(a) What is the definition of an admissible heuristic? (b) Is the statement "The greedy best-first search algorithm is complete" is correct? Briefiy explain the reason why. (c) What is a shortcoming of the hill climbing algorithm? (d) When comparing tree-search algorithms, we measure the number of nodes expanded. How many nodes are expanded (in the worst case) by each of the following search techniques when searching a tree with branching factor f to find a goal at a depth of d ? Try to calculate the exact number if it is not infinity. Do not use big O notation. (i) breadth-first search (ii) depth-first search (iii) depth-limited search (limit = m)