Top

As explained in Advanced Algorithms and Data Structures

The top operation retrieves the element currently having the highest priority at the top of a priority queue or heap, optionally removing it according to the interface semantics.

The top operation returns the element with the highest priority and removes it from a priority queue. In a heap, that element is stored at the root. section 2.4 section 2.6.4

Implement top on an array-backed heap by preserving the heap property after removing the root:

• Reject the operation when the heap is empty. section 2.6.4
• Save the root as the result, remove the last array element, and use that element to fill the root position. section 2.6.4
• Push the replacement downward until every parent-child relationship again satisfies the heap property. section 2.6.4

Task management

A priority queue containing bug reports returns “UI breaks on browser X” first at severity 9, then “CSS style causes misalignment” at severity 8. Each call to top removes its result, reducing the queue size from five to four and then three, regardless of insertion order. section 2.4.1

A heap requires at most logarithmically many swaps for top. For a d-ary heap, comparisons are approximately O(D·log_D(n)); increasing the branching factor reduces height but makes each level more expensive. Dynamic arrays provide an amortized logarithmic bound. section 2.10 section 2.6.4

Figure 2.10 Removing the top element from a binary heap. (A) From a valid ternary heap, we remove the root of the heap (storing it in a temporary location, in order to return it at the end). (B) We replace the old root with the last element in the array (which is also removed from its tail). The new root might violate heap’s properties (and it does, in this example), so we need to push it down, comparing it to its children to check that the heap’s properties are not violated. (C) We move the new root down toward the heap’s leaves, until we find a valid spot for it (that is, the first one that does not violate the heap’s properties).

Follow the root-removal sequence: save the top element, replace the root with the former last element, and push it down to a valid position. section 2.6.4

How Advanced Algorithms and Data Structures covers it

How deep it goes

Explains empty checks, root replacement, push-down repair, and d-ary costs, while deferring full implementation details.

Examples

Demonstrates bug-report scheduling, binary or ternary heap removal, and d-ary branching-factor measurements.

What it assumes

Assumes priority ordering and heap properties, while establishing the distinction between top, which removes, and peek, which does not.

What you can do after

Apply it via a priority queue API or implement it with root replacement and push-down repair.

How it connects

Connects priority queues, heaps, peek, insert, push-down, heap invariants, and treaps.

liveBookmanning.com

Read Advanced Algorithms and Data Structures on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  Grokking Data StructuresA priority queue top method is an operation that removes and returns the element with the highest priority.

Compare how 2 books explain top →

Related concepts

• pushdown operationuses · A pushdown operation restores heap ordering by repeatedly moving an element toward the leaves and exchanging it with a higher-priority child when necessary.
• peekcontrasts with · Peek is an operation that observes the next or otherwise accessible element without consuming, removing, or advancing past it.
• branching factorcontrasts with · A branching factor is the number of successor nodes or choices available from a node, commonly represented by a maximum or average value.
• priority queuepart of · A priority queue is an abstract data type that retrieves or removes elements according to assigned priority rather than insertion order.
• heappart of · A binary heap is an almost complete binary tree in which each parent satisfies an ordering property relative to its children, enabling efficient access to a minimum or maximum element.

This explainer was generated by Manning's knowledge graph from the text of Advanced Algorithms and Data Structures. The section links point to the parts of the book it draws on.