exercises for help with exercisesplease visit the sitewww wiley com/college/goodrich reinforcement - the following questions refer to the tree of figure which node is the rootb what are the internal nodesc how many descendants does node cs haved how many ancestors does node cs havee what are the siblings of node homeworks/ which nodes are in the subtree rooted at node projects/ what is the depth of node papers/ what is the height of the treer- show tree achieving the worst-case running time for algorithm depth - give justification of proposition - what is the running time of call to height (pwhen called on position distinct from the root of (see code fragment - describe an algorithmrelying only on the binarytree operationsthat counts the number of leaves in binary tree that are the left child of their respective parent - let be an -node binary tree that may be improper describe how to represent by means of proper binary tree with (nnodes - what are the minimum and maximum number of internal and external nodes in an improper binary tree with nodesr- answer the following questions so as to justify proposition what is the minimum number of external nodes for proper binary tree with height hjustify your answer what is the maximum number of external nodes for proper binary tree with height hjustify your answer let be proper binary tree with height and nodes show that log( < <( )/ for which values of and can the above lower and upper bounds on be attained with equalityr- give proof by induction of proposition - give direct implementation of the num children method within the class binarytree