Binary Heap

void swap(int *a, int *b)
{
  int temp = *b;
  *b = *a;
  *a = temp;
}

void heapify(int array[], int size, int i)
{
  if (size == 1) return;

  int largest = i;
  int left = 2 * i + 1;
  int right = 2 * i + 2;

  // is left or right branch largest ?
  if (left < size && array[left] > array[largest])
    largest = left;

  if (right < size && array[right] > array[largest])
    largest = right;

  // if it was, swap with the child and re-apply the process on child
  if (largest != i) {
    swap(&array[i], &array[largest]);
    heapify(array, size, largest);
  }
}

void insert(int array[], int newNum, int* size)
{
  if (*size == 0) {
    array[0] = newNum;
    *size += 1;
  } else {
    array[*size] = newNum;
    *size += 1;
    for (int i = *size / 2 - 1; i >= 0; i--) {
      heapify(array, *size, i);
    }
  }
}

int extract_max(int max_heap[], int* size) {
  if(*size <= 0) return max_heap[0];

  int max = max_heap[0];
  max_heap[0] = max_heap[*size - 1];
  *size -= 1;
  heapify(max_heap, *size, 0);
  return max;
}

source