Add C++ Solutions for House Robber (LeetCode 198) [Recursion + Memoization, Tabulation, Space Optimized] #515

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	class Solution {
	public:
	int solveMem(int n, vector<int> &nums, vector<int> &dp){
	if(n == 0) return 0;

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

	if(dp[n] != -1) return dp[n];

	int include = nums[n - 1] + solveMem(n - 2, nums, dp);
	int exclude = 0 + solveMem(n - 1, nums, dp);
	dp[n] = max(include, exclude);

	return dp[n];
	}

	int solveTab(int n, vector<int> &nums){
	vector<int> dp(n + 1, 0);

	dp[1] = nums[0];

	for(int i = 2; i <= n; i++){
	int include = nums[i - 1] + dp[i - 2];
	int exclude = 0 + dp[i - 1];
	dp[i] = max(include, exclude);
	}
	return dp[n];
	}

	int solveOptimal(int n, vector<int> &nums){

	if(n == 0) return 0;

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

	int prev2 = 0;
	int prev1 = nums[0];

	for(int i = 2; i <= n; i++){
	int include = nums[i - 1] + prev2;
	int exclude = 0 + prev1;
	int ans = max(include, exclude);

	prev2 = prev1;
	prev1 = ans;
	}
	return prev1;
	}

	int rob(vector<int>& nums){
	int n = nums.size();
	//vector<int> dp(n + 1, -1);
	//return solveMem(n, nums, dp);
	//return solveTab(n, nums);

	return solveOptimal(n, nums);
	}
	};

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