Admissible heuristics

Hello, can someone help me with questions b, c and d please ?

Thank you

Show the solution path (i.e., the sequence of puzzle states from the initial to the goal state) found by each of the following algorithms, assuming transitions have unit cost. You must ensure that puzzle states that have been explored are not added to the search queue. Given multiple states to explore that are otherwise equivalent in priority, the algorithm should prefer the state that involves moving a lower-numbered piece. Breadth first search Uniform cost search Depth first search Iterative deepening b) Suppose now that transitions have differing costs. In particular, the cost of a transition is equal to the number of the piece that is moved (e.g., moving the "4" costs 4). If we employ the Manhattan distance heuristic for the original unit cost version of the eight-puzzle presented in class (Lecture 3, slide 13, h_2), would this heuristic still be an admissible heuristic for A* search in the new variant? Justify your answer. Design an admissible heuristic that dominates the heuristic from part b, under the same transition cost scheme as part b. Now consider another variant of the problem in which moving pieces to the left or right costs 2, whereas moving pieces up or down costs 0.5. Would the Manhattan distance heuristic from part b still be admissible? Justify your