198. House Robber

class Solution {
public:
    int rob(vector<int>& nums)
    {
        int n = nums.size();
        if (n == 1) return nums[0];
        vector<int> dp(n);
        dp[0] = nums[0];
        dp[1] = max(nums[0], nums[1]);

        for (int i = 2; i < n; ++i)
        {
            dp[i] = max(dp[i - 1], dp[i - 2] + nums[i]);
        }
        return dp.back();
    }
};

• T: $O(N)$
• S: $O(N)$

DP Improved

class Solution {
public:
    int rob(vector<int>& nums)
    {
        int n = nums.size();

        if (n == 1) return nums[0];

        int prevPrevMax = nums[0];
        int prevMax = max(nums[0], nums[1]);
        int currentMax = 0;

        for (int i = 2; i < n; ++i)
        {
            currentMax = max(prevMax, prevPrevMax + nums[i]);
            prevPrevMax = prevMax;
            prevMax = currentMax;
        }

        return prevMax;
    }
};

• T: $O(N)$
• S: $O(1)$