Bessie the cow is trying to walk from her favorite pasture back to her barn. and the barn in the bottom-right
coner. Bessie wants to get home as soon as possible, so she will only walk down and to the rig ot. There are haybales in some The pasture and farm are on an N xN grid (2< N< 50),with her pasture in the top-left cornel
locations that Bessie cannot walk through; she must walk around them.
Bessie is feeling a little tired today, so she wants to change the direction she walks at most K tin es (1 ≤ K≤3)
How many distinct paths can Bessie walk from her favorite pasture to the barn? Two paths are di stinct if Bessie walks in a square in one path but not in the other.

The idea that, for each pair of devices v and w, there’s a strict dichotomy between being “in range” or “out of range” is a simplified abstraction. more accurately, there’s a power decay function f (·) that specifies, for a pair of devices at distance δ, the signal strength f(δ) that they’ll be able to achieve on their wireless connection. (we’ll assume that f (δ) decreases with increasing δ.) we might want to build this into our notion of back-up sets as follows: among the k devices in the back-up set of v, there should be at least one that can be reached with very high signal strength, at least one other that can be reached with moderately high signal strength, and so forth. more concretely, we have values p1 ≥ p2 ≥ . . ≥ pk, so that if the back-up set for v consists of devices at distances d1≤d2≤≤dk, thenweshouldhavef(dj)≥pj foreachj. give an algorithm that determines whether it is possible to choose a back-up set for each device subject to this more detailed condition, still requiring that no device should appear in the back-up set of more than b other devices. again, the algorithm should output the back-up sets themselves, provided they can be found.\