Question

Source

• lintcode: (366) Fibonacci

Problem

Find the _N_th number in Fibonacci sequence.

A Fibonacci sequence is defined as follow:

• The first two numbers are 0 and 1.
• The i th number is the sum of i-1 th number and i-2 th number.

The first ten numbers in Fibonacci sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

Example

Given 1 , return 0

Given 2 , return 1

Given 10 , return 34

Note

The _N_th fibonacci number won't exceed the max value of signed 32-bit integer in the test cases.

题解

斐波那契数列使用递归极其容易实现，其实使用非递归的方法也很容易，不断向前滚动即可。

C++

class Solution{
public:
  /**
   * @param n: an integer
   * @return an integer f(n)
   */
  int fibonacci(int n) {
    if (n <= 0) return -1;
    if (n == 1) return 0;
    if (n == 2) return 1;

    int fn = 0, fn1 = 0, fn2 = 1;
    for (int i = 3; i <= n; i++) {
      fn = fn1 + fn2;
      fn1 = fn2;
      fn2 = fn;
    }
    return fn;
  }
};

Java

class Solution {
  /**
   * @param n: an integer
   * @return an integer f(n)
   */
  public int fibonacci(int n) {
    if (n <= 0) return -1;
    if (n == 1) return 0;
    if (n == 2) return 1;

    int fn = 0, fn1 = 1, fn2 = 0;
    for (int i = 3; i <= n; i++) {
      fn = fn1 + fn2;
      fn2 = fn1;
      fn1 = fn;
    }

    return fn;
  }
}

源码分析

1. corner cases
2. 初始化 fn, fn1, fn2, 建立地推关系。
3. 注意 fn, fn2, fn1 的递推顺序。

复杂度分析

遍历一次，时间复杂度为 O(n)O(n)O(n), 使用了两个额外变量，空间复杂度为 O(1)O(1)O(1).