CF492B Vanya and Lanterns

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?

Print the minimum light radius $ d $ , needed to light the whole street. The answer will be considered correct if its absolute or relative error doesn't exceed $ 10^{-9} $ .

Vanya walks late at night along a straight street of length $ l $ , lit by $ n $ lanterns. Consider the coordinate system with the beginning of the street corresponding to the point $ 0 $ , and its end corresponding to the point $ l $ . Then the $ i $ -th lantern is at the point $ a_{i} $ . The lantern lights all points of the street that are at the distance of at most $ d $ from it, where $ d $ is some positive number, common for all lanterns. Vanya wonders: what is the minimum light radius $ d $ should the lanterns have to light the whole street?