priority queues (heaps figure input for exercises and merge the two leftist heaps in figure show the result of inserting keys to in order into an initially empty leftist heap prove or disprovea perfectly balanced tree forms if keys to are inserted in order into an initially empty leftist heap give an example of input that generates the best leftist heap can leftist heaps efficiently support decreasekeyb what changesif any (if possible)are required to do this one way to delete nodes from known position in leftist heap is to use lazy strategy to delete nodemerely mark it deleted when findmin or deletemin is performedthere is potential problem if the root is marked deletedsince then the node has to be actually deleted and the real minimum needs to be foundwhich may involve deleting other marked nodes in this strategyremoves cost one unitbut the cost of deletemin or findmin depends on the number of nodes that are marked deleted suppose that after deletemin or findmin there are fewer marked nodes than before the operation show how to perform the deletemin in ( log ntime  propose an implementationwith an analysis to show that the time to perform the deletemin is ( log( / ) we can perform buildheap in linear time for leftist heaps by considering each element as one-node leftist heapplacing all these heaps on queueand performing the following stepuntil only one heap is on the queuedequeue two heapsmerge themand enqueue the result prove that this algorithm is (nin the worst case why might this algorithm be preferable to the algorithm described in the text merge the two skew heaps in figure show the result of inserting keys to in order into skew heap prove or disprovea perfectly balanced tree forms if the keys to - are inserted in order into an initially empty skew heap skew heap of elements can be built using the standard binary heap algorithm can we use the same merging strategy described in exercise for skew heaps to get an (nrunning timeprove that binomial treebk has binomial trees bk- as children of the root