1D Dynamic Programming

def rob(nums: list[int]) -> int:
    if not nums:
        return 0
    if len(nums) == 1:
        return nums[0]
        
    # State: dp[i] = max money robbing from house 0..i
    # Transition: dp[i] = max(dp[i-1], dp[i-2] + nums[i])
    # Space optimized: only need previous two values
    prev2 = nums[0]
    prev1 = max(nums[0], nums[1])
    
    for i in range(2, len(nums)):
        curr = max(prev1, prev2 + nums[i])
        prev2 = prev1
        prev1 = curr
        
    return prev1