Total and leaf correspondence are more sophisticated correspondence techniques. In both of these techniques, half the elements are located in the min PQ and the other half in the max PQ. When the number of elements is odd, one element is stored in a buffer. This buffered element is not the member of either PQ. In total correspondence technique, each element x in the min PQ is paired with a distinct element y of the max PQ. (x, y) is a corresponding pair of elements such that priority(x)

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 ... Read More

Dual HeapExistence 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(aNode) operation (this operation eliminates the node aNode from the PQ). The simplest of these methods, dual structure method, keeps track of 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 consisting the same element.Figure A displays a dual heap structure for the elements 7, 8, 3, 6, 5. Correspondence ... Read More

Now we shall explain the technique for removing the min elements in the deap data structure. During deletion, our main target to delete the minimal value from deaps. As the height of the tree is always log n, it consumes time of order of log n. We can discuss deletion operation as follows −Procedure deap_deletion(b[],m): if(m

To insert element into deap data structure, we might need the procedures to calculate the minimum and maximum values as depicted below −Procedure min_value(m): //To calculate the minimum value in deap. return m-2log2((m-1) ;Procedure max_value(m): //To calculate the maximum value in deap. return m+2log2(m-1);The insertion operation in deap data structure can be done in following way −For any heap b[], we should check if m is a position within the maximum-heap of deap.We shall then calculate the minimum and maximum values in deap.Now, comparison is done between the key values at left sub-tree and right sub-tree.At last, we perform the ... Read More

A min-max heap is defined as a complete binary tree containing alternating min (or even) and max (or odd) levels. Even levels are denoted as for example 0, 2, 4, etc, and odd levels are denoted as 1, 3, 5, etc.We consider in the next points that the root element is at the first level, i.e., 0.Example of Min-max heapFeatures of Min-max heapEach node in a min-max heap is associated with a data member (usually called key) whose value is implemented to calculate the order of the node in the min-max heap.The root element is the minimum element in the ... Read More

Deap is defined as a data structure which has no element or key value at the root node. It is formed by implementing the following rules −There is no element at root node that indicates root node is empty.Left subtree of the deap shall indicate min heap.Right subtree of deap shall indicate max heap.Thus, correctness to the following statement can be provided mathematically by a deap structure −If the left sub tree and right sub tree of certain nodes are non-empty, and their corresponding nodes can be represented by ‘a’ and ‘b’ respectively, then −a.KeyValue

A double-ended priority queue(DEPQ) or interval heap features the following operations −isEmpty()This function performs to check if DEPQ is empty and returns true if empty.size()This function performs to return the total number of elements present in the DEPQ.getMin()This function performs to return the element having lowest priority.getMax()This function performs to return the element having maximum priority.put(z)This function performs to insert the element z in the DEPQ.removeMin()This function performs to remove an element with smallest priority and returns this element.removeMax()This function performs to remove an element with highest priority and returns this element.The operations isEmpty(), size(), getMin(), and getMax() consume O(1) ... Read More

An interval heap is same as an embedded min-max heap in which each node contains two elements. It is defined as a complete binary tree in whichThe left element is smaller than or equal to the right element.Both the elements define a interval which is closed.Interval represented by any node other than the root is a sub-interval of the parent node.Elements on the left hand side represent a min heap.Elements on the right hand side represent a max heap.Depending on the number of elements, two cases are permitted -Even number of elements: In this case, each node contains two elements ... Read More

In an interval heap, the smallest element is the element on the left hand side of the root node. This element is eliminated and returned.For filling the vacancy created on the left hand side of the root node, an element from the last node is eliminated and again inserted into the root node.This element is next compared successively with all the left hand elements of the descending nodes and the process terminates when all the conditions for an interval heap are met.In case if the left hand side element in the node becomes higher than the right side element at ... Read More