Cs50 Tideman Solution 'link' 〈No Ads〉

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.

High-level algorithm (functions)

1. bool vote(int rank, char *name, int ranks[])

   • Map voter choice name to candidate index.
   • Return false if invalid name; otherwise set ranks[rank] and return true.

2. void record_preferences(int ranks[])

   • For each i < j: preferences[ranks[i]][ranks[j]]++

3. void add_pairs(void)

   • For every i != j:
     • if preferences[i][j] > preferences[j][i], add i, j, preferences[i][j] - preferences[j][i] to pairs[].

4. void sort_pairs(void)

   • Sort pairs[] in descending order by margin. Use qsort or selection sort for clarity.

5. bool creates_cycle(int winner, int loser)

   • Recursively (or with DFS) check if adding edge winner->loser would create a path from loser back to winner.
   • Base: if loser == winner return true.
   • For each k: if locked[loser][k] and creates_cycle(winner, k) return true.
   • Return false otherwise.

6. void lock_pairs(void)

   • For each pair in sorted order:
     • if (!creates_cycle(pair.winner, pair.loser)) locked[winner][loser] = true;

7. void print_winner(void)

   • Find candidate i where no j has locked[j][i] == true.
   • Print candidate name.

Understanding the Tideman Algorithm

Before touching code, you must understand the three core stages:

1. Record preferences – tally each pair of candidates to see who voters prefer.
2. Sort pairs – order all possible candidate pairs by the strength of victory (largest margin first).
3. Lock pairs without cycles – add pairs to a directed graph, skipping any pair that would create a cycle.

The winner is the candidate who ends up at the “source” of the locked graph (no incoming edges). Cs50 Tideman Solution

2. The CS50 Tideman Function Structure

The distribution code provides a skeleton with these functions:

• vote(int rank, string name, int ranks[]): Records a voter’s preference order.
• record_preferences(int ranks[]): Updates the global preferences[i][j] matrix (how many voters prefer i over j).
• add_pairs(void): Adds all pairs where one candidate beats another to the pairs array.
• sort_pairs(void): Sorts the pairs by decreasing margin of victory.
• lock_pairs(void): Locks pairs in order, avoiding cycles.
• print_winner(void): Prints the candidate with no incoming edges in the locked graph.

The main challenge is lock_pairs. Many students implement everything else correctly but fail cycle detection.

Abstract

This paper explores the algorithmic logic and implementation required to solve the "Tideman" problem from Harvard University’s CS50: Introduction to Computer Science course. The Tideman voting method (also known as Ranked Pairs) is a Condorcet method used to determine election results where voters rank candidates. This paper details the data structures used to represent the voting graph, the critical process of "locking" pairs to prevent cycles, and the specific programming strategies used to implement the sort_pairs, lock_pairs, and print_winner functions. Here’s a helpful, explanatory text for understanding and

tideman.c

#include <stdio.h>
#include <stdlib.h>
// Structure to represent a candidate
typedef struct candidate 
    int id;
    int votes;
 candidate_t;
// Structure to represent a voter
typedef struct voter 
    int *preferences;
 voter_t;
// Function to read input
void read_input(int *voters, int *candidates, voter_t **voters_prefs) 
    // Read in the number of voters and candidates
    scanf("%d %d", voters, candidates);
// Allocate memory for voters and candidates
    *voters_prefs = malloc(*voters * sizeof(voter_t));
    candidate_t *candidates_list = malloc(*candidates * sizeof(candidate_t));
// Read in voter preferences
    for (int i = 0; i < *voters; i++) 
        (*voters_prefs)[i].preferences = malloc(*candidates * sizeof(int));
        for (int j = 0; j < *candidates; j++) 
            scanf("%d", &(*voters_prefs)[i].preferences[j]);
// Function to count first-place votes
void count_first_place_votes(voter_t *voters_prefs, int voters, candidate_t *candidates_list, int candidates) 
    // Initialize vote counts to 0
    for (int i = 0; i < candidates; i++) 
        candidates_list[i].votes = 0;
// Count first-place votes
    for (int i = 0; i < voters; i++) 
        for (int j = 0; j < candidates; j++) 
            if (j == 0) 
                candidates_list[voters_prefs[i].preferences[j] - 1].votes++;
// Function to check for winner
int check_for_winner(candidate_t *candidates_list, int candidates) 
    // Check if any candidate has more than half of the first-place votes
    for (int i = 0; i < candidates; i++) 
        if (candidates_list[i].votes > candidates / 2) 
            return i + 1;
return -1;
// Function to eliminate candidate
void eliminate_candidate(candidate_t *candidates_list, int candidates, int eliminated) 
    // Decrement vote counts for eliminated candidate
    for (int i = 0; i < candidates; i++) 
        if (candidates_list[i].id == eliminated) 
            candidates_list[i].votes = 0;
// Function to recount votes
void recount_votes(voter_t *voters_prefs, int voters, candidate_t *candidates_list, int candidates) 
    // Recount votes
    for (int i = 0; i < voters; i++) 
        for (int j = 0; j < candidates; j++) 
            if (candidates_list[voters_prefs[i].preferences[j] - 1].votes == 0) 
                // Move to next preference
                voters_prefs[i].preferences[j] = -1;
             else 
                break;
int main() 
    int voters, candidates;
    voter_t *voters_prefs;
    read_input(&voters, &candidates, &voters_prefs);
candidate_t *candidates_list = malloc(candidates * sizeof(candidate_t));
    for (int i = 0; i < candidates; i++) 
        candidates_list[i].id = i + 1;
count_first_place_votes(voters_prefs, voters, candidates_list, candidates);
int winner = check_for_winner(candidates_list, candidates);
    while (winner == -1) 
        // Eliminate candidate with fewest votes
        int eliminated = -1;
        int min_votes = voters + 1;
        for (int i = 0; i < candidates; i++) 
            if (candidates_list[i].votes < min_votes) 
                min_votes = candidates_list[i].votes;
                eliminated = candidates_list[i].id;
eliminate_candidate(candidates_list, candidates, eliminated);
recount_votes(voters_prefs, voters, candidates_list, candidates);
count_first_place_votes(voters_prefs, voters, candidates_list, candidates);
winner = check_for_winner(candidates_list, candidates);
printf("The winner is: %d\n", winner);
return 0;