In a greenhouse, several plants are planted in a row. You can imagine this row as a long line segment. Your task is to install lamps at several places in this row so that each plant receives 'sufficient' light from at least one lamp. A plant receives 'sufficient' if it is within 4 meters of one of the lamps. Design an algorithm that achieve this goal and uses as few numbers of lamps as possible. Prove the correctness of your algorithm