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# Questions tagged [heaps]

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### Expected depth of modified kind of treap

If we have $n$ elements $s_1, \dots, s_n$ and build a kind of treap (tree-heap) out of it. Each $s_k$ has a priority, which is an integer in $\{ 1, 2, 3 \dots, \lceil \log n \rceil\}$. Since the ...
29k views

### Heap - Give an $O(n \lg k)$ time algorithm to merge $k$ sorted lists into one sorted list

Most probably, this question is asked before. It's from CLRS (2nd Ed) problem 6.5-8 -- Give an $O(n \lg k)$ time algorithm to merge $k$ sorted lists into one sorted list, where $n$ is the total ...
29k views

### How to perform bottom-up construction of heaps?

What are the steps to perform bottom-up heap construction on a short sequence, like 1, 6, 7, 2, 4? At this link there are instructions on how to do for a list of ...
450 views

### When two siblings in a heap are equal, how do you bubble down?

I have a heap where both child nodes of the root are 10, and I'd like to perform an operation to remove the min value 9. I proceed to replacing the root with its next of kin, 18. However when I ...
36k views

### Increase-key and decrease-key in a binary min-heap

In many discussions of binary heap, normally only decrease-key is listed as supported operation for a min-heap. For example, CLR chapter 6.1 and this wikipedia page. Why isn't increase key normally ...
1k views

### Leftist heap - determining time complexity

The time complexity of merge (union) operation is said to be $O(\lg (n_1 + n_2))$, where $n_1$ and $n_2$ are the numbers of elements in the merged heaps, respectively. I do not understand this - the ...
14k views

### Is search a binary heap operation?

According to the Wikipedia page, search is "not an operation" on binary heaps (see complexity box at top-right). Why not? Binary heaps may not be sorted, but they are ordered, and a full graph ...
12k views

### How can I prove that a build max heap's amortized cost is $O(n)$?
Suppose a build max-heap operation runs bubble down over a heap. How does its amortized cost equal $O(n)$?
How many different max-heaps exist for a list of $n$ integers? Example: list [1, 2, 3, 4] The max-heap can be either 4 3 2 1: ...