
        return candidate2

Testing:

To test the implementation, we can create a sample election with a few candidates and voter preferences, and then verify that the output is correct. Candidate Input: Allow users to input a list

candidates = ["Alice", "Bob", "Charlie"]
voter_preferences = [
    ["Alice", "Bob", "Charlie"],
    ["Bob", "Charlie", "Alice"],
    ["Charlie", "Alice", "Bob"]
]
winner, ranked_candidates = tideman_election(candidates, voter_preferences)
print("Winner:", winner)
print("Ranked Candidates:", ranked_candidates)

This should output:

Winner: Bob
Ranked Candidates: ['Bob', 'Alice', 'Charlie']

Here’s a helpful, explanatory text for understanding and implementing the Tideman problem from CS50 (the “locked pairs” voting method). It’s not the full code, but a reasoning guide to help you write your own solution.

The Complete Solution (Step-by-Step)

Let’s implement lock_pairs and its helper creates_cycle.

Important implementation notes & pitfalls

Initialize preferences and locked arrays to 0/false each run.
Use clear base cases in cycle detection to avoid false positives.
DFS recursion depth is at most candidate_count (safe).
When computing margin, use absolute difference but add pair only when winner has strictly more votes.
When sorting, break ties consistently (though not required).
Ensure pair_count correct: increment only when adding a pair.
Validate input: guard against candidate_count > MAX and voter ranks duplicates.
Use stable types: int for counts; bool for locked (include <stdbool.h>).
For qsort comparator: compare pair.margins (descending).

The Core Concept: Graphs and Cycles

Think of the locked array as a directed graph. Each candidate is a node. When you lock a pair (winner → loser), you draw an arrow from the winner to the loser. bool for locked (include &lt

A cycle looks like this: Alice → Bob → Charlie → Alice.
Why is a cycle bad? In a ranked-pair system, a cycle would make every candidate have at least one arrow pointing to them and pointing away. There would be no clear "source" winner. The algorithm forbids cycles to ensure one ultimate winner.

Your goal in lock_pairs: Before locking a new edge (winner → loser), check if it would create a cycle. If yes, skip it.