Maximum sum such that no two elements are adjacent

At each house, you only have two choices:
Skip it: keep whatever total you had up to the previous house.
Rob it: take this house’s money + the best total up to two houses back (since you can’t use the previous one).

You pick whichever is bigger:
best at house i = max(best at i-1,  nums[i] + best at i-2)

def rob(nums):
    prev2 = 0   # best up to two houses back
    prev1 = 0   # best up to the previous house

    for x in nums:
        current = max(prev1, x + prev2)
        prev2 = prev1
        prev1 = current

    return prev1