Priority Queue

Time Complexity §

Operation	find-max	delete-max	insert	increase-key	Merge
Binary-Heap	$\Theta (1)$	$\Theta (\log n)$	$O(\log n)$	$O(\log n)$	$\Theta (n)$
Fibbonacci Heap	$\Theta (1)$	$O(\log n)$	$\Theta (1)$	$\Theta (1)$	$\Theta (1)$

Tournament Tree §

• Getting the largest item is $O(n)$ which is same as the naive approach but…
• Getting the next-largest element after having built the tree is $O(\log n)$ time
  • Getting the next-$k$ largest elements is $O(k\log n)$ time