$1)(4)$ Name which algorithm design technique is illustrated by the following algorithm and give a one sentence justification. Choose from among Greedy, Divide and Conquer, and Dynamic Programming, and Backtracking. A given algorithm can be the answer for more than one criteria or not at all. A choice without justification is worth $0.$

$$

$$

$$A salesperson is scheduled to visit $50$ cities in the US$.$ The salesperson is using the following the algorithms to find the route that saves the most money in travel.

$$

a$.$ Divide the cities in half. Find the best route around all the cities in each half. Then find the cheapest travel between the $2$ halves and travels around one half, flies the other half and then returns to the start.

b$.$ Systematically build up a route by starting at $1$ city, and then considering all other unvisited cities. A lower bound is computed on the cost of visiting the rest of the cities. The algorithm considers the cheapest bound and again considers all the remaining unvisited cities.$$ This is continued until the best route is found.$$ The algorithm may explore other possible routes if the actual cost of a route is more than the potential lower bound.

c$.$ Choose any city to start. Find the cheapest unvisited city for the $2$nd city. Continue in this fashion without ever changing a city once it is chosen until all cities are visited.

d$.$ A solution is built from the bottom up$.$ All $2$ city circuits are used to compute the best circuit for $3$ cities. Which are used to find all $4$ city circuits and so on until the best $50$ city circuit if found.