The program accepts a list of candidates via command-line arguments. These are stored in a global array of strings.
Here is the entire tideman.c solution put together:
#include <cs50.h> #include <stdio.h> #include <string.h>#define MAX 9
int preferences[MAX][MAX]; bool locked[MAX][MAX]; string candidates[MAX]; int pair_count; int candidate_count;
typedef struct int winner; int loser; pair;
pair pairs[MAX * (MAX - 1) / 2];
bool vote(int rank, string name, int ranks[]); void record_preferences(int ranks[]); void add_pairs(void); void sort_pairs(void); void lock_pairs(void); void print_winner(void); bool is_path(int start, int end);
// ... (implement all functions as described above) ...
bool is_path(int start, int end) if (start == end) return true; for (int i = 0; i < candidate_count; i++) if (locked[start][i] && is_path(i, end)) return true; return false;
void lock_pairs(void) for (int i = 0; i < pair_count; i++) int w = pairs[i].winner; int l = pairs[i].loser; if (!is_path(l, w)) locked[w][l] = true; return;
int main(int argc, string argv[]) // Standard main from distribution – unchanged if (argc < 2) printf("Usage: tideman [candidate ...]\n"); return 1; candidate_count = argc - 1; if (candidate_count > MAX) printf("Maximum number of candidates is %i\n", MAX); return 2; for (int i = 0; i < candidate_count; i++) candidates[i] = argv[i + 1];
for (int i = 0; i < candidate_count; i++) for (int j = 0; j < candidate_count; j++) preferences[i][j] = 0; int voter_count = get_int("Number of voters: "); for (int i = 0; i < voter_count; i++) int ranks[candidate_count]; for (int j = 0; j < candidate_count; j++) string name = get_string("Rank %i: ", j + 1); if (!vote(j, name, ranks)) printf("Invalid vote.\n"); return 3; record_preferences(ranks); printf("\n"); add_pairs(); sort_pairs(); lock_pairs(); print_winner(); return 0;
Tideman is hard because it forces you
The CS50 Tideman problem set is widely considered the most difficult assignment in Harvard’s introductory computer science course. It tasks students with implementing the Tideman voting method (also known as Ranked Pairs), a system designed to find a "Condorcet winner"—a candidate who would win against any other candidate in a head-to-head matchup. 1. Record Voter Preferences Cs50 Tideman Solution
The first step is to process every voter's ballot. For each voter, the code must update a 2D preferences[i][j] array, where the value at index [i][j] represents the number of voters who preferred candidate i over candidate j. 2. Identify and Sort Matchups
Once all votes are in, the program identifies every possible head-to-head pair.
Identify: A pair is added to a pairs array if one candidate has more votes than the other.
Sort: The pairs are then sorted in descending order based on the "strength of victory" (the difference in votes between the winner and loser of that pair). 3. Build the Winner Graph
This is the most complex phase. The program iterates through the sorted pairs and "locks" them into a directed graph (using a locked[i][j] boolean matrix).
Cycle Detection: A pair is only locked if it does not create a cycle in the graph. For example, if A beats B and B beats C, you cannot lock a pair where C beats A, as this would create a loop where no clear winner exists.
Recursion: Most students use a recursive helper function to "trace" the path from the winner of the current pair to see if it eventually leads back to the loser. 4. Identify the Source
After all valid pairs are locked, the winner of the election is the "source" of the graph. This is the candidate who has zero arrows pointing toward them (no locked[i][j] is true where j is that candidate). Key Challenges & Academic Honesty
Complexity: Unlike earlier problems like Runoff or Cash, Tideman requires advanced logic for graph theory and recursion.
Academic Integrity: Because of its difficulty, students are frequently warned that looking up a full "Tideman solution" is considered a violation of academic honesty.
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:
Tideman's Algorithm Overview:
Tideman's algorithm works by:
Example Use Case:
Suppose we have an election with three candidates: Alice, Bob, and Charlie. The voters input their ranked preferences as follows:
The Tideman algorithm would then:
The algorithm would then rank the candidates as follows:
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.
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']
CS50 Tideman problem set challenges students to implement a Ranked Pairs voting system. This method is designed to find a Condorcet winner
—a candidate who would defeat every other candidate in a head-to-head matchup. Unlike simpler systems, Tideman uses a directed graph to model candidate relationships, prioritizing the strongest victories while strictly avoiding cycles to ensure a clear winner is found. 1. Record Voter Preferences
The program first captures how many voters prefer one candidate over another using two primary functions:
: Validates the candidate's name and records their rank (0 for 1st choice, 1 for 2nd, etc.) in a temporary array for each voter. record_preferences : Uses the array to update a global 2D preferences[i][j] array. If a voter ranks candidate above candidate preferences[i][j] is incremented by one. Dev Genius 2. Generate and Sort Pairs The program accepts a list of candidates via
Once preferences are recorded, the algorithm identifies head-to-head matchups: : Compares preferences[i][j] preferences[j][i] . If more people prefer , a "pair" is created with as the winner and as the loser. sort_pairs : Orders these pairs in decreasing order of victory strength
(the margin by which the winner defeated the loser). Sorting ensures that the most significant mandates are "locked" into the graph first. 3. Lock Pairs and Avoid Cycles This is the core and most difficult part of the algorithm. lock_pairs
: Iterates through the sorted pairs and attempts to add them to a directed graph ( locked[i][j] = true Cycle Detection
: Before locking a pair, the program must check if doing so would create a cycle (e.g., A beats B, B beats C, and C beats A). This is typically solved using
to trace the path from the current loser back to the winner.
If a path exists from the current loser back to the winner, the pair is skipped. 4. Identify the Winner print_winner
: After all non-cyclical pairs are locked, the program scans the The "Source" : The winner is the candidate who is the
of the graph—meaning they have no edges pointing to them (no one has "locked" a win against them). Final Solution Summary
The complete Tideman solution successfully simulates an election where the strongest preferences are honored without creating logical loops. The result is a system that identifies the most broadly preferred candidate by prioritizing majorities and maintaining a stable, acyclic hierarchy of winners. needed for the lock_pairs cycle check? (CS50) TIDEMAN - PROBLEM SET 3 | SOLUTION
This is the wall where most students get stuck. The Tideman method requires you to "lock in" the winner of each pair, starting with the strongest victory. Unless... locking that arrow creates a cycle.
A cycle happens if the last arrow points back to a candidate who has already "won" a chain, effectively creating an infinite loop where nobody is the ultimate source.
The Logic: I realized I needed a recursive function. The prompt asks: Does locking this pair create a cycle?
To check this, I wrote a helper function (let's call it creates_cycle).
It looked something like this mentally:
If the cycle is detected, do not lock. If the path ends without hitting the target, lock it in.