suppose we need to perform percolateups and deletemins on -heap that initially has elements what is the total running time of all operations in terms of mnand db if what is the running time of all heap operationsc if ( )what is the total running timed what choice of minimizes the total running time suppose that binary heaps are represented using explicit links give simple algorithm to find the tree node that is at implicit position suppose that binary heaps are represented using explicit links consider the problem of merging binary heap lhs with rhs assume both heaps are perfect binary treescontaining and nodesrespectively give an (log nalgorithm to merge the two heaps if give an (log nalgorithm to merge the two heaps if | give an (log nalgorithm to merge the two heaps regardless of and min-max heap is data structure that supports both deletemin and deletemax in (log nper operation the structure is identical to binary heapbut the heaporder property is that for any nodexat even depththe element stored at is smaller than the parent but larger than the grandparent (where this makes sense)and for any nodexat odd depththe element stored at is larger than the parent but smaller than the grandparent see figure how do we find the minimum and maximum elementsb give an algorithm to insert new node into the min-max heap give an algorithm to perform deletemin and deletemax can you build min-max heap in linear time suppose we would like to support deletemindeletemaxand merge propose data structure to support all operations in (log ntime figure min-max heap