Dual Priority Queues

Existence of general methods to arrive at efficient DEPQ(Double Ended Priority Queue) data structures from single-ended priority queue (PQ) data structures that also provide an efficient implementation of the remove(bNode) operation (this operation eliminates the node bNode from the PQ). The simplest of these methods, dual structure method, maintains both a min PQ and a max PQ of all the DEPQ elements associated with correspondence pointers between the nodes of the min PQ and the max PQ that consist the same element.

Figure D displays a dual heap structure for the elements 7, 8, 3, 6, 5. Correspondence pointers are displayed as red arrows.

Figure D: Dual heap

Although the figure displays each element stored in both the min and the max heap, it is required to store each element in only one of the two heaps.

The isEmpty and size operations are applied by implementing a variable size that keeps track of the number of elements in the DEPQ. The minimum element is located at the root of the min heap and the maximum element is located at the root of the max heap. To insert an element B, we insert B into both the min and the max heaps and then set up correspondence pointers between the locations of B in the min and max heaps. To eliminate the minimum element, we do a removeMin from the min heap and a remove(bNode), where bNode is the corresponding node for the removed element, from the max heap. The maximum element is eliminated in an analogous way.