/* Priority queues, implemented as heaps
 * 15-122 Principles of Imperative Computation, Fall 2010
 * Frank Pfenning
 */

typedef struct heap* heap;
heap heap_new(int limit);	/* create new heap of size limit */
bool heap_empty(heap H);	/* is H empty? */
void heap_insert(heap H, int x); /* insert x into H */
int heap_min(heap H);		/* find minimum */
int heap_delmin(heap H);	/* delete minimum */

struct heap {
  int limit;
  int next;
  int[] heap;
};

bool is_heap(heap H)
//@requires H != NULL && H->limit <= \length(H->heap);
{
  if (H == NULL) return false;
  if (!(1 <= H->next && H->next <= H->limit)) return false;
  { int i;
    for (i = 2; i < H->next; i++) {
      if (H->heap[i] < H->heap[i/2]) return false;
    }
  }
  return true;
}