Heap ordering
Each parent has higher service precedence than its children. Therefore, the highest-priority item is always stored at index 0.
What is a Priority Queue?
A priority queue removes the most important item rather than the oldest item. This simulator uses a stable binary max heap: a larger priority number is served first, while items with equal priority preserve FIFO insertion order.
EnqueueO(log n)
DequeueO(log n)
PeekO(1)
Stable tiesFIFO
Priority queue operations
Logical service order
Example priority queue loaded. Choose an operation.
Queue size0
Highest priority—
Comparisons0
Swaps0
Heap array
| Index | Value | Priority | Arrival # | Parent |
|---|
Operation history
- No operations yet.
Priority queue concepts
Stable equal priorities
When priorities are equal, the smaller arrival number wins. This preserves first-in, first-out behavior among tied items.
Logical versus physical order
The heap array is not fully sorted. The service-order row is produced from a sorted copy to show the order in which items would leave.
Common applications
Priority queues are used in CPU scheduling, event simulation, Dijkstra's algorithm, A* search, bandwidth management, and emergency processing.
Binary heap relationships
| Relationship | Formula |
|---|---|
| Parent | floor((i − 1) / 2) |
| Left child | 2i + 1 |
| Right child | 2i + 2 |
| Stable comparison | Higher priority first; earlier arrival breaks ties. |