This is a coding question. However, I do not require the answer in code. I just need help in figuring out the math behind this question.

Question

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 system connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

 

NOTE: The "list" is actually an array of integers where the index of element means the position of the house and the element is the amount of money stashed in it. Robber cant rob adjacent indices. As a sample, the array is as follows

 

[10 50 7 15 500 100]

Answer 1

Not sure if this is what you were needing: 

[10 50 7 15 500 100]

 

if list[0]+list[2]+list[4] > list[1]+list[3]+list[5]

list[0]+list[2]+list[4] = 517  OR ∑⁴_n=0 a_n=a₀+a₂+a₄+a_n+2

else

list[1]+list[3]+list[5] = 165 OR ∑⁵_n=1 a_n = a₁+a₃+a₅+a_n+2