```c
#include "snake.h"
#include <stdlib.h>

struct snake* add_snake(struct snake* snake, int x, int y) {
    // Allocate memory for the new snake part
    struct snake* new_part = (struct snake*)malloc(sizeof(struct snake));
    if (new_part == NULL) {
        return NULL; // Memory allocation failed
    }
    
    // Set the coordinates of the new part
    new_part->x = x;
    new_part->y = y;
    
    // Set the next pointer of the new part to the current head of the snake
    new_part->next = snake;
    
    // Return the new head of the snake
    return new_part;
}

struct snake* remove_snake(struct snake* snake) {
    // Check if the snake is empty
    if (snake == NULL) {
        return NULL; // Snake is empty, no part to remove
    }
    
    // Save the next part of the snake
    struct snake* next_part = snake->next;
    
    // Free the current head of the snake
    free(snake);
    
    // Return the new head of the snake
    return next_part;
}

int is_snake(struct snake* snake, int x, int y) {
    // Traverse the snake
    while (snake != NULL) {
        // Check if the coordinates match
        if (snake->x == x && snake->y == y) {
            return 1; // Coordinates are part of the snake
        }
        // Move to the next part of the snake
        snake = snake->next;
    }
    // Coordinates are not part of the snake
    return 0;
}

void free_snake(struct snake* sn) {
    // Traverse the snake
    while (sn != NULL) {
        // Save the next part of the snake
        struct snake* next_part = sn->next;
        
        // Free the current part of the snake
        free(sn);
        
        // Move to the next part of the snake
        sn = next_part;
    }
}