Lessons from House Robber

House Robber teaches a core DP pattern: When can't take adjacent elements, your transition considers two choices: skip the current element, or take it plus the best answer from two positions back.

The recurrence $dp[i] = \max(dp[i-1], dp[i-2] + nums[i])$ captures this exactly. Skip house $i$ and keep $dp[i-1]$, or rob house $i$ and add to $dp[i-2]$.

This pattern appears in many problems: picking non-adjacent elements, scheduling with cooldowns, or any situation where taking one option blocks the next. the space reduction: you only need the last two values. This reduces $O(n)$ space to $O(1)$. Watch for this pattern in other DP problems.