Suppose you were to drive from Madison to Rapid City (Black Hills), South Dakota along I-90. Your gas tank when full holds enough gas to travel m miles and you have a map that gives distances between gas stations along the route Let d1 < d2 <...< dn be the locations of all the gas stations along the route where di is the distance from Madison to the gas station i. You can assume that the distance between neighboring gas stations is at most m miles. Your goal is to make as few gas stops as possible along the way. Give a greedy algorithm you can find to determine at which gas stations you should stop and prove that your strategy yields an optimal solution.