CS50 Problem Set 3

Here’s my answer for the CS50 Problem Set 3. Hope that will help you a bit.

Problem 1: Sort

sort1 uses: bubble sort

How do you know?: When sorting the sorted numbers, bubble sort's time complexity is omega(n); while sorting the random numbers, bubble sort's time complexity is O(n^2).

sort2 uses: merge sort

How do you know?: the time sort2 uses to sort every kind of txt is the least between the three sorts.

sort3 uses: selection sort

How do you know?: the time it uses to sort three kinds of txt is almost the same, but it cost more time than sort2.answers.txt

Problem 2: Plurality

#include <cs50.h>
#include <stdio.h>
#include <string.h>

// Max number of candidates
#define MAX 9

// Candidates have name and vote count
typedef struct
{
    string name;
    int votes;
} candidate;

// Array of candidates
candidate candidates[MAX];

// Number of candidates
int candidate_count;

// Function prototypes
bool vote(string name);
void print_winner(void);

int main(int argc, string argv[])
{
    // Check for invalid usage
    if (argc < 2)
    {
        printf("Usage: plurality [candidate ...]\n");
        return 1;
    }

    // Populate array of candidates
    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].name = argv[i + 1];
        candidates[i].votes = 0;
    }

    int voter_count = get_int("Number of voters: ");

    // Loop over all voters
    for (int i = 0; i < voter_count; i++)
    {
        string name = get_string("Vote: ");

        // Check for invalid vote
        if (!vote(name))
        {
            printf("Invalid vote.\n");
        }
    }

    // Display winner of election
    print_winner();
}

// Update vote totals given a new vote
bool vote(string name)
{
    for (int i = 0; i < candidate_count; i++)
    {
        if (strcmp(candidates[i].name, name) == 0)
        {
            candidates[i].votes += 1;
            return true;
        }
    }
    return false;
}

// Print the winner (or winners) of the election
void print_winner(void)
{
    int highest = 0;
    string name;
    for (int i = 0; i < candidate_count; i++)
    {
        if (candidates[i].votes > highest)
        {
            highest = candidates[i].votes;
        }
    }
    for (int i = 0; i < candidate_count; i++)
    {
        if (candidates[i].votes == highest)
        {
            printf("%s\n", candidates[i].name);
        }
    }
    return;
}plurality.c

Problem 3: Runoff

#include <cs50.h>
#include <stdio.h>
#include <string.h>

// Max voters and candidates
#define MAX_VOTERS 100
#define MAX_CANDIDATES 9

// preferences[i][j] is jth preference for voter i
int preferences[MAX_VOTERS][MAX_CANDIDATES];

// Candidates have name, vote count, eliminated status
typedef struct
{
    string name;
    int votes;
    bool eliminated;
} candidate;

// Array of candidates
candidate candidates[MAX_CANDIDATES];

// Numbers of voters and candidates
int voter_count;
int candidate_count;

// Function prototypes
bool vote(int voter, int rank, string name);
void tabulate(void);
bool print_winner(void);
int find_min(void);
bool is_tie(int min);
void eliminate(int min);

int main(int argc, string argv[])
{
    // Check for invalid usage
    if (argc < 2)
    {
        printf("Usage: runoff [candidate ...]\n");
        return 1;
    }

    // Populate array of candidates
    candidate_count = argc - 1;
    if (candidate_count > MAX_CANDIDATES)
    {
        printf("Maximum number of candidates is %i\n", MAX_CANDIDATES);
        return 2;
    }
    for (int i = 0; i < candidate_count; i++)
    {
        candidates[i].name = argv[i + 1];
        candidates[i].votes = 0;
        candidates[i].eliminated = false;
    }

    voter_count = get_int("Number of voters: ");
    if (voter_count > MAX_VOTERS)
    {
        printf("Maximum number of voters is %i\n", MAX_VOTERS);
        return 3;
    }

    // Keep querying for votes
    for (int i = 0; i < voter_count; i++)
    {

        // Query for each rank
        for (int j = 0; j < candidate_count; j++)
        {
            string name = get_string("Rank %i: ", j + 1);

            // Record vote, unless it's invalid
            if (!vote(i, j, name))
            {
                printf("Invalid vote.\n");
                return 4;
            }
        }

        printf("\n");
    }

    // Keep holding runoffs until winner exists
    while (true)
    {
        // Calculate votes given remaining candidates
        tabulate();

        // Check if election has been won
        bool won = print_winner();
        if (won)
        {
            break;
        }

        // Eliminate last-place candidates
        int min = find_min();
        bool tie = is_tie(min);

        // If tie, everyone wins
        if (tie)
        {
            for (int i = 0; i < candidate_count; i++)
            {
                if (!candidates[i].eliminated)
                {
                    printf("%s\n", candidates[i].name);
                }
            }
            break;
        }

        // Eliminate anyone with minimum number of votes
        eliminate(min);

        // Reset vote counts back to zero
        for (int i = 0; i < candidate_count; i++)
        {
            candidates[i].votes = 0;
        }
    }
    return 0;
}

// Record preference if vote is valid
bool vote(int voter, int rank, string name)
{
    for (int i = 0; i < candidate_count; i++)
    {
        if (strcmp(candidates[i].name, name) == 0)
        {
            preferences[voter][rank] = i;
            return true;
        }
    }
    return false;
}

// Tabulate votes for non-eliminated candidates
void tabulate(void)
{
    for (int i = 0; i < voter_count; i++)
    {
        for (int j = 0; j < candidate_count; j++)
        {
            if (!candidates[preferences[i][j]].eliminated == true)
            {
                candidates[preferences[i][j]].votes += 1;
                break;
            }
        }
    }
    return;
}

// Print the winner of the election, if there is one
bool print_winner(void)
{
    int limit = voter_count / 2;
    for (int i = 0; i < candidate_count; i++)
    {
        if (!candidates[i].eliminated && (candidates[i].votes > limit))
        {
            printf("%s\n", candidates[i].name);
            return true;
        }
    }
    return false;
}

// Return the minimum number of votes any remaining candidate has
int find_min(void)
{
    int min = 0;
    for (int i = 0; i < candidate_count; i++)
    {
        if (!candidates[i].eliminated)
        {
            if (i == 0)
            {
                min = candidates[i].votes;
            }
            if (candidates[i].votes < min)
            {
                min = candidates[i].votes;
            }
        }
    }
    return min;
}

// Return true if the election is tied between all candidates, false otherwise
bool is_tie(int min)
{
    for (int i = 0; i < candidate_count; i++)
    {
        if (!candidates[i].eliminated && candidates[i].votes != min)
        {
            return false;
        }
    }
    return true;
}

// Eliminate the candidate (or candidates) in last place
void eliminate(int min)
{
    for (int i = 0; i < candidate_count; i++)
    {
        if (!candidates[i].eliminated && candidates[i].votes == min)
        {
            candidates[i].eliminated = true;
        }
    }
    return;
}runoff.c