House Robber

LeetCode #198 — Medium

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 nums representing the amount of money in each house, return the maximum amount of money you can rob tonight without alerting the police.

Examples

Example 1

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

Example 2

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

Constraints

• 1 <= nums.length <= 100
• 0 <= nums[i] <= 400

What to practise

• Define dp[i] = max money robbing houses [0..i].
• Recurrence: dp[i] = max(dp[i-1], dp[i-2] + nums[i]) — at each house, either skip it or take it (and skip the previous).
• Optimise to O(1) space by keeping only the two most recent values.
• This is the canonical skip-or-take 1D DP, distinct from Fibonacci's "always combine".