Fibonacci Number

LeetCode https://leetcode.cn/problems/fibonacci-number/

• Recursive

class Solution {
    public int fib(int n) {
        // base case
        if (n == 0 || n == 1) {
            return n;
        }

        return fib(n - 1) + fib(n - 2);
    }
}

Complexity

• Time = O(2^n)
• Space = O(n)

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• DP

class Solution {

    public int fib(int n) {

        if (n == 0 || n == 1) {
            return n;
        }
        
        int[] dp = new int[n+1];      // sub-solutions
        dp[0] = 0;                    // base case
        dp[1] = 1;
        for (int i = 2; i <= n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];             
        }

        return dp[n];
    }
}

Complexity

• Time = O(n)
• Space = O(n)

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