1. (a) (3 points) Your friend wish to drive by car from point A to point B on a highway and want to make as few gas stops as possible along the way. The car, when full, has enough gas to travel k miles, and your friend has a map which gives distances between different gas stations on the route. Give an efficient method to determine which gas stations your friend should stop. Prove that your strategy yields an optimal solution (b) (3 points) Consider the problem of making change for n cents using the least number of coins. Describe a greedy algorithm to make change consisting of quarters, dimes, nickels and pennies. Prove that your algorithm yields an optimal solution (c) (3 points) Does your algorithm in part (b) give an optimal solution for any types of dk, for some integer k. Assume that each d, is an integer coin denominations d1, d2, , and 1 is part of it. Note that part (b) has 4 types of coin denominations: 25, 10, 5, and 1. If your answer is yes then prove it, otherwise give a counter example