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动态规划-leetcode509

斐波那契数 (通常用 F(n) 表示)形成的序列称为 斐波那契数列 。该数列由 0 和 1 开始,后面的每一项数字都是前面两项数字的和。也就是:

F(0) = 0,F(1) = 1
F(n) = F(n - 1) + F(n - 2),其中 n > 1

给定 n ,请计算 F(n) 。

示例 1:

输入:n = 2
输出:1
解释:F(2) = F(1) + F(0) = 1 + 0 = 1

示例 2:

输入:n = 3
输出:2
解释:F(3) = F(2) + F(1) = 1 + 1 = 2

示例 3:

输入:n = 4
输出:3
解释:F(4) = F(3) + F(2) = 2 + 1 = 3

提示:

  • 0 <= n <= 30


思路:动态规划,递推公式都给了


//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
    //F(0) = 0,F(1) = 1
    //F(n) = F(n - 1) + F(n - 2),其中 n > 1
    public int fib(int n) {
        if(n==0){
            return 0;
        }

        if(n==1){
            return 1;
        }

        return fib(n-1) + fib(n-2) ;
    }
}
//leetcode submit region end(Prohibit modification and deletion)


思路:上面的效率太低,重复计算过多,使用备忘录算法优化



//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
    //F(0) = 0,F(1) = 1
    //F(n) = F(n - 1) + F(n - 2),其中 n > 1
    public int fib(int n) {
        int[] memo = new int[n + 1];
        return dp(memo, n);
    }

    int dp(int[] memo, int n) {
        if (n == 0 || n == 1) {
            return n;
        }

        if (memo[n] != 0) {
            return memo[n];
        }

        memo[n] = dp(memo, n - 1) + dp(memo, n - 2);
        return memo[n];
    }
}
//leetcode submit region end(Prohibit modification and deletion)

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