7. 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. We are back again at the same greenhouse from problem-1, but this time our task is to water the plants. Each plant in the greenhouse has some minimum amount of water (in L) per day to stay alive. Suppose there are n plants in the greenhouse and let the minimum amount of water (in L) they need per day be 11,12,13,ln. You generally order n water bottles (1 bottle for each plant) of max(11,12,13,.ln) capacity per day to water the plants, but due to some logistics issue on a bad day, you received n bottles of different capacities (in L). Suppose c1, c2,c3cn be the capacities of the water bottles, and you are required to use one bottle completely to water one plant. In other words, you will allocate one bottle per plant, and use the entire water present (even if it is more than the minimum amount of water required for that plant) in that bottle to water a particular plant. You cannot use more than one bottle (or partial amount of water) to water a single plant (You need to use exactly one bottle per plant). Suggest an algorithm to determine whether it is possible to come up with an arrangement such that every plant receives more than or equal to its minimum water requirement. Prove the correctness of your algorithm