Could you please help me with the pset3 Tideman? The following is the distribution code to which I am supposed to add codes to complete the Tideman program. I am sorry that it is quite long, but here `bool locked[MAX][MAX]` is left uninitialized early in the program, and then every element of `locked` is assigned `false` about half the way down `main` using for loops. I have learned the default value of booleans is false, so it seems to me `locked` doesn't need to be assigned `false` explicitly. Would you teach me for what purpose `locked` is assigned `false` in this program? Thank you so much for your help in advance. I appreciate it. ``` #include <cs50.h> #include <stdio.h> // Max number of candidates #define MAX 9 // preferences[i][j] is number of voters who prefer i over j int preferences[MAX][MAX]; // locked[i][j] means i is locked in over j bool locked[MAX][MAX]; // Each pair has a winner, loser typedef struct { int winner; int loser; } pair; // Array of candidates string candidates[MAX]; pair pairs[MAX * (MAX - 1) / 2]; int pair_count; int candidate_count; // Function prototypes 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); int main(int argc, string argv[]) { // Check for invalid usage if (argc < 2) { printf("Usage: tideman [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] = argv[i + 1]; } // Clear graph of locked in pairs for (int i = 0; i < candidate_count; i++) { for (int j = 0; j < candidate_count; j++) { locked[i][j] = false; } } pair_count = 0; int voter_count = get_int("Number of voters: "); // Query for votes for (int i = 0; i < voter_count; i++) { // ranks[i] is voter's ith preference int ranks[candidate_count]; // Query for each rank 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; } // Update ranks given a new vote bool vote(int rank, string name, int ranks[]) { // TODO return false; } // Update preferences given one voter's ranks void record_preferences(int ranks[]) { // TODO return; } // Record pairs of candidates where one is preferred over the other void add_pairs(void) { // TODO return; } // Sort pairs in decreasing order by strength of victory void sort_pairs(void) { // TODO return; } // Lock pairs into the candidate graph in order, without creating cycles void lock_pairs(void) { // TODO return; } // Print the winner of the election void print_winner(void) { // TODO return; } ```