198. House Robber

Approach 1: Keeping track of amount robbed using DP

class Solution(object):
    def rob(self, nums):
        """
        https://leetcode.com/problems/house-robber/description/
        :type nums: List[int]
        :rtype: int
        """
        lea = len(nums)
        if lea == 0:
            return 0
        if lea == 1:
            return nums[0]
        if lea == 2:
            return max(nums)
        if lea == 3:
            return max(nums[0] + nums[2], nums[1])
        dp = [0] * lea
        dp[0], dp[1], dp[2] = nums[0], nums[1], nums[0] + nums[2]
        for i in range(3, lea):
            dp[i] = nums[i] + max(dp[i-2], dp[i-3])
        return max(dp[-1], dp[-2])

Here we keep track of the max sum from position 0 to i in dp[i]. This is calculated as follows dp[i] = nums[i] + max(dp[i-2], dp[i-3])

Moreover the initial conditions are dp[0], dp[1] and dp[2] which are initalised as nums[0], nums[1] and nums[0] + nums[2] respectively.

In the end we only have to check the last two entries to see which one is greater and return the larger one.

Time Complexity: O(N)

Space Complexity: O(N)