Question

I. Let the states' space (v1, ..., v7) and the transition function illustrated in the following graph : an arc from the state vi to the state v; means that v; is one of the successor of vi; the label of each arc designates the transition's cost between two states. And h is the heuristic function. 12 l'igure 1 For each of the following graph search strategies, work out the order in which states are expanded, as well as the path returned by graph search. In all cases, assume ties resolve in such a way that states with earlier alphabetical order are expanded first. The start and goal state are vo and vo, respectively. Remember that in graph search, a state is expanded only once.

1. e) ?∗ search with the same heuristic.

Answer 1

A* algorithm → It is an informed search algorithm. → That means we have domain knowledge in tems of heuristic function hen). → This search algorithm expands less search tree and provides optimal results faster. → In A* algorithm search heuristics are used. As well as the cost to reach the word node. f(n) - gen) + hen) Estimated costbreach Cost to reach cost of the node n. node n to goal node cheapest solution from start state * At each point in the search space only those node i's expanded which have the lowest value of fin). and the algorithm terminates and the goal node is found. Time complexity is o(b") where 'B is branching - factor d is depth Space complexity is 0 (39) state h Nak V3 Vs 2 V7

* Working out the order in which states are expanded as well as the path boreturned by graph search * Vo V, = 2+12 = 14 ✓ VoV₂ = 4+1 = 15 Vo V₃ = 2t 2 = 4 since it is expanded first from Vo we have to select the path Vov, Vov, V7 = 241+2=5 Von V; → V4 - 2+2+15=19 can't be expanded further since it can't reach goal state Vov, VqV6 = 2+2+4+0=8 Hence, we reached goal node Vo from starting node Vo with the cost of 8. Advantages: + At algorithm is optimal and complete. + Best algorithm for solving complex problems. Disadvantages - 7 Huge memory is required to store all the generated nodes.