Question

Could someone please show how to find the order of growth (big O) for the swim and sink functions on binary heaps? I need to check my work. Thank you!

1.) Swim

private void swim(int k) {
   while (k > 1 && less(k/2, k)) {
      exch(k, k/2);
      k = k/2;
   }
}

2.) Sink

private void sink(int k) {
   while (2*k <= N) {
      int j = 2*k;
      if (j < N && less(j, j+1)) j++;
      if (!less(k, j)) break;
      exch(k, j);
      k = j;
   }
}

Answer 1

1. Swim() - O(log n) time complexity. Because in each iteration k's value is getting half, that is value of k is decreasing exponentially.
2. Sink() - O(log n) time complexity. Because in each iteration k's value is getting doubled, so again k's value is increasing exponentially.