4. There are n houses that are built in a line, each of which contains some amount of money c_i in it. A thief is trying to steal the maximum amount of money from these houses, but he/she cant steal from two adjacent houses (because the owner of a robbed house will inform his/her neighbors on both sides).

What is the maximum amount of money that the thief can steal?

(a) Formulate the problem as an integer programming problem.

(b) Formulate the problem as a dynamic programming problem and propose an efficient solution algorithm for its solution.

(c) Let there be n = 5 houses with the following c_i values: (5, 3, 4, 11, 2). Use your approach in part (b) to find which houses that the thief should target to maximize the amount of money stolen.