amortized analysis will drop the big-oh notation and charge one unit of time for each node on the paths since the heaps have no structureit is possible that all the nodes in both heaps lie on the right pathand this would give (nworst-case bound to merge the heaps (exercise asks you to construct an examplewe will show that the amortized time to merge two skew heaps is (log nwhat is needed is some sort of potential function that captures the effect of skew heap operations recall that the effect of merge is that every node on the right path is moved to the left pathand its old left child becomes the new right child one idea might be to classify each node as right node or left nodedepending on whether or not it is right childand use the number of right nodes as potential function although the potential is initially and always nonnegativethe problem is that the potential does not decrease after merge and thus does not adequately reflect the savings in the data structure the result is that this potential function cannot be used to prove the desired bound similar idea is to classify nodes as either heavy or lightdepending on whether or not the right subtree of any node has more nodes than the left subtree definition nodepis heavy if the number of descendants of ' right subtree is at least half of the number of descendants of pand light otherwise note that the number of descendants of node includes the node itself as an examplefigure shows skew heap the nodes with values and are heavyand all other nodes are light the potential function we will use is the number of heavy nodes in the (collection ofheaps this seems like good choicebecause long right path will contain an inordinate number of heavy nodes because nodes on this path have their children swappedthese nodes will be converted to light nodes as result of the merge theorem the amortized time to merge two skew heaps is (log figure skew heap--heavy nodes are and