509. 斐波那契数

题目描述

方法一：递归，O(2^N)

//递归
class Solution {
    public int fib(int n) {
        if (n == 0) {
            return 0;
        }
        if (n == 1) {
            return 1;
        }
        return fib(n - 1) + fib(n - 2);
    }
}

方法二：动态规划，O(N)，O(N)

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

方法三：动态规划空间优化，O(N)，O(1)

class Solution {
    public int fib(int n) {
        if (n == 0 || n == 1) return n;
        int p = 0;
        int q = 1;
        int r = 0;
        for(int i = 2; i <= n; i++) {
            r = p + q;
            p = q;
            q = r;
        }
        return r;
    }
}