summary notes power-of- heap is left-heap-ordered tree consisting of root node with an empty right subtree and complete left subtree the tree corresponding to power-of- heap by the left-childright-sibling correspondence is called binomial tree binomial trees and power-of- heaps are equivalent work with both representations because binomial trees are slightly easier to visualizewhereas the simple representation of power-of- heaps leads to simpler implementations keywords binomial queuea binomial queue is priority queue that is implemented not as single tree but as collection of heap-ordered trees leftist heapa leftist heap is heap-ordered binary tree which has very special shape called leftist tree leftist treea leftist tree is tree which tends to ``lean'to the left the tendency to lean to the left is defined in terms of the shortest path from the root to an external node skew heapa skew heap is heap-ordered binary tree self assessment fill in the blanks collection of trees is called every node in binary tree has associated with it quantity called its the null path length of an empty tree is leftist tree is tree in which the shortest path to an external node is always on the the method of the leftistheap class is used to put items into the heap the method locates the item with the smallest key in given priority queue skew heaps as proposed by each of the trees in binomial queue has very special shape called review questions what do you mean by leftist heaps describe null path and null path length write the methods to implement queues by the simple but slow technique of keeping the front of the queue always in the first position of linear array prove that "consider leftist tree which contains internal nodes the path leading from the root of downwards to the rightmost external node contains at most log ( nodes lovely professional university