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According to the following state space in Figure 1. Consider A is the start 10.points state and G is the goal state. The cost is shown on each edge, also the heuristic value is shown for each node. Assume alphabetical tiebreaking (nodes expanded according to the alphabet order). 1- Write a possible path returned for each of the following algorithms: a) Depth-first search b) Breadth first search c) Uniform Cost search d) Greedy search e) A search 2- For Figure 2, suppose you are designing a new heuristic h for it, where h(F)=0.5, other values of h still not known. a) What is the range of possible values for h(D) if h must be admissible? b) What is the range of possible values for h(D) if h must be admissible and consistent. (Assume in all cases that h is nonnegative). 3- Figure 3, suppose that h(F)=0.5,h(E)=1.1, and all other heuristic values except h(B) are fixed to zero (see figure 3 ). What is the range of possible values for h(B) that make A search algorithm makes the following: B expanded before E expanded before F