/* 
 * Hash sets, implemented with separate chaining
 *
 * 15-122 Principles of Imperative Computation 
 */

#use <util>
#use <conio>

/************************/
/*** Client interface ***/
/************************/

// typedef _______ elem;
bool elem_equiv(elem x, elem y);
int elem_hash(elem x);

/*************************/
/*** Library interface ***/
/*************************/

// typedef ______* hset_t;
typedef struct hset_header* hset_t;

hset_t hset_new(int capacity)
  /*@requires capacity > 0; @*/
  /*@ensures \result != NULL; @*/ ;

bool hset_contains(hset_t H, elem x)
  /*@requires H != NULL; @*/ ;

void hset_add(hset_t H, elem x)
  /*@requires H != NULL; @*/
  /*@ensures hset_contains(H, x); @*/ ;

/**********************/
/*** Implementation ***/
/**********************/

typedef struct chain_node chain;
struct chain_node {
  elem data;
  chain* next;
};

typedef struct hset_header hset;
struct hset_header {
  int size;
  int capacity;               /* 0 < capacity */
  chain*[] table;             /* \length(table) == capacity */
};

int elemhash(hset* H, elem x) 
//@requires H != NULL && H->capacity > 0;
//@ensures 0 <= \result && \result < H->capacity;
{
  return abs(elem_hash(x) % H->capacity);
}

bool is_table_expected_length(chain*[] table, int length) {
  //@assert \length(table) == length;
  return true;
}

bool is_hset(hset* H) {
  return  H != NULL
    && H->capacity > 0
    && H->size >= 0
    && is_table_expected_length(H->table, H->capacity);
  /* && table contains correct number non-NULL elements in correct places */
}

hset* hset_new(int capacity)
//@requires capacity > 0;
//@ensures is_hset(\result);
{
  hset* H = alloc(hset);
  H->size = 0;
  H->capacity = capacity;
  H->table = alloc_array(chain*, capacity);
  return H;
}

bool hset_contains(hset* H, elem x)
//@requires is_hset(H);
{
  int i = elemhash(H, x);
  for (chain* p = H->table[i]; p != NULL; p = p->next) {
    if (elem_equiv(p->data, x)) {
      return true;
    }
  }

  return false;
}

void hset_add(hset* H, elem x) 
//@requires is_hset(H);
//@ensures is_hset(H);
//@ensures hset_contains(H, x);
{
  int i = elemhash(H, x);
  for (chain* p = H->table[i]; p != NULL; p = p->next) {
    if (elem_equiv(p->data, x)) {
      p->data = x;
      return;
    }
  }
  
  // prepend new element
  chain* p = alloc(chain);
  p->data = x;
  p->next = H->table[i];
  H->table[i] = p;
  (H->size)++;
}