1.House Robber

You are a professional robber planning to rob houses along a street. Each house has a certain amount of money stashed, the only constraint stopping you from robbing each of them is that adjacent houses have security system connected and it will automatically contact the police if two adjacent houses were broken into on the same night.

Given a list of non-negative integers representing the amount of money of each house, determine the maximum amount of money you can rob tonight without alerting the police.

Example 1:

Input: nums = [1,2,3,1]
Output: 4
Explanation: Rob house 1 (money = 1) and then rob house 3 (money = 3).
             Total amount you can rob = 1 + 3 = 4.

Example 2:

Input: nums = [2,7,9,3,1]
Output: 12
Explanation: Rob house 1 (money = 2), rob house 3 (money = 9) and rob house 5 (money = 1).
             Total amount you can rob = 2 + 9 + 1 = 12

Maximum sum such that no two elements are adjacent

Algorithm:

Maintaining 2 variable : - max sum including prev element - max sum excluduing prev element - maxInc = max(maxInc, maxEnc + current element) - maxEnc = previous max Inc

class Solution {
public:
    int rob(vector<int>& nums) {
        
        if(nums.size()==0){return 0;}
        
        int maxInc = nums[0];
        int maxExc = 0;
        
        for(int i=1;i<nums.size();i++){
            int temp = maxInc;
            maxInc = max(maxExc+nums[i],maxInc);
            maxExc = temp;
        }
        
        return maxInc;
        
    }
};

House Robber II

All houses at this place are arranged in a circle. Max adjacent sum in a circular array

Approach: Find Max Adjacent from 0 to n-2 and 1 to n-1. Return the max of two numbers

class Solution
{
public:
    int maxAdj(vector<int> v, int start, int end)
    {

        int maxInc = v[start];
        int maxExc = 0;

        for (int i = start + 1; i <= end; i++)
        {
            int temp = maxInc;
            maxInc = max(maxInc, maxExc + v[i]);
            maxExc = temp;
        }

        return maxInc;
    }

    int rob(vector<int> &nums)
    {
        if (nums.size() == 1)
        {
            return nums[0];
        }
        return max(maxAdj(nums, 0, nums.size() - 2), maxAdj(nums, 1, nums.size() - 1));
    }
};