A sensor of range r 0 is modelled as an interval [x-r, x centered at a point x, where x e [0,1]. Two sensors 81, 82 are dropped in the unit : one occupies position x1 and the other position x2 such that 0 x1, T2 1 . We want to move the sensors (if needed) to ensure that every point in the unit interval is within the range of a sensor (i.e., the interval is interval [0, covered by the two sensors) 1. [3 pts] Give an optimal algorithm to accomplish this coverage task which minimizes the sum of the movements of the two sensors (as a function of x1,x2) assuming that r = 1/2 2. [7 pts] (*) Now suppose the two sensors are dropped at random in the unit interval. What is the expected sum of the movements of the two sensors for the algorithm you designed