$2D$ Grid Search $(3$pts$)$

Consider the unbounded $2$D grid shown below. The start state is at the origin $(0,0),$ the black dot

and the goal state is at $($x$,$y$).$

What is the branching factor $b$ in this state space?

How many distinct states are there at depth $k($for $k$ larger than $0).$

What is the maximum number of nodes expanded by breadth$-$first tree search?

What is the maximum number of nodes expanded by breadth$-$first graph search?

Is $h=|u-x|+|v-y|$ an admissible heuristic for a state at $(u,v)?$ Explain.

How many nodes are expanded by $A^{**}$ graph search using $h?$

Does $h$ remain admissible if some links are removed?

Does $h$ remain admissible if some links are added between nonadjacent states? NO AI answers please