# 509. Fibonacci Number

The Fibonacci numbers, commonly denoted `F(n)` form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from `0` and `1`. That is,

``````F(0) = 0,   F(1) = 1
F(N) = F(N - 1) + F(N - 2), for N > 1.
``````

Given `N`, calculate `F(N)`.

Example 1:

``````Input: 2
Output: 1
Explanation: F(2) = F(1) + F(0) = 1 + 0 = 1.
``````

Example 2:

``````Input: 3
Output: 2
Explanation: F(3) = F(2) + F(1) = 1 + 1 = 2.
``````

Example 3:

``````Input: 4
Output: 3
Explanation: F(4) = F(3) + F(2) = 2 + 1 = 3.
``````

Note:

0 ≤ `N` ≤ 30.

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

``````class Solution {
public:
int fib(int N) {
if (N <= 1) return N;
vector<int> dp(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];
}
};
``````

``````class Solution {
public:
int fib(int N) {
if (N <= 1) return N;
int a = 0, b = 1;
for (int i = 2; i <= N; ++i) {
int sum = a + b;
a = b;
b = sum;
}
return b;
}
};
``````

``````class Solution {
public:
int fib(int N) {
vector<int> fibs{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040};
return fibs[N];
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/509

Split Array into Fibonacci Sequence

Length of Longest Fibonacci Subsequence

https://leetcode.com/problems/fibonacci-number/

https://leetcode.com/problems/fibonacci-number/discuss/215992/Java-Solutions

https://leetcode.com/problems/fibonacci-number/discuss/216245/Java-O(1)-time

LeetCode All in One 题目讲解汇总(持续更新中…)

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