1. Compare DFS, BFS and DLS in terms of time and space complexity for a state space tree of branching factor b. Use proper notations as needed. 2. Iterative deepening is a modification of depth limited search. How does it guarantee a solution? Describe it in terms of completeness, optimality, time complexity and space complexity. 3. Simple hill climbing is sometimes not able to reach the goal node. How can it be modified to find a goal if it exists? 4. Compare A* algorithm with the B&B in terms of completeness and optimality. Why does A* provide an optimal solution? What if the heuristic function is not given or not available? 5. Consider the filling of magic square square partially correct entries: 123 456 789 Using necessary operators or appropriate algorithms convert it into a perfect magic square. If needed a heuristic function may be used by you.