typedef struct array {
  int* mem;  	      // the memory
  int size;  	      // the size of the memory region
  int num_elements;   // the actual number of elements (<= size)
} array;

// create a new, empty array, with an initial size of 10 but no elements
array new_array();

// add a new element to the end of the array
void add_element(array* arr, int new_elt);

// access an element in the array. Returns -1 if the index is out of range.
int get(array* arr, int index);

// change an element in the array. Returns the old element if the index is
// in range, or -1 otherwise
int set(array* arr, int index, int new_val);

// remove an element from the array, shifting rightward elements to the left
void remove_element(array* arr, int index);

// returns the number of elements in an array
int num_elements(array* arr);

// release the memory used for this array (but not the array structure itself)
void free_array(array* arr);

// (a bit harder)
// adds an element at the given (non-negative) index, enlarging the array
// and shifting elements to the right to make it fit
void add_element_at(array* arr, int index, int new_elt);