# Question

Formatted question description: https://leetcode.ca/all/198.html

 198	House Robber

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.

Example 1:

Input: [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
Total amount you can rob = 1 + 3 = 4.

Example 2:

Input: [2,7,9,3,1]
Output: 12
Explanation: Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1).
Total amount you can rob = 2 + 9 + 1 = 12.

@tag-dp


# Algorithm

Dynamic Programming to solve, maintain a 1D array dp, where dp[i] represents the maximum value that can be grabbed in the [0, i] interval.

For the current i, there are two mutually exclusive options for robbing and not robbing. Not robbing is dp[i-1] (equivalent to removing nums[i], while robbing is the maximum value of [0, i-1]), robbing is dp[i-2] + nums[i] (equivalent to removing nums[i-1]).

 dp[i] = max(num[i] + dp[i - 2], dp[i - 1])

Java