Problem 4. Assume there are n points on the number line at 1,2,3,,n. For the following problems you may assume that n is "nice". In each case you will state your condition on n (such as " n is even", or " n is divisible by 3 ", etc.). (a) What point is a 1-center solution? What is your condition on n ? How far is the furthest point from the center? (b) What two points are a 2-center solution? What is your condition on n ? How far is the furthest point from a center? (c) What three points are a 3-center solution? What is your condition on n ? How far is the furthest point from a center? (d) Assume that you use the point at 1 as an approximation for the 1-center. Using your condition on n, how far is the furthest point from this approximate center? Using your condition on n, how "good" an approximation is this? (e) Assume that you use the point at 1 as an approximation for the 1-center. What does our approximation algorithm give for a 2-center approximation? Using your condition on n, how far is the furthest point from an approximate center? Using your condition on n, how "good" an approximation is this