Let x$1<$ x$2<...<$ xn be real numbers representing coordinates of n villages

located along a straight road. A post of$$ce needs to be built in one of these

villages.

a$.$ Design an ef$$cient algorithm to $$nd the post$-$of$$ce location minimizing

the average distance between the villages and the post of$$ce$.$

b$.$ Design an ef$$cient algorithm to $$nd the post$-$of$$ce location minimizing

the maximum distance from a village to the post of$$ce$.$