You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security systems connected and it will automatically contact the police if two adjacent houses were broken into on the same night. Given an integer array M representing the amount of money of each house, return the maximum amount of money you can rob tonight without alerting the police. You don't need to write real C++ codes, but you are welcome to do so. Pseudocodes are necessary.

Example 1: M = {1, 2, 3, 1}.

Output: 4.

Explanation: House 1 and 3, in total 4, which is the largest. House 2 and 4, in total 3.

Example 2: M = {2, 7, 9, 3, 1}.

Output: 12.

Explanation: House 1, 3, 5, in total 12, which is the largest. House 2, 4, 6, in total 11.

a)Use brute-force method to solve this problem. Design an algorithm and analyze the time and space complexity.

b)Optimize the brute-force solution. Design a new algorithm and analyze the time and space complexity.