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)