509. Fibonacci Number

• Recursion

class Solution {
public:
    int fib(int n)
    {
        if(n < 2) return n;
        return fib(n - 1) + fib(n - 2);
    }
};

• T: $O(2^N)$

• S: $O(N)$

• DP

class Solution {
public:
    int fib(int n)
    {
        if(n < 2) return n;
        vector<int> dp(n + 1);
        dp[0] = 0, dp[1] = 1;
        for(int i = 2; i < n + 1; i++)
        {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }
};

• T: $O(N)$
• S: $O(N)$

DP improved

class Solution {
public:
    int fib(int n)
    {
        if(n < 2) return n;
        int first = 1, second = 1;
        for(int i = 2; i < n; i++)
        {
            int temp = first;
            first = first + second;
            second = temp;
        }
        return first;
    }
};

• T: $O(N)$
• S: $O(1)$